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Search for correlated radio and optical events in long-term studies of extragalactic sources

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Search for correlated radio and optical events in long-term studies of extragalactic sources
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Pomphrey, Richard Bryan, 1946-
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xvi, 243 leaves : ill. ; 28 cm.

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Thesis--University of Florida.
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Includes bibliographical references (leaves 238-242).
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Vita.
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by Richard Bryan Pomphrey.

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SEARCH FOR CORRELATED RADIO AND OPTICAL EVENTS IN LONG-TERM STUDIES OF EXTRAGALACTIC SOURCES













by

RICHARD BRYAN POMPHREY















A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY










UNIVERSITY OF FLORIDA 1977
















ACKNOWLEDGEMENTS



I wish to express my appreciation to my committee chairman,

Dr. A. G. Smith, not only for his assistance, but in particular for his support and direction when the future was uncertain; to my committee co-chairman, Dr. C. N. Olsson, for being a true friend who said things that needed to be said, and for his support and advice through both favorable and adverse situations. I also wish to thank Drs. T. L. Bailey, G. R. Lebo, and S. T. Gottesman for their assistance and contributions to my research experience.

The study documented in this dissertation makes use of data from many observatories. I am indebted to Drs. J. M. MacLeod, G. A. Harvey, and B. H. Andrew of the Algonquin Radio Observatory, and to Drs. K. P. Tritton, M. V. Penston, and R. A. Selmes of the Royal Greenwich Observatory for permitting me to make extensive use of their previously unpublished data. The Rosemary Hill observations were made by Drs. A. G. Smith, G. H. Folsom, K. R. Hackney, R. L. Hackney, R. J. Leacock, B. Q. McGimsey, and R. L. Scott, and by J. T. Pollock and Patricia Edwards. In addition Dr. J. D. G. Rather graciously made his data bank available while it was still in preparation.

Much of the initial analysis was supported by a Research Corporation grant and was carried out at the Electronics Research Laboratory of The Aerospace Corporation. While there I received the generous assistance of many of the staff to whom I am grateful: G. G. Berry, H. Dyson, ii










Dr. E. E. Epstein, W. A. Johnson, H. E. King, J. W. Montgomery, T. T.

Mori, Dr. J. Mottmann, now at the California Polytechnic Institute at San Luis Obispo, Ms. J. D. White, and Dr. W. J. Wilson, now at the Univerity of Texas at Austin. In addition, Mrs. Suzanne Hansen typed much of the manuscript and J. Petersen assisted in the preparation of the illustrations.

During my graduate career, I have been supported by the Research

Corporation grant, a University of Florida Graduate School research assistantship, a University of Florida teaching assistantship, part-time employment at The Aerospace Corporation, and full-time employment at the Jet Propulsion Laboratory. I am grateful to D. J. Lynn, R. M. Ruiz, and Dr. D. A. Elliott of JPL for their support, patience, and understanding while I was finishing this work. The analysis was also aided by funds from the Northeast Regional Data Center of the State University System of Florida.

I also wish to thank Dr. W. G. Fogarty of Universidade Mackenzie,

Dr. J. T. McClave of the Department of Statistics and Dr. M. A. Lynch of the Department of Physics and Astronomy, University of Florida, for helpful discussions; and W. W. Richardson and H. W. Schrader of the University of Florida for extensive technical assistance.

Annual Reviews of Astronomy and Astrophysics, Springer-Verlag New York, Reviews of Modern Physics, The Astronomical Journal and The Astrophysical Journal generously granted permission to reproduce illustrations from their publications. The Astrophysical Journal required that the identical copyright notice as it appears in the Journal be included in the manuscript. This copyright notice follows:



iii










So that the author and publisher may be protected from the
consequences of unauthorized use of the contents of the
manuscript, we consider it essential to secure a copyright.
Therefore, it is mutually agreed that upon the acceptance
of the submitted manuscript for publication by this Journal,
the author grants and assigns exclusively to the American
Astronomical Society for its use any and all rights of whatsoever kind or nature now or hereafter protected by the Copyright Laws (common or statutory) of the United States and
all foreign countries in all languages, including all subsidiary rights. The American Astronomical Society, in turn,
grants to the author the right of republication without
charge in any book or periodical of which he is an author, contributing author, or editor, subject only to his giving
proper credit in the book or periodical to the original
Journal publication of the paper by The University of Chicago
Press for the American Astronomical Society.


I am indebted to many friends for their help throughout my graduate work. The assistance and companionship of Dr. James R. Kennedy and Jack G. Schudel, III were invaluable in the completion of a major portion of this work. Long discussions with Jim Kennedy helped formulate the direction I have taken in this research; the subroutine PPLOT which appears in the Appendix is his, while the subroutine CORREL incorporates many of his ideas. Jack Schudel assisted significantly in the computations and a number of the illustrations. I also wish to thank Dr. Carl Olsson's family, John Young, Eric Van Horn, Al and Isa Adams, Jim and Jerry Hatch, and Jim and Barb Thieman for their help, support, and friendship.

There are some individuals who have had a significant influence on my attitudes and my work during my graduate career. I wish to express my sincere gratitude to Ray and Andy Bloomer, Kit Harvel, Jim and Cathy Kennedy, and Joe and Liz Mullen not only for their support and direction, but also for helping me learn how to play the game.

In addition I wish to gratefully acknowledge my brother and his family, and the countless relatives and friends of my family who,



iv










while not able to assist me directly, expressed their concern and support verbally and in prayer.

Finally, I dedicate this work to Dr. George Horvat and to my parents for their prayers and support, both that which I am aware of and that which I have not even recognized.



















































v















TABLE OF CONTENTS


Page

ACKNOWLEDGEMENTS .ii

LIST OF TABLES . ix

LIST OF FIGURES . . x

ABSTRACT xiv

CHAPTER

I INTRODUCTION . 1

Extragalactic Variables . . . . 3 State of Our Knowledge . . . . 5

II THEORY APPLIED TO SPECTRAL ENERGY DISTRIBUTIONS 10

Spectral Energy Distributions . . . 10 Radio Frequency Spectra . . . . 12 Radiation From a Single Electron . . 14 Radiation From a Distribution of Electrons 18 Time Variations 23

Expanding Source Model . . . . 24

Expanding Source Model Difficulties and
Alternatives . 27

Inverse Compton Scattering . . . 29 Optical Spectra . 36

Galactic Infrared Radiation . . . 55 Extragalactic Infrared Radiation 61






vi










Page

III ANALYSIS OF THE LONG-TERM OPTICAL AND RADIO RECORDS. 65

The Research Problem . 65 The Radio and Optical Data Records 66 Cross-Correlation Analysis . 68 Choice of Correlation Parameters . 72 IV RESULTS OF THE CORRELATION ANALYSIS . 74

OJ 287 . 76

3C 454.3 . . 80

BL Lac . 98

CTA 26 (PKS 0336-01) . 102 PKS 0405-12 . . 102

PKS 0420-01 . . 108

3C 120 . 108

NRAO 190 (PKS 0440-00) . . 118 PKS 0458-02 . . 118

3C 138 (PKS 0518+16) . . 124 PKS 0735+17 . . 128

PKS 0736+01 . . 135

OI 363 . 135

OK 290 . . . . 143

3C 273 . . 147

PKS 1354+19 . . 153

OQ 208 . . 161

PKS 1510-08 . . 161

NRAO 512 . . 161





vii











Page

3C 371 168 3C 446 176

PKS 2345-16 176

Summary ............. 186

V CONCLUSIONS 191

Spectral Energy Distributions . . . 191 Lack of Correlation 197 OJ 287, BL Lac, and 3C 454.3 . . . 199 Implications of Correlation . . . 204 Further Work 207

APPENDIX

I COMPUTER PROGRAMS USED IN THE STATISTICAL ANALYSIS 210 II FURTHER USE OF COMPUTER PROGRAMS AND DATA BATK 236 BIBLIOGRAPHY . 238

BIOGRAPHICAL SKETCH . 243





























viii

















LIST OF TABLES



TABLE Page

1 INTERCOMPARISON OF WAVELENGTHS WITH FREQUENCIES . 9

2 RANGE OF ELECTRON ENERGIES FOR A GIVEN POWER LAW
INDEX . 20

3 LACERTID OPTICAL AND NEAR-IR SPECTRAL INDICES 39

4 SU1MARY OF RESULTS OF THE LINEAR CROSS-CORRELATION
ANALYSIS 75

5 SUMMARY OF CORRELATION ANALYSIS RELATIVE TO OPTICAL
AND RADIO VARIABILITY SUBCLASSES . . . 187

6 RADIO AND OPTICAL AMPLITUDES FOR OJ 287 FLARE 203 7 RADIO AND OPTICAL AMPLITUDES FOR BL Lac FLARE 204 8 RADIO AND OPTICAL AMPLITUDES FOR 3C 454.3 FLARE 204 A-i DATA BANK FORMAT .... ...... 236

























ix















LIST OF FIGURES



Figure Page

1 Spectral Energy Distributions for Five Quasi-Stellar
Objects and the Seyfert Galaxy NGC 1068 . . 11

2 Four Classes of Radio Frequency Spectra . . 13

3 Synchrotron Spectrum from a Single Electron as a
Function of x = v /v . . . . . 16
c
4 Expected Synchrotron and Inverse Compton Spectra
for the Galactic Halo . . . . . 34

5 3C 120. Optical and Near-Infrared Spectrum 38 6 BL Lac. Optical and Near-Infrared Spectrum . 40 7 OJ 287. Optical Spectrum . . . . 41

8 OJ 287. Optical and Near-Infrared Spectrum
Extrapolated to Short Radio Wavelengths . . 43

9 BL Lac. Changes in Optical and Near-Infrared
Spectrum with Time . . . . . 45

10 Selected Quasars. Optical and Near-Infrared Spectra 47 11 Selected Quasars. Optical and Near-Infrared Spectra 49 12 Selected Quasars. Optical and Near-Infrared Spectra 51

13 3C 345, 3C 446, 3C 454.3. Changes in Optical
Spectral Index with Time . . . . 52

14 Spectral Energy Distributions Showing Known Infrared 57
Components .

15 Schematic Extinction Curve . . . . 58 16 OJ 287. Optical and Radio Curves . . . 77 17 OJ 287. R vs At for all Data . .. . 78 18 OJ 287. Radio Flux vs Optical Magnitude . . 79



x










Figure Page

19 OJ 287, Part I. R vs At 81 20 OJ 287, Part II. R vs At . . . . 82 21 OJ 287, Part I. Radio Flux vs Optical Magnitude. 83 22 OJ 287, Part II. Radio Flux vs Optical Magnitude 84 23 3C 454.3. Three Independent Optical Data Records 86 24 3C 454.3. Optical and Radio Curves . . . 88 25 3C 454.3. R vs At for all Data . . . 90 26 3C 454.3. R vs At for Part of Optical Data 91 27 3C 454.3. Radio Flux vs Optical Magnitude. 92 28 3C 454.3. Radio Flux vs Optical Magnitude. 93 29 3C 454.3. R vs At for Part of Radio Data . 95 30 3C 454.3. Two Independent Radio Data Records. 96 31 3C 454.3. R vs At for Two Radio Records . . 97 32 BL Lac. Optical and Radio Curves. . . . 99 33 BL Lac. R vs At for all Data . . . . 100 34 BL Lac. R vs At for all Data . . . . 101 35 CTA 26. Optical and Radio Curves. . . . 103 36 CTA 26. R vs At for all Data . . . . 104 37 CTA 26. Radio Flux vs Optical Magnitude . 105 38 CTA 26. Radio Flux vs Optical Magnitude . 106 39 PKS 0405-12. Optical and Radio Curves . . 107 40 PKS 0405-12. R vs At for all Data . . . 109 41 PKS 0420-01. Optical and Radio Curves . . 111 42 PKS 0420-01. R vs At for Part of Radio Data 112 43 PKS 0420-01. R vs At for all Data . . . 113 44 3C 120. Optical and Radio Curves. . . . 115


xi










Figure Page 45 3C 120. R vs At for all Data . . . . 117 46 NRAO 190. Optical and Radio Curves . . 119 47 NRAO 190. R vs At for Part of Radio Data . 120 48 NRAO 190. R vs At for all Data . . . 121 49 PKS 0458-02. Optical and Radio Curves . . 122 50 PKS 0458-02. R vs At for all Data . . . 123 51 3C 138. Optical and Radio Curves. . . . 125 52 3C 138. R vs At for all Data . . . . 127 53 PKS 0735+17. Two Independent Radio Data Records. 129 54 PKS 0735+17. R vs At for Two Radio Records 130 55 PKS 0735+17. Optical and Radio Curves . . 131 56 PKS 0735+17. R vs At for Part of Radio Data 132 57 PKS 0735+17. R vs At for Part of Radio Data 133 58 PKS 0735+17. R vs At for all Data . . . 134 59 PKS 0735+17. Radio Flux vs Optical Magnitude. 136 60 PKS 0735+17. Radio Flux vs Optical Magnitude. 137 61 PKS 0736+01. Optical and Radio Curves . . 139 62 PKS 0736+01. R vs At for Part of Radio Data 140 63 PKS 0736+01. R vs At for all Data . . . 141 64 01 363. Optical and Radio Curves. . . . 142 65 0I 363. R vs At for all Data . . . . 144 66 OK 290. Optical and Radio Curves. . . . 145 67 OK 290. R vs At for all Data . . . . 146 68 3C 273. Two Independent Radio Data Records 148 69 3C 273. R vs At for Two Radio Records . . 150 70 3C 273. Optical and Radio Curves. . . . 152


xii










Figure Page

71 3C 273. R vs At for Part of Radio Data. . . 154 72 3C 273. R vs At for Part of Radio Data. . . 155 73 3C 273. R vs At for all Data . . . . 157 74 PKS 1354+19. Optical and Radio Curves . . 158 75 PKS 1354+19. R vs At for all Data . . . 160 76 OQ 208. Optical and Radio Curves. . . . 162 77 OQ 208. R vs At for all Data . . . . 163 78 PKS 1510-08. Optical and Radio Curves 164 79 PKS 1510-08. R vs At for all Data . . . 165 80 NRAO 512. Optical and Radio Curves . . . 167 81 NNRAO 512. R vs At for all Data . . . 170 82 NRAO 512. R vs At for Part of Optical Data 172 83 3C 371. Optical and Radio Curves. . . . 174 84 3C 371. R vs At for all Data . . . . 175 85 3C 446. Two Independent Radio Data Records 177 86 3C 446. R vs At for Two Radio Records . . 179 87 3C 446. Optical and Radio Curves. . . . 181 88 3C 446. R vs At for all Data . . . . 182 89 PKS 2345-16. Optical and Radio Curves . . 183 90 PKS 2345-16. R vs At for all Data . . . 185

91 Radio and Infrared Spectra of Selected Extragalactic
Sources . . 193

92 Idealized Spectrum of an Extragalactic Variable 194

93 OJ 287. Monthly Mean Fluxes at Different
Wavelengths . . . 201







xiii
















Abstract of Dissertation Presented to the Graduate
Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy



SEARCH FOR CORRELATED RADIO AND OPTICAL EVENTS IN LONG-TERM STUDIES OF EXTRAGALACTIC SOURCES



By

Richard Bryan Pomphrey

March, 1977



Chairman: Dr. Alex G. Smith
Major Department: Astronomy


Much of the research on extragalactic variables has attempted to determine the radiation mechanisms that cause the observed spectral energy distributions. This knowledge in turn should help to define the source of energy in these variable objects.

This work documents the first attempt to assemble the long-term

records of optical and radio fluxes of a large sample of variable extragalactic sources in a search for correlated radio and optical events, using a linear cross-correlation analysis to reinforce visual comparisons. The results of such research may help to parameterize either the radiation mechanism involved or the source structure which can then be used in the study of the radiation mechanism.

Chapter I presents the general background of this research topic, including the definitions of quasi-stellar objects, Seyfert galaxies, xiv










N galaxies, and Lacertids, and the similarities among these objects which are used as the justification for studying these objects as different manifestations of some common basic phenomenon. Both Chapters I and II address what is presently known, hypothesized, or speculated about these variables.

Chapter II gives a brief but extensive overview of the theoretical considerations involved in research on variable extragalactic objects as a reference against which the results of the search for correlations can be studied. This chapter includes reviews of the character of the radio, infrared, and optical spectra, their changes with time and possible causes, with special emphasis on the synchrotron and inverse Compton mechanisms and the expanding source model.

A simple method of synthesizing evenly spaced time series by

stepping through the data in given increments of time is discussed in Chapter III, along with the method used to linearly cross-correlate optical magnitudes with radio fluxes and the problems of this approach.

A relatively complete documentation of the long-term optical and radio variations is presented graphically in Chapter IV, where optical data from the Rosemary Hill, Royal Greenwich, Yale, and Goethe Link Observatories has been combined with radio data from Algonquin Observatory and the University of Massachusetts. The results of the correlation analysis are presented through discussion and extensive linear correlation and regression plots, which document a significant correlation for OJ 287 and a potential correlation for 3C 454.3.

The lack of correlation in most of the sources studied allows a decrease in the energy requirements of events in these sources and carries implications for the source structure, which are discussed in Chapter V.
xv










The possible implications of the correlation for OJ 287 are reviewed, but no firm conclusions concerning source structure or radiation mechanism can be drawn without further data. Finally, extensions of the investigation begun in this work are suggested.

A summary of the correlation analysis results is reported in a paper by R. B. Pomphrey, A. G. Smith, R. J. Leacock, C. N. Olsson, R. L. Scott, J. T. Pollock, Patricia Edwards, and W. A. Dent, "A Search for Correlated Radio and Optical Events in Long-Term Studies of Extragalactic Sources", in The Astronomical Journal, 81, 489, (1976).










































xvi
















CHAPTER I
INTRODUCTION


In the early 1960's, the discovery that quasi-stellar objects were a unique source of radiation initiated a period of intense observational and theoretical research which still continues. Although a great deal of data has helped define these objects phenomenologically, we are still not able satisfactorily to explain them theoretically. Moreover, the search for QSO's has revealed that there are many classes of sources which are quite similar to quasars: Seyfert, N-type, and compact galaxies, and Lacertids.

In this work I will use the term quasi-stellar object (QSO or quasar) to refer to all objects variously called quasi-stellar radio sources or quasi-stellar sources whether or not they are radio emitters. These objects possess the following general characteristics: a) faint, star-like appearance on a photographic plate; b) an excess of ultraviolet and infrared radiation (relative to stellar spectra); c) broad emission lines (widths of up to 100 A) with absorption lines sometimes present; d) optical spectra exhibiting large emission line redshifts [0.06 < z a 3.53, where z = (X X0) / X1]. Some quasars exhibit multiple absorption redshifts while a few have multiple emission redshifts. If the spectral redshifts are assumed to be cosmological, they indicate objects which are receding from us at a significant fraction of the speed of light, up to 0.91c for OQ 172 (z = 3.53). There has been some discussion (Chiu et al. 1973) concerning the creation of two classes of



1










quasars, one of which would be used to explain the Lacertid phenomenon.

Seyfert, N-type, and compact galaxies are often grouped together

because they all possess certain characteristics in common, and depending on who is classifying them, the defining criteria are not always mutually exclusive. Morgan (1972) presents an extensive summary of classification criteria.

Seyfert galaxies are generally characterized by small, intensely bright nuclei (described as stellar in visual appearance) in which violent activity appears to take place, manifesting itself in broad hydrogen emission lines charactized by Doppler velocity widths of a few thousand km/s; and by an excess of ultraviolet and infrared radiation. Many Seyfert galaxies are spirals and some exhibit forbidden emission lines which are much narrower than the broad lines and are not normally seen in galactic spectra.

N and compact galaxies basically are classifications of form and are thus somewhat a function of the distance and observing instrument. An N galaxy is defined as one having a small, brilliant nucleus containing a considerable fraction of the total luminosity, superimposed on a much fainter main body. A compact galaxy exhibits .high surface brightness and is only partially resolved on a medium to high resolution photographic plate.

BL Lac is the defining source for the Lacertid class of objects,

which exhibit (Strittmatter et al. 1972) a) rapid intensity variations in the radio, infrared, and optical, lasting days to weeks; b) an energy distribution which indicates most of the energy is emitted at infrared wavelengths; c) an absence of emission lines, and in many cases an absence of absorption lines; d) a strong and rapidly varying






3


polarization; e) in some cases a stellar appearance (OJ 287) while in other cases a non-stellar appearance (BL Lac).

In general, N galaxies have been regarded as intermediate in form and luminosity between quasars and Seyfert galaxies.



Extragalactic Variables

As early as 1963, Burbidge et al. suggested a possible relationship between quasars and Seyfert galaxies; Sandage (1970) and Kristian (1973) have provided evidence that quasars are like N-type galaxies.

For the purposes of this study, the most important point is that

many quasars, Seyfert and N-type galaxies, and Lacertids are strong radio emitters and exhibit intensity variations in both optical and radio emission. Moreover, apart from differences in absolute luminosity, these classes of objects are generally indistinguishable on the basis of their radio spectra or their time variations (Kellermann and Pauliny-Toth 1968).

Because real differences appear to exist among the optical classifications, I will generally note the specific type of object being discussed at any point. However, because of the increasing circumstantial evidence that there is a relationship among all these variable sources with respect to the nature of the radiation mechanism and energy source active in each of them, unless otherwise noted I will treat all these classes of objects as somewhat different manifestations of the same basic phenomena, and refer to all members of this general class as Extragalactic Variables (EGV).

Why are EGV's such an intriguing area of research? Stated simply, they emit far too much energy in too little time from too small a volume to be completely explained by any present theories. If they are at






4



cosmological distances, quasars have optical luminosities of 1045 to
46 &3 45
10 ergs/sec and radio luminosities of 10 to 10 ergs/sec (Burbidge and Burbidge 1967).

The optical intensity of many quasars varies on a time scale which is characteristically on the order of a tenth of a year, which implies that the active region of the quasar must be very compact. If we make the assumption that we can use the Hubble expansion constant to determine the distance of the quasars from their redshift, then we are confronted with a major scientific problem. Although not theoretically impossible, we are considering the largest masses ever seen in such small volumes,
8 19
10 to 1012 solar masses in a spherical volume roughly one tenth of a light year in diameter (Morrison 1973). Making long lasting stable models for such massive and compact systems, and developing highly efficient mechanisms for converting rest mass into radiation energy remain among the most perplexing problems associated with quasars.

From another perspective, beyond the basic phenomena used to

classify the types of EGV's, one almost immediately enters a labyrinth of controversial if not contradictory observations, explanations, hypotheses, interpretations, and plain speculations which are fed by generally commendable attempts to bring some meaning to this intriguing area of research by using the best data available, which regrettably often suffer from inadequate time or spatial resolution or inadequate signal to noise ratios. It seems that as researchers make every effort to increase time and spatial resolution, there often is that much more structure to be found, structure which is changing! In addition these research efforts follow on the heels of, and in fact act as significant motivation for, better receiving systems all the way from centimeter to X-ray wavelengths.






5


Thus whatever I present in this study does not represent incontrovertible truth, but rather that which appears to be most generally accepted by its frequency in the literature and which seems reasonable to me. It also represents the most successful effort to date to analyze the available variability data.



State of our Knowledge

Some of the most basic questions which remain unresolved are the

following: a) Are these objects at the cosmological distances indicated by the redshift of their spectra, or are they in fact much closer? b) What is the source of energy emitted, which in some cases is awesome even if the source is not at a cosmological distance? c) How is the energy converted into radiation? d) What kind of radiation is emitted? Because the radiation emission is what we observe, hopefully by answering

(d) we can make progress on the other basic questions. In this work, where necessary, I will assume the extragalactic variables are at cosmological distances. I will not address the question of energy source and energy conversion other than to note that the most popular theories (Kellermann 1974) involve the collisions of stars or galaxies; the collapse of stars, superstars, galaxies, or intergalactic matter; the explosion of stars, superstars, or galaxies, including chain reactions; positron-electron annihilation and creation of matter; quark interactions; and a pulsar-like mechanism referred to as the "spinar" model. What then do we know from the observations of extragalactic variables?

a) Very Long Baseline Interferometry measurements indicate that

the variable sources often have multiple, compact components,

typically on the order of 1.0 to 0.001 arc seconds; the physical






6


dimensions deduced from these measurements are a function of distance and expansion velocity of the source. In weak radio galaxies which have nuclear structure apparently identical to quasars, the radio emission is concentrated in a very small region near the nucleus, with dimensions ranging from 100 pc to less than

0.1 pc.

b) Radio and optical variations on time scales of a day to a few years have been observed in different sources. Assuming an event cannot occur in a time much shorter than the light travel time across the active region, the duration gives an estimate of the size of the active region which is independent of the distance to the source, but dependent on whether or not a relativistic expansion is taking place. It is possible that the source of energy could be much larger than the active region if there exists some energy coupling or transfer mechanism. c) There are at least two observations at optical frequencies that provide evidence for solid material in or at least near the nuclei of Seyfert galaxies and quasars (Burbidge and Stein 1970). d) Based on observations of variable nuclei, Burbidge (1970) has speculated that activity in galactic nuclei is a widespread and probably quite general phenomenon, taking place in many if not all types of galaxies. In general there is a wide range of power levels observed and activity has been seen over the full range of distance from nearby galaxies to the most distant objects observed. Thus considering light travel time, this activity has been observed over the full range of observed time. This has been reinforced by a recent discovery by Crane et al. (1976) of centimeter






7



variations from the nucleus of M81, a nearby spiral galaxy.

e) A strong correlation exists between high optical polarization

and variability.

The radio, optical, and infrared data collected on EGV's all seem to indicate a high probability that what we are observing are different manifestations of some basic phenomenon common to all EGV's and very likely common also to our own galaxy.

The obvious question, then, is just what is the basic phenomenon? This question has refused to yield to almost 13 years of concerted effort, for the answer is anything but obvious.

To begin with, we don't even know what the basic phenomenon is for which we are looking. Most likely it is either a common energy source, or a common mechanism which couples the energy generated to the energy emitted. This then is probably comouflaged by the magnitude of generated energy, the characteristics of the material surrounding the generator, and the number of such generators in a limited region of space.

If a basic phenomenon exists in all EGV's, then theories which attempt to address themselves to the phenomenon must be applicable in all cases; however, because of the many differences among observed EGV parameters, any theory which is not applicable to all EGV's is not necessarily completely invalid. It may simply be valid for certain conditions found in only some of the EGV's, and may require further refinement to apply more generally.

Our approach then must also be basic; what can we observe?

Because we are searching for something common to all these variables, what relationships can we find among the varied observations; and finally, what do these relationships tell us, if anything? This then






8



is the basic approach used in carrying out the research described herein.

Analysis of intensity variations may provide critical data on the radiation mechanisms involved, their relationship to one another, distribution of radiation energy, and possible source structure. This is particularly true if a correlation between activity at different wavelengths can be established and will become clearer after reviewing the character of the spectral energy distributions of the variable sources, and the attempts made thus far to explain them theoretically.

For the study and intercomparision of radio, infrared, and optical data which follows, the use of Table 1 is indispensable. The entries
0 0 0
for 3675 A, 4400 A, and 5490 A correspond to Johnson mU, gm, and MV respectively, before correction for atmospheric extinction.












TABLE 1

INTERCOMPARISON OF WAVELENGTHS WITH FREQUENCIES


INVERSE LOG INVERSE LOG WAVELENGTH WAVELENGTH WAVELENGTH FREQUENCY FREQUENCY o -1
(y) (A) (mm) (cm ) (Hz)


0.3 3000 3.3 x 10 4.5 1.0 x 1015 15.0 14
3675 2.7 4.4 8.2 x 10 14.9 0.4 4000 2.5 4.4 7.5 14.9 4400 2.2 4.4 6.8 14.8 0.55 5490 1.8 4.3 5.4 14.7 1.0 10,000 1.0 4.0 3.0 14.5 1.2 8.3 x 103 3.9 2.5 14.4 1.6 6.2 3.8 1.9 14.3 2.2 4.5 3.7 1.4 14.1 13
3.5 2.9 3.5 8.6 x 10 13.9 4.8 2.1 3.3 6.2 13.8 8.5 1.2 3.1 3.5 13.5
10.0 1.0 3.0 3.0 13.5 20.0 5.0 x 102 2.7 1.5 13.2 30.0 3.3 2.5 1.0 13.0 12
100.0 0.1 1.0 2.0 3.0 x 10 12.5 300.0 3.3 x 101 1.5 1.0 12.0 1000.0 1.0 1.0 1.0 3.0 x 10 11.5 3.3 3.0 x 10 0.5 9.1 x 10 11.0 9.0 1.1 0.4 3.3 10.5 10.0 1.0 0.0 3.0 10.5 28.0 1.07 10.0
















CHAPTER II
THEORY APPLIED TO SPECTRAL ENERGY DISTRIBUTIONS Spectral Energy Distributions

Much of the theoretical effort expended on EGV's and also on nonvariable quasars has been devoted to attempts to explain the radiation mechanisms which give rise to the spectral energy distributions of these sources. Knowledge of the radiation mechanisms, the parameters controlling these mechanisms, and the possible relationships between mechanisms (if more than one is responsible) will provide the information necessary to help explain the energy source and coupling mechanisms. A number of characteristic energy distributions are portrayed in Figure 1 (Neugebauer et al. 1971 and Telesco et al. 1976) where the log flux density (with vertical offset C) vs the log rest frequency have been plotted for the quasars 3C 273 (C = 31.0), 3C 446 (C = 31.0), 3C 48 (C = 30.0), 4C 29.68 (C = 30.0), 3C 249.1 (C = 29.0), and the Seyfert galaxy NGC 1068 (C = 33.0). The dashed lines simply connect observed portions of the spectra; thus they extend across most of the infrared portion of the spectrum where little data has been collected due to the lack of atmospheric observing windows at most of these frequencies.

Subsequent data in the near and far infrared now indicate that

there are probably two basic types of spectra, one which shows a large increase in the infrared spectrum, as in NGC 1068, and another which follows the dotted line for 3C 273 to within the accuracy of measurement (Simon 1976). Quasars and Seyfert galaxies exhibit both types of 10















10

NGC1068

9- /


8 c4


7 I




3C273









S4C2 9.68 N 3C249.1









8 9 30 11 12 13 14 15 16
quency for the quasars 3C 273, 3C 446, 3C 48, 4C 29.68, and 3C 249.1.







Reproduced from Neugebauer et al. (1971) with permission of the authors and the Annual Review of Astronomy and Astrophysics. More recent data obtained from Telesco et al. (1976) and Rieke and Low (1975) were used to plot the curve for the Seyfert galaxy NGC 1068. used to plot the curve for the Seyfert galaxy NGC 1068.






12



spectra. In addition, there is now evidence of a possible near-infrared "dust bump" in the energy distribution of a number of quasi-stellar objects (Becklin 1976). The bump may be described as a small departure from the otherwise smooth spectra, as opposed to the large infrared contribution in the spectra of NGC 1068.

In general, the known spectral energy distributions for any source can be divided into three regions whose boundaries overlap. The radio spectrum extends from about 1 mm (3 x 1011 Hz) to all longer wavelengths. The infrared spectrum extends from about 0.7 1 (1014 Hz) to about 1 mm; and the optical spectrum encompasses the region from about 3000 A
15 0
(-10 Hz) to 7000 A.



Radio Frequency Spectra

With respect to radio spectra, magnetic field strength, or time scale of flux density variations, no distinction can be made between quasars and compact radio galaxies (Kellermann and Pauliny-Toth 1969); thus they are grouped together in this section. A detailed study indicates three basic types of radio spectra (Kellermann 1974):

a) Straight (Class S) spectra, where the flux density decreases

monotonically over the whole range of observed frequencies, as in

Figure 2d;

b) Curved (Class C) spectra, which are steeper at shorter wavelengths (C-) as in Figure 2c, or have a sharp cut-off at shorter

wavelengths (C max) as in Figure 2b;

c) Complex (CPX) spectra, which have one or more maxima or minima

as in Figure 2a.























100" "' 100

1934-63

10, galaxy



10
4C 39.25


(a) 10 102 103 104 105 10 102 103 104 105


1000 -0

1001000
100100
100


10 3C 123
0 galaxy
101 3C 2 ,
"OSS *

1 (d)
(c) 1........ ...... ................
_,,.,_ .LL~ - 10 102 103 104 105 10 102 103 104 105





Figure 2. Ill.ustraLion of three basic groups of radio frequency spectrla: () 4C 39.25, Class CPX (Comlex); (b) 1934-63, Class C max (Curved); (c) 3C 123, Class C ((Curved); (d) 3C 2, Class S (SraighL) Reproduced from Calaci c and Extrgalac i adio Astr g. my, editLed by C. L. Verschiuur and K. I. Kelierman (p. 332). Copyr Lr Ighl .1974 by Spri er-Veriag New York, Inc. Used with perimiss:i.on of publisher and editors.






14



It is generally accepted that magnetic fields and a flux of high energy relativistic electrons exist in the EGV's. From such physical conditions, energy may be emitted by electrostatic bremsstrahlung scattered from plasma waves, synchrotron radiation, inverse Compton scattering, or by plasma shock waves if the source is turbulent. While there are other possibilities, these are most often discussed in the literature.

The good qualitative and in some cases quantitative agreement between the synchrotron hypothesis and the observations has presently established this as the most likely radiation mechanism, at least at radio wavelengths.



Radiation from a Single Electron

In the presence of a magnetic field of strength B, a non-relativistic electron will move in a helical path about a field line and emit radiation at a single gyro or cyclotron frequency (v ) which is given by





v 1 eB
= -- = (Hz) (1) g 2 R 27 me



where R is the perpendicular distance of the electron from the magnetic field line, m is the electron rest mass, v is the electron velocity, e is the electron charge (emu), B is the magnetic flux density, and c is the velocity of light.

Blumenthal and Gould (1970) have shown that a relativistic electron spiraling in a magnetic field emits a total instantaneous power given by






15



Se3 B v (2) P(v) = 2v K5/3( )d( me c V /c




where the critical frequency is expressed by


3 eB 2 Vc Yr
2 27rme

13 2
= 1.608 x 10 B E (3)
-& GeV
2
= 4.21 B. Yr (MHz)




and where

eBA
= -- t
Yrmc
(4)
-1/22
12 -1/2 Yr v = (1 2
c



K5/3(E) is a modified Bessel function of the 5/3 order, E is the

electron energy (E = y mc2), and B = B sine where e is the pitch angle, the constant angle between the electron velocity and the magnetic field. The synchrotron spectrum from a single electron as a function of x = v/ve is illustrated in Figure 3. As can be seen from equations (2) and (3), for a single particle emitting synchrotron radiation in a homogeneous magnetic field, the emission received at a particular frequency is directly related to the energy of the electron producing this radiation, and the strength of the magnetic field.






16



























06



04








0 1.0 2.0 3.0 4.0 5.0












Figure 3. Synchrotron spectrum from a single electron as a function of x = /v Reproduced from Blumenthal and Gould (1970) with permission of the authors and the Reviews of Modern Physics.






17



The distribution P(v) has a broad peak near v lu 0.28v At higher
C
frequencies (v >> v ), the spectrum approaches




LP) 3 1/2 e K3B, v12 e -(v/vc) (5) me c



While at very low frequencies (v<<'v ) the spectrum can be approximated
C
by


e B 1/3
P(v) = 2 L] 7) (6)






where F(1/3) is the Gamma function. P(v) varies little over a large range of frequencies, decreasing to half its maximum value at v/vc = 0.011 and 1.47 (Oort and Walraven 1956). Most of the radiation is concentrated in a narrow cone, the axis of which coincides with the instantaneous velocity vector of the electron. The angle between the axis and the sides of the cone is given by




< 2> 1/2 r 1 me 2 (7) Yr (7)





As a result the radiation is strongly polarized. In the case where the
0
pitch angle, 0e, is 90 the electric vector is polarized parallel to the plane of the electron orbit. An observer in this plane will receive a pulse of radiation every time the electron completes an orbit, at





18



intervals T such that



T= Yr = (8)



The duration of the pulse follows from equation (7) and is given by



At 2 Y 1 ) (9) Yr Vg



While it can be seen from equations (1), (2), and (4) that the

synchrotron spectrum is made up of discrete frequencies, the radiation is concentrated in the higher-order harmonics of the classical gyrofrequency, v (Kellermann 1974) and thus is often considered continuous.
0
In the case where e = 90 an observer receives all the radiation
0
emitted during the time At. For 8e # 90 the observed spectrum is

e
reduced by a factor of (sin-2 8e)-I, because the distance between the electron and the observer changes with time. However, for a distribution of electrons, the emitted and received powers are again equal.



Radiation from a Distribution of Electrons

Brown (1974), has shown that a homogeneous and isotropic ensenble of electrons having a number density per unit energy of N(E)dE and located in a vacuum in the presence of a uniform magnetic field B of spatial extent L, will radiate a specific intensity I(v) given by


3 e2 BL
I() 2 N(E)dE -- K5/3 ()dE (10) mc c
c





19


3
where N(E)dE is the number of electrons per cm with energies in the interval E to E + dE. If the electrons are characterized by a power law energy distribution between particular limits E1 and E2, given by


dN(E) = N(E)dE = KE-Y dE (E1 < E < E2) (11)



then the specific intensity takes the form



e L 3e (y-)/2 a(y)KB(+)/2 (y-l)/2 (12)
mc 2 4mc



where K is a constant, a(y) is a slowly varying function of y and in general a(y) = 0.1. The specific intensity radiated will be observed as a brightness distribution, and the integral of this brightness distribution over the whole source yields the flux density S. Thus from equations (11) and (12) it can be seen that a power law distribution of electrons of spectral index y emits a power law photon spectrum which is characterized by


S v (13) where the two indices are related by



6= - (14)



Thus assuming that a power law electron energy distribution is the source of emitted radiation, the index y can be obtained by measuring the slope a of the observed spectral energy distribution (Figure 1).






20



The range of electron energies which contribute to synchrotron emission at a given frequency is strongly a function of the electron spectrum and thus of the index y. Table 2 (from Brown 1974) lists the range of values E1 to E2 which is responsible for 90% of the emission at a particular frequency, for a given value of y.

TABLE 2

RANGE OF ELECTRON ENERGIES FOR A GIVEN POWER LAW INDEX



y 1.0 1.5 2.0 2.5 3.0 4.0 5.0 (E2/E1)90% 1620 117 56 22 15 8.9 6.1



Thus as y increases, the range of electron energies increasingly narrows, indicating that the assumption or approximation of a power law distribution of electron energies needs to hold only over a narrow energy range. The shape of the electron energy distribution may deviate enormously from a power law outside the specified energy range without significantly affecting the synchrotron emission spectrum. The validity of the assumption of a power law distribution ranges from y a 1.0 (Kellermann 1974) to y 5 5.0 (Brown 1974). Finally, it should be noted from equation (6) that no form of electron energy distribution can give a synchrotron spectrum that rises faster than the low frequency asymptotic limit of v1/3 for a single electron.

The straight radio frequency spectrum in Figure 2d is believed to result from synchrotron emission from a power law distribution of electrons as just discussed, Such spectra generally have indices in the range -1.3 < a < -0.6, with a median value of about -0.8, which corresponds to y = 2.6. Deviations from this straight spectra can arise from





21



numerous causes. To maintain a consistent presentation of the synchrotron hypothesis, I will discuss here only gross spectral changes which have synchrotron-related causes,and defer discussion of other causes to another investigation.

The turnover or low frequency cutoff in Figure 2b can result from synchrotron self-absorption. Theory predicts that as the brightness temperature of the source approaches the equivalent kinetic energy of the electrons, self-absorption will become important, and the source will become completely opaque at a frequency given by Sm B1/5 1/5
Sm 34 B (1 + Z) (MHz) (15)
m 2



where 8 is the angular extent of the source in arc seconds, B is in gauss, the (1 + Z) term accounts for the effect of the redshift, (Sm/e) is the surface brightness of the source, and Sm is the maximum flux density at vm.

A study of the values of vm vs surface brightness for sources for which 6 has been measured, shows that the observed cutoffs in the radio spectra can be accounted for by synchrotron self-absorption with a magnetic field of B = 1041 gauss. This corresponds to a maximum brightness temperature of T 10 to 1012 K. It is hypothesized that this
m
brightness temperature of 1012 K corresponds to the case where energy loss by synchrotron radiation is just equal to the energy loss caused by inverse Compton scattering. According to this hypothesis, inverse Compton scattering would cause a rapid "cooling" of a source which has a T = 1012 K.
m






22



According to synchrotron theory, as v (< v ) increases, one

receives more radiation from deeper in the source and the flux increases until v = v, at which point the source becomes optically thin and the
m
flux received becomes a function of the electron energy distribution as in Figure 2d. For frequencies v < v the spectral index is independent of the electron energy distribution and the theory predicts a value of

2.5. Although the apparent effect of synchrotron self-absorption is evident in many sources and values of a = +1.0 are often observed at long wavelengths, no source has been observed with the a = +2.5 value predicted by theory. This might be explained by a gradual rather than an abrupt transition from the transparent to opaque condition, caused by a range of opacities resulting from different parts of the source becoming opaque at different frequencies. Alternatively, O'Dell and Sartori (1970) have proposed "cyclotron turnover" as the possible low frequency cutoff mechanism.

The spectrum shown in Figure 2a is referred to as a "complex" or "peculiar" spectrum and cannot be explained by a single source of synchrotron radiation. Thus this type is believed to be a superposition of two or more curved or straight spectra, and is generally associated with compact radio sources. Because of their composite nature, such spectra often have relatively small values of spectral index over a portion of the frequency range and are thus sometimes referred to as "flat". A good correlation exists between composite radio spectra and violent optical and radio variability. The frequency at which selfabsorption becomes significant is a function of the surface brightness temperature (S / e2), as is shown in equation (15). Thus for a given flux, if the angular extent (e) of the active region is large, the






23



surface brightness temperature will be lower, resulting in a lower value of V
m
The relatively good agreement between theory and observations of

the self-absorption cutoff frequency vm, the angular size of individual compact components as measured by VLBI, and the observed peak brightness temperature of 1011 to 1012 K pose strong arguments that the radio emission from the very comapct sources is indeed ordinary, incoherent synchrotron emission (Kellermann 1970).



Time Variations

We finally come to the purpose of this research, which is to search for a relation between observed optical and radio variations. In general, time variations might be caused by

a) changes in the rate of production or acceleration of relativistic particles;

b) loss of energy due to synchrotron radiation, inverse Compton

scattering, or adiabatic expansion;

c) changes in magnetic field;

d) (in the opaque region of the spectrum) changes in the angular

size of the source as a result of expansion.

In addition it should be noted that plasma ejection from a massive rotating body (spinar) could also be the cause of time variations. However, once the plasma has been ejected, any or all of (a) through (d) would apply. In fact it is most likely that all of (a) through (d) contribute to some degree among the different sources and at different periods of time within individual sources.





24


One unknown factor to keep in mind is that while we have strong

evidence (from measured time of variations) that the optical, infrared, and high frequency radio flux come from very small regions, we do not know presently if these regions are one and the same or whether different parts of the spectrum arise from differnt regions.



Expanding Source Model

Based on short wavelength (2 to 10 cm) radio observations, the

initial expanding source model assumed that radio emission from a variable extragalactic object is due to synchrotron radiation from a spherical cloud of relativistic electrons moving in a magnetic field while the cloud expands adiabatically.

Shklovsky (1960) originally hypothesized the expanding source model, using it to predict decreases in radio flux from supernovae remnants. If we assume

a) the electron energy distribution is a power law of the form

given in equation (11);

b) the magnetic field is fixed in the expanding cloud, so that

magnetic flux is conserved, B2 = B1 (rl/r2 2

c) each electron loses energy due to cloud expansion at a rate

proportional to its energy, so that the form of the energy distribution is unchanged, that is E2 = E1 (rl/r2) for each electron;

d) no additional particles enter or leave the region, so that

K2 = K1 (r1/r2)y + 2





25



then for an optically thin source


-2y
S2 = S 1 r (16)




where rl is the radius at time t1 and r2 is the expanded radius at time t2.

However, examination of the radio spectra indicates that for a

given frequency if we extrapolate back in time, at some point the density of relativistic electrons is such that the source is no longer completely transparent to its own radiation. At this point, from equation (15) the brightness temperature depends only on the value of the magnetic field, and the flux density is given by S(3,t) B-1/2(t) 62(t) 5/2 (17)



If the expansion is constant in time and if the magnetic flux is conserved during expansion, then ti can be substituted for ri in
1 i

assumption (b), and equation (17) can be used to derive



S(t2) = S(t1) [-] (18)




If the magnetic flux is constant, such that B(t2) = B(tl), then



S(t2) = S(t1) 2 (19)



In either case, the rate of change of the flux density is independent of the electron energy distribution, because as long as the source is





26



optically thick, the observed radiation comes from only a fraction of the electrons.

From expressions for the frequency vm, at which the synchrotron self-absorption ceases, it can be shown that



y + 4 7y + 3
S(Om2) t 4y + 6
S (V m) t L (20)



Again it can be shown that the complete expression for flux density as a function of frequency v and time t is given by



+- 4 -(2y+3)

S5/t2 3/2 1-exprm ()(-T(2 (21) l-exp -T


where Sml is the flux density corresponding to any frequency Vml at time t1 ;

t2 is the time of observation at frequency V; T is the optical depth of any frequency vm.

Thus the model suggests that the varying components are sources of synchrotron radiation which initially are optically thick but become optically thin at progressively longer wavelengths as they expand (van der Laan 1966). The simple model predicts that outbursts will be seen earlier, and will have greater flux amplitude and a shorter outburst duration at higher frequencies.

In principle, a measure of the radio spectrum at any time and its time rate of change may be used to predict the future behavior of the





27



spectrum at all frequencies. In practice this is difficult because many variable source show multiple overlapping outbursts over short periods of time. In fact, long-term observations have shown that repeated outbursts of relativistic particles over time periods of a year or less are not uncommon in EGV's especially in the Lacertids. If one assumes that the expanding source model is valid, flares will be separated and better defined at higher frequencies due to shorter duration and less overlap. Extending this knowledge to lower frequencies can help identify the possible location in time of individual flares, from which the relative flare amplitude and duration may be estimated, within the constraints of the recorded flux level as a function of time. If this data can be obtained successfully, it allows one to study how a given event propagates in the frequency domain, and thus how it affects the spectral energy distribution. However, estimates of absolute amplitude and duration of a flare are almost impossible due to the difficulty in finding the quiescent radiation level.



Expanding Source Model Difficulties and Alternatives

While the model has been successful in quantitatively explaining centimeter variations from certain sources including 3C 120 (Dent 1968, Pauliny-Toth and Kellermann 1966, Seielstad 1974), discrepancies exist between 11.0 and 2.8 cm, and the theory appears to break down at short centimeter to millimeter wavelengths (Medd et al. 1968, Kellermann and Pauliny-Toth 1968, Lock et al. 1969, Kinman et al. 1974). The discrepancies include incorrect form of the outbursts, lack of time delay and/or lack of amplitude change between events seen at different frequencies. The latter two discrepancies could be caused by the source





28



becoming optically thin, or by continuous injection of relativistic electrons. Peterson and Dent (1973) proposed a continuous injection version of the expanding source model with some limited success. Some of the additional modifications or combinations of parameters which might be tried include: variable expansion of the cloud; a mechanism to accelerate particles after an explosive event; possible escape of particles from the cloud; lack of conservation of magnetic flux; an expanding shell rather than a spherical cloud, introduced by van der Laan (1962) and Lequeux (1962); multiple interacting sources; relativistic expansion (Ryle and Longair 1967, Rees and Simon 1968); non-isotropic radiation; coherent rather than incoherent radiation; changing electron energy distribution due to loss of energy by inverse Compton scattering, ordinary bremsstrahlung, and ionization.

Thus there exists myriad possible combinations of parameters. Because the simple model does have basic qualitative validity despite signigicant discrepancies, work is proceeding on revisions of the simple model. In particular, Peterson and Dent's limited success with the obvious possibility of extended injection has motivated continuing investigations in that area.

Peterson and King (1975) have attempted to extend the application of the continuous injection model into the optical wavelengths. Because of the gap in the observable spectrum between centimeter and optical wavelengths, it is not even known if a relationship exists between the activity observed at these two different frequencies. However, the limited observations at millimeter wavelengths indicate that the large and rapid variations predicted by the simple expanding model at these short wavelengths do not occur.






29



Inverse Compton Scattering

Inverse Compton scattering will take place in a region with a sufficiently large radiation density and a sufficiently strong magnetic field. Thus while this radiation mechanism most likely functions in the types of sources under discussion, the main question that must be answered is how significant a role does this process play? The inverse Compton mechanism is highly inefficient and if a significant amount of the observed radiation is caused by the inverse Compton mechanism, the already awesome energy requirement increases much further.

Inverse Compton scattering refers to the collision of a fast electron with a low energy photon and the resulting production of a high energy recoil photon and a corresponding decrease in electron energy. The solution for the total spectrum of inverse Compton photons scattered per unit time and volume by a distribution of relativistic electrons passing through a photon gas is very complicated in the completely general case, and thus has not been attempted. However, simplifications result in limiting cases which have astrophysical applications. In the rest frame of the electron, if the energy of the photon before scattering is much less than mc the incident and scattered photons will have roughly the same energy and the scattering corresponds to the Thompson limit in which the Compton cross section is independent of the energy of the incoming photon. While in the laboratory frame, the characteristic energy of the scattered photon is large relative to the incident photon energy, it is still small compared with the electon energy and thus the electron loses a small fraction of its energy in any single inverse Compton scattering. However, in the limiting case where the
2
energy of the photon before scattering is much greater than mc the






30



scattered photon carried away a large fraction of the electron energy, and thus the electron does not lose its energy continuously.

Felten and Morrison (1966) present inverse Compton scattering in a manner that stresses its relationship with synchrotron radiation. Given a power law energy distribution of electrons as in equation (11), as long as the energy spectrum is not too steep, the distribution of recoil photon energies will be determined primarily by equation (11), and will in fact be a power law distribution itself.

The electron lifetime against synchrotron radiation loss is given by


t s B-3/2 -1/2 (22)
s m


where ts is in years, B in gauss, and vm in GHz; while the electron lifetime against energy loss to inverse Compton scattering (in the Thompson limit) is given by


6 x 10 (23)
t \ (23) c yrP


where t is in years and p is the energy density of the surrounding
3
radiation field (photon distribution) in eV/cm3. To give an example of the significance of the radiation energy density on inverse Compton losses, consider a 5 GeV electron (yr a 10 ) trapped in the galaxy where p 10-1 eV/cm3 compared to one trapped near the solar surface where p 2 x 1012 eV/cm3. In the galaxy, the electron will have a lifetime
1019 3
t c 10 years, whereas near the solar surface, t c 10 sec.
C C






31



The total instantaneous power scattered by an electron is given by



Pc (Yr P) OT CYP (24)

8 2
where oT is the Thompson cross section (a = -rro ); whereas the instantaneous synchrotron power radiated by an electron is given by


2 2 22 (25)
P (r H) = -r cy B (25)


where r is the classical. electron radius and c is the velocity of light. Thus the ratio of the two powers for a single electron is given by

2 2 2
P (yr,B) ro C (H sine ) P (yr,p) = 2 2 c r' (16/3)r 2cyr 2


= B28 sin 2 (26)
2 p e


Then assuming that the electron velocity is randomly oriented with respect to the magnetic field, the time or ensemble average gives
2 2
< sin e > = ; and thus
e 3

s B2/8w
/8 (27) P p


where (B2/87) is the energy density of the magnetic field. Thus the ratio of losses from synchrotron radiation and from inverse Compton scattering is equal to the ratio of the energy densities. (Note that in some notation H is substituted for B, but as long as consideration is limited to vacuum, B = H.) The assumption of equipartition of energy





32



between the energy density of the magnetic field and the energy density of the radiation field requires the least total energy from a source. If the energy of the radiation field exceeds twice the energy density of the magnetic field, catastrophic inverse Compton losses result.

Kellermann and Pauliny-Toth (1969) have expressed these conditions in terms of the maximum brightness temperature (T ) observed in compact sources. According to their development, for a homogeneous and isotropic source, the intensity of the radiation from inverse Compton scattering relative to the intensity of radiation from synchrotron emission (Lc/Ls) is given by


L P T T
L P 2 12 m 2 12 Vm (28)



where v is the cutoff frequency in MHz due to synchrotron self-absorpm
tion. Assuming a roughly typical value of v m 100 GHz, if T < 1011 K, L /L << 1 and inverse Compton scattering is insignificant. But if
c s
T > 1012 K, the bracketed term, which represents the effect of second 12 10
order scattering, becomes important and L /L n (T /10 ) Thus it c s m
is argued that the catastrophic energy losses due to inverse Compton scattering "cool" the source, causing a decrease of T to between 1011 to 1012 K, where losses to both processes are roughly the same. As an example, assume that v M' 1 GHz. Then for T 101 K, the half-life of m m
an electron is n 104 years, whereas if T 1 1012 K, the half-life drops to about a day.

Felten and Morrison developed still another expression relating the radiation intensities, which may prove useful,






33




(I)s Ks 2/8 2 x 10T 2
--- (29)
(I) K p B

where K and K represent the constants and parameters entering the
S c
respective coefficients. They then use that expression neglecting inverse Compton scattering from the 3 K background radiation to compute the expected spectra from synchrotron and inverse Compton radiation for the galactic halo with an imposed high frequency cutoff, as shown in Figure 4. Conditions in the galactic halo are far different from conditions in compact variable sources; the point is that if both synchrotron and inverse Compton components exist and can be resolved in an observed spectral energy distribution, equation (29) will provide a useful estimate of physical conditions in the source.

Finally, a relation between the characteristic synchrotron frequency (v ) emitted by an electron at a given energy, and the characC
teristic energy (el) of the Compton scattered photon is given by


2 T
0.9 x 10 2 v (30)
1 B. c


where EI is in eV, B, in n-gauss, and vc in MHz. From this it can be seen that for a given brightness temperature T, the characteristic Compton scattering energy, and therefore frequency, decreases for increasing magnetic field strength. (It should be noted that in my notation, yr, y, e, and vc correspond to Felten and Morrison's y, m, T, and vs.)

In summary, it should be emphasized that values of the magnetic fields and electron half-lives against inverse Compton scattering can be estimated using equations (15) and (28), without assuming a distance























visible
radij o waves r. x tys.mm rays

2002



1010 10 0 10 /0 I I




Pholon frequency v (cps)




Figure 4. The expected qualitative features of inverse Compton scattering and synchrotron radiation spectra from a power law energy
distribution of electrons in the galactic halo, neglecting inverse Compton scattering from the 30K background radiation. Reproduced from Felten and Morrison (1966) with permission of the authors and The Astrophysical Journal, which is published by the University of Chicago Press.





35



to the source or equipartition of energy. Possibly large uncertainties do exist in the determination of the angular size (6) and cutoff frequencies (vm), especially in sources possessing complex brightness distributions which are characteristic of EGV's.

If the distance to the source is known, the energy content of the relativistic electrons, Ee, and the magnetic field, Em, can be uniquely determined (Kellermann and Pauliny-Toth 1969). However, for typical spectral indices (y n 2.5) the ratio E /E depends on the 1'20th power
e m
of the cutoff frequency, vm, and the angular extent 8; thus departures from energy equipartition are difficult to detect.

The major controversy centered around synchrotron radiation versus inverse Compton scattering is based on the lifetimes of electrons against energy loss. If one assumes, based on an "average" outburst duration, a typical size of %1017 cm (one light month) for an active region, this implies lifetimes of the relativistic electrons of approximately that same length. Thus some argue that it is unlikely that any significant portion of the emitted radiation could be due to inverse Compton scattering, because that would imply electron lifetimes as short as one day. From this point, Hoyle, Burbidge, and Sargent (1966) calculated the ratio of magnetic to radiation density assuming synchrotron radiation was the dominant process and the source 3C 273 was at a cosmological distance. The resulting ratio of energy densities indicated catastrophic inverse Compton losses, from which they concluded that the source was not at a cosmological distance. However, Woltjer (1966) countered by assuming a non-isotropic radiation field, explained away the energy density problem and put 3C 273 back at cosmological distances. This presents a specific example of the controversial






36



nature of this research.

The considerations listed here have prompted some to develop

radiation models which include both synchrotron and inverse Compton radiation (Takarada 1968, Cavaliere et al. 1970, Rees 1971, Blanford and Rees 1972).



Optical Spectra

To study the absolute energy distributions of EGV's at optical wavelengths, data recorded as stellar magnitudes are converted to an energy scale using the absolute energy distribution of aLyra as a reference. This source was calibrated by Oke and Shild (1970), who formulated a conversion expression m = -2.5 log F C (31)



where m is the magnitude, F is the corresponding energy flux in units of 1026 Janskys (1 Jansky = 10-26 Watts/m2/Hz) and C is a constant. For all conversions made in this study, C = 56.04.

Extragalactic variables that exhibit large amplitude optical variations are usually those that have significant optical polarization, steep power law optical spectra, and that tend to be associated with compact radio sources having flat radio spectra at gigahertz frequencies (Kinman 1975). The non-thermal continuum of the Seyfert galaxy 3C 120 is relatively flat in the UV, increases towards the red in the visual range and turns up sharply in the IR (Shields et al. 1972), as shown in Figure 5. This appears roughly similar to the energy distribution of the QSO 3C 273.


























Figure 5. 3C 120. Optical and near-infrared spectrum together with a model for continuum emission. The total continuum after correction for reddening is represented by the solid line, while the dashed line shows the continuum remaining after recombination radiation has been subtracted. The dotted line shows a model of a flat continuum with f= 0.8 x 1025 ergs/sec/cm2/Hz plus the radiation from a typical spiral galaxy with M = -20.0. Reproduced from Shields et al. (1972) with permission of the authors and The Astrophysical Journal, which is published by the University of Chicago Press.





















3C120
-24.0
2- Continuum corrected for reddening I .2 --- Corrected continuum Minus thermal component E -...- Golaxy plus f, = const.




S.6



..


















Oc
cc






39


The optical and near infrared spectral distribution of BL Lac and OJ 287 are presented in Figures 6, 7, and 8. The Lacertids in general exhibit approximate power law spectra which grow steeper (more negative) between the near infrared and the optical as can be seen from the values in Table 3, from Rieke and Kinman (1974) and Oke and Gunn (1974). The somewhat flatter infrared index may be the result of positive curvature in the non-thermal spectrum and inclusion of some stellar radiation at 2.2i. (Note that for BL Lac, the values for the infrared and the optical spectral indices were derived from observations that were separated in time.)


TABLE 3

LACERTID OPTICAL AND NEAR-IR SPECTRAL INDICES

IR OPTICAL
SOURCE (10.5v 0.44) (0.55P 0.36)

0735 + 17 -1.20 + 0.15 -1.9

OJ 287 -0.86

ON 231 -1.13 + 0.12 -2.0 BL Lac -1.15 + 0.2 -1.55 (10.51 2.2) (


Caution must be exercised when comparing optical spectral indices of such violent variables because the variations do affect the spectra, as will be discussed. In addition, while BL Lac has no emission lines, if it is at the nucleus of an ordinary giant elliptical galaxy, as is indicated by the work of Oke and Gunn (1974), then it may have a significant stellar component at optical wavelengths, which is presumed to disappear at 10u (Rieke and Kinman 1974). Its optical spectrum at















WAVELENGTH (/I)
22 165 10 08 060050040 030
-268 I T-270 BL LAC
-272

-274

-27.6
N
I
N -27.8

t -28O

-- -28.2

-284

-286 LL
U



-28.8
0
-29.0

-292

-294

-296

-29.8
141 .2 .3 4 .5 6 7 .8 9 150 15
LOG FREQUENCY (HZ)

Figure 6. BL Lac: spectral energy distribution from 0.31 to 2.2 p. The solid line represents the energy distribution after a correction for 0.31 magnitudes of visual absorption has been applied. Reproduced from Oke eL al. (1969) with permission of the authors and The Asltrophysical o ?urnal, which is published by the Ulnivers ity of Chicago Press. 4-


















-2400 G








-24-20


-24-30
I .9









0 -24-40


OJ 287

-24 50 Avero e of the observations on18 th and 21st Jan.,1972
0@Observations on 19thJan.,1972

-2460
14-90 14-80 14-70 14-60 14-50 LOG v


Figure 7. 0.i1 287: optical spectrum. A fitted sttraighlit line for all the contiltuum points has a slope of
1.248. Reproduced from Visvanthaln (1973b) witLh permission ( f the antLhor and The Astrophiysical IJouIrnal which is published by the U.niversi:ity of Chicano Press.


























Figure 8. OJ 287. Millimeter, infrared, and optical flux compared with the results of included equation. Filled circles represent data taken on 1972 Feburary 17 (Epstein et al. 1972) and encircled filled circles represent data taken on 1972 January 17 and 21, scaled to the V-magnitude on 1972 February 17. Reproduced from Visvanathan (1973b) with permission of the author and The Astrophysical Journal, which is published by the University of Chicago Press.























I I I

-22 OJ287 F=257 10- -06 4F ( d
2










I

E



0)



LL


-- 24






A-v2 6xiO'4c/s

B: V2= 9xlO4 C/S

= observed dolo A

-25

11 12 13 14 15 LOG v




-






44



wavelengths
At the time of observation (Oke et al. 1970), the optical continua of twenty-eight quasars between 0.3 and 2.21 could generally be approximated by power law spectra having indices of a = -0.2 to -1.6, with the entire range being populated, as seen in Figures 10, 11, and 12. However, the presence of broad emission lines combined with limited spectral resolution makes it difficult to determine if the continuum is power law or curved from this data. Observations from 0.9 to 0.4v by Visvanathan (1973a) of three of the most active quasars, 3C 345, 3C 446, and 3C 454.3, indicate that these optical continua can be represented by a power law in both active and quiet phases, as illustrated in Figure 13. Observations such as those in Figure 13 have yet to indicate any relation between optical activity and quasar color in any individual source or among the sources as a group. Sometimes the QSO grows redder (more negative slope) during activity, while at other times it grows bluer. This lack of relation between brightness and color may be an indication that the continuum source region consists of many centers of activity, but it also raises the question of whether there might be material in the general region of the quasars but not







45





















BL LAC

-24.6 .


-24.8


-25.0


-25.2


-2 5.4 *
OCT 20, 968 JULY 16, 1969
-25.6- a 2.850.09 a =2.92 0.03


L -24.41


-24.6


-24.a


-25.0


-25.2 4 14


2 5'. 4


-25 6 AUG 19, 1969 DEC 5, 1969 %
0 3.17 0.06 = 2.93 +0.04
-25.8
14.5 14.7 14.9 14.5 14.7 14.9 log Z/








Figure 9. BL Lac: continuum measurements of the optical spectrum on different days, indicating change of power law index. Straight lines are least squares fits for all the continuum points. Reproduced from Visvanathan (1973a) with permission of the author and The Astrophysical Journal, which is published by the University of Chicago Press.





























Figure 10. Observed optical and near-infrared spectra of selected quasars plotted as a function of rest frequency vo = v(l+z). Standard deviation error bars are indicated for the infrared photometry and for all spectral scanner observations where the standard deviation in log f is greater than 0.02. Note that Ton 256 and PHL 938 are radio quiet. Reproduced from Oke et al. (1970) with permission of the authors and The Astrophysical Journal, which is published by the University of Chicago Press.
























Ha [Om) Hf3 MgH IIlu ll] Ml 11 1 P1 1. S-8.2- H28a I I4 -CI : 3C 323.1 -28 6 Z= 2 202
-284 Z=0.264
1 -283
-28.6 -290 I Ip
-288 I -29 2
N
N -29.0- .. .. -294
----- ---t--+-- --+I --t--t- 3c,
3c 9
-288 Z 202
-- -282 PKS 2135-14 29 >- -290
U)Z=0.202
l -284 "* .-292x C) -294
-286 x LL __ -296 I I I I-II I ----- LL '- :
-29 6

-28 TON 256 0 Z= 0.1307
-284 "- I -----4- ----I --- l ----I- I -" ** PlIL 93,,-286 Z-190

-28.8

-290 I
142 .3 4 5 6 7 8 .9 150 -1
LOG FREQUENCY (HZ) -?C- .
1-15 6 7 9 I 2 3 4 LOG FREQUENCY (HZ)







4-





























Figure 11. A continuation of observed optical and near-infrared spectra of selected quasars begun in Figure 10. Note that the visual and infrared measurements for both 3C 279 and 3C 345 show variability. The inconsistency between the spectral scanner data and the UBV measurements for PHL 658 is unresolved and probably instrumental. Reproduced from Oke et al. (1970) with permission of the authors and The Astrophysical Journal, which is published by the University of Chicago Press.























Ho loin H, M tI CIll -280 Ha [HO ll] HG Mgll CIl Ha 1OB] H,3 Mgl" CII
2820 0-276
3C i8 -28 2 3C 279 3C 3415
SZ 40-278 Z 0595
-2-284 --280
286
-286 -282 i-28 8 <..

S-290 o 24-25 MAY.8 JUNE 66 -28.4
.2-90 19-20 AUJG o -286 I"
- -292 MAY6 .-28 r -29 : JUNE 67 *
-29.4 APR 68 -28 8 MAY JUNE JULY G66
S --- ----- --- -296 24-25 JUNE 68 -290 10 Y-AUG 67
fPS25 11-9 -7-810 11 AUG 67
S292 PKS 225I > +--- --4 >- -292 APR-MAY 68 SZ0323 288 I.. PHL 658- 21-22 JUNE 68
-84 Z0450 ) -294 20 JULY 68 w Lu -290 z
-28 "-.9rP 0405-12 x X -292 X
---28 Ii --- -- ----+-----------I- -280005-12
b2 3C 2771 I 3C 351 L90 Z 0320 ( -282 Z 0371 0 -282
-29 2 -J -284 -28 4

-294 f -.I -286
-, --. .-28.2 PKS 1510-08
S--28Z 361
i 3C 2491 -284 3C 334
8 Z 0311 -286 Z 0556
286
28 6 -268
-288 -.. .
8 -290-290- -292
-34567 950 142.34 56789150 2 423 4 5 6 7 8 9 150
LOG FREQUENCY (HZ) LOG FREQUENCY (HZ) LOG FREQUENCY (HiZ)





























Figure 12. A continuation of Figure 10. Note that while 3C 454.3 and 3C 446 exhibited variations in the visual, infrared photometry was not obtained to check for variability. The UBV measurements of 4C 29.68 were unpublished data from Sandage. The 2.2-y points in 3C 309.1 and 3C 432 are only limiting values. Reproduced from Oke et al. (1970) with permission of the authors and The Astrophysical Journal, which is published by the University of Chicago Press.






















SH ]H Mgl m c H Cm C Ha [O]Hf Mgll CImi CE
83C 454 3 CTA 102 3C 4 2 3C 4 54
Z-280 Z0859 -290 Z 1037 -290 Z 180

-282i -292 i _292

284 . -294- -294 I .

-286 '. -296 " -296 7-8 AUG 67
:: 8 L .--4-- -- _--- I --_20 JUNE, 19 JULY 684C 3C 44
-290 AUG-NOV 68 -290 4C 298 284 I 4
-'(IV d Z=1012 -284j I.
3C 286 I[.-.. -2
-- 288 08294 -288

-290- -29 O
-9PKS2145'06 W- oSEP 65 "
292 .' -286- Z0990 -292 19-23 JULY 66 o S -------- I 288 294 JUNE-SEP 67
PKS 1354+19 1 9-10 AUG.28-30 SEP.
-286 Z 0720 -290 -296 I OCT 67 O 1 0 20-21 JUNE 68
-J 28 -i -292- -298,- 19-20 JULY 68

290 -294 --- -----+--I--1-- --- -+-- -+-I-1--- --- ----------- -290 ZC 2 09
L290- 3C 208
288I 3C 3Z 0691 -292 . -292

-294 3C 3091 -294 ;' -296- 09 -26

45 i 8 9 150 1 2 5 3 345 f 78 9 10 2 3 14456789150 2
LOG FREQUENCY (HZ) LOG FREQUENCY (HZ) LOG FREQUENCY (HZ)










U]

















3C 345 3C 446 3C 454.3

-26.0 ,-26.2 -25.6




-2-26.6.2
-26.4 JUNE 30,1968 -25.8 JUNE 30,1968
-26.4 -JUNE 28,1968 a 2.20 0.24 a 2.05 0.16


a-267.20l *-25.8 *
-26.0 -26 -2

-26.2 JULY 16, 1969 a" -6 -26.2 = 1.34+0.03 LL -26.4 22 0 L
S -26.4 JULY16,1969

U 1.200.11 AUG 19, 1969 -26.0 S= 2.100.08 2.0

-26.2- -25.4 -26.2
.x AUG 19, 1969
-26.4 AUG 18, 1969 -25.6 -26.4 a = 1.57 0.13 a 0.82 _0.11
-25.8

-260 -20 -26.0
-26.o -26.0 *," ..

APRIL I, 1970 DEC 5, 1969 0e -26.2 DEC 5, 1969 *
-26.2
a 0.750.07 -26.2 Q=1.77+0.04 '** .03 0.08*

-26.4 H MgI CV -264 Mg CIII 14.8 15.0 15.0 15.2 14.8 15.0 15.2 log vo


Figure 13. 3C 345, 3C 446, 3C 454.3. Continuum measurements of thie optical flux ploLted against: rest frequlecy v, = v(+.-Fz) for different days, indicating change of power Iaw index. Straight lines represent least sqllares fits for all. continuum points. Circled points represent emiss ion ]ines. Reproduc ed from Visvanathan (1973a) with permtssion of Lhe author and 'he As.trophysi ea. Joul, which- is pub].ishd by thle University of Chicango Press.






53


immediately associated with them, whose character or nature changes with time.

Kinman (1975) argues that in the case of the Lacertids, variations of the optical spectral index do not merely consist of changes in the slope of a power law relation, but also consist of variable curvature in the energy distribution. However, observations by Rieke and Kinman (1974) and by Smith et al. (1975) indicate that the UBV color of OJ 287 remained constant during a long-term decline of three magnitudes in its mean brightness, with short-term changes in the color which have not yet shown any relationship to the short-term changes in brightness. In addition, the observations of Smith et al. contain some evidence for a slower rate of decline in the infrared, in contradiction to the 10.5-1 observations of Rieke and Kinman. However, Kinman (1975) states that the spectral index becomes flatter towards the infrared.

All classes of extragalactic variables, especially the Lacertids, exhibit significant linear optical polarization (Kinman et al. 1974); in addition, 3C 279, 3C 345, 3C 446, 3C 454.3 and BL Lac have shown changes in the polarization position angle during bursts as compared with the position angles before and after activity. This has been interpreted as an indication that changes in the magnetic field configuration of the region emitting the continuum is a characteristic feature of the burst phase of these sources (Visvanathan 1973a). Moreover, observations of both radio and optical polarization in 3C 345 and 3C 454.3, for 2 and 1 years respectively, indicated agreement in the measured position angles in 3C 345, but disagreement in 3C 454.3. In the case of 3C 345, this can be interpreted to mean the optical and radio emission came from the same region. This is vital information if





54



one is trying to correlate activity at different wavelengths from a multiple-component source. In the case of 3C 454.3, one interpretation is that the radio and optical continua originate from different volumes of space, but this may come about in two different ways. If a correlation exists between optical and radio observations, a single source may emit the optical radiation observed at time tI, then undergo an expansion and a change in magnetic field configuration before emitting the radio radiation observed at time t1 + At. On the other hand, the optical and radio emission may arise from two different, spatially separated sources.

The non-thermal character of the optical continuum emission from extragalactic variables appears generally accepted. The observations of apparent power law spectra at optical wavelengths, rapid variability, and linear polarization which appears to be independent of wavelength, leads to a conclusion by many that the optical continuum has a synchrotron origin. Inverse Compton scattering has also been suggested, but the lack of detection of an X-ray flux from almost all these sources sets an upper limit to the X-ray flux which is apparently incompatible with the X-ray flux expected form inverse Compton scattering. FurtherO
more, 3500 to 8000 A observations of 3C 345, 3C 446, 3C 454.3, and BL Lac between 1968 and 1969 again indicated that both the degree of polarization and the position angle were independent of wavelength. This strongly suggests that the same mechanism is responsible for the continuum radiation in these sources from ultraviolet to infrared wavelengths.





55




Galactic Infrared Radiation

Infrared astronomy is still in an early stage of development because the atmosphere restricts ground-based observations to roughly the

1 to 20 i range. Observations at longer wavelengths are made from balloons, aircraft, rockets, and high altitude observatories. As previously noted, extragalactic variables in general show as infrared excess and, as shown in Figure 1, some emit the majority of their luminosity in the infrared. Attempts to explain this radiation must be based on what we have learned about sources of infrared radiation in our own and in other galaxies. Figure 14, while dated (Low and Aumann 1970), gives a summation of the infrared observations of the H II regions Orion A and M 17, the galaxy M82, and the galactic nucleus Sagitarius A. More recent data from Telesco et al. (1976) has been included for the Seyfert galaxy NGC 1068. Again dashed lines connect known measurements at the time of publication.

A significant amount of the infrared radiation in our galaxy is

thermal radiation from dust particles or grains, which both scatter and absorb incident radiation. Absorption of starlight from 3000 to 10,000 A increases with increasing frequency, causing an extinction or "reddening" as illustrated in Figure 15 (Greenberg 1968). The absorbed radiation heats the grains, thus redistributing higher frequency radiation into the infrared.

An infrared excess refers to an amount of radiation within a given infrared radiation interval which is in excess of what would normally be expected from the type of source observed. Such excess infrared radiation in our galaxy arises from H II regions, some hot Be and Of stars,


































Figure 14. Spectral energy distributions of galactic and extragalactic sources. Dashed lines indicate a lack of data for that wavelength interval. Upper limits are indicated for M82 at 70 y and Sgr IRA at 1000 p. Reproduced from Low and Aumann (1970) with permission of the authors and The Astrophysical Journal, which is published by the University of Chicago Press. More recent data obtained from Telesco et al. (1976) and Rieke and Low (1975) were used to plot the curve for NGC 1068.





57




6 3cm 3mm 300,u 30p 3.
T-"

Sgr IRA
5

iti 4i / I I


3 M 17 / .M 17
OR 10N A / \-RA
i \ \ AND IRB
2 ll x Sgr A Sgr IRA



1
M 82

M 82


0 /NG 1068 NGC 10681

10 11 12 13 14
LOG FREQUENCY (Hz)




58














1.0 0.5 0.33 1.5-
E
z 1.0
-

w I V B IU
0 1 I 1 1 1
0 1 2 3
-1 -1





Figure 15. Schematic diagram illustrating extinction or "reddening" as a function of frequency and wavelength.





59



protostars which are believed to exist in dense gas and dust regions, circumstellar grains surrounding stars, and the galactic nucleus, which is a highly luminous infrared source whatever its nature is.

Observations indicate that a significant fraction of both interstellar and circumstellar grains are silicate particles similar to material returned from the moon, thus indicating a possible relationship between the material found in galactic interstellar space and that from which the bodies of the solar system may have formed. In addition, infrared observations of early hot stars can be interpreted as arising from free-free emission of ionized hydrogen; observations of planetary nebulae may indicate that grains can condense in high velocity fields within destructive ultraviolet radiation fields, that is in almost any environment where the grain temperature is maintained below its evaporation temperature; and limited observations of novae indicate that material ejected during stellar mass loss can condense into dust particles (Stein 1975, and Neugebauer et al. 1971). Furthermore, infrared observations of H II regions have provided evidence that grains can exist in ionized regions and that the emission can arise from grains at different temperatures (Wynn-Williams and Becklin 1974).

The galactic nucleus is complex but can be represented by three main components defined by their spatial and wavelength distributions as follows: an extended source measured over a 1 region and observed
O O
between 1 and 5 p; a 2 x 4 source which has fine structure and is found at 100 1; a 15" source coincident with the non-thermal radio source Sgr A. The galactic center up to 100 has an estimated infrared luminosity of 109 La, which is much less than the infrared emission from extragalactic variables. Most of the 1 to 5 p emission is believed to





60



be stellar radiation, altered by about 30 magnitudes of visual absorption, from a high spatial density of stars. Observations of the nucleus of M31 show similar characteristics. The origin of the 100-p flux is unknown, although a significant portion again may be thermal re-radiation of starlight. Of most interest here is the 15" (%0.7 pc) source which radiates between 3 and 20 V with an energy distribution that can be approximated by a power law of slope a = -2. Thus it resembles the spectra of the nuclei of several extragalactic variables and leads to obvious speculation about similar physical processes involved. The radiation from this source could be due to a reasonably sized dust cloud of mass > 3 x 103 Me surrounding a concentration of stars or some other source of energy. It might also be non-thermal but this is unclear for a number of reasons. While the 15" source is coincident with Sgr A, the non-thermal radio emission from the latter comes from an area five times the diameter of the infrared source. In addition, the flux density at 20 p is ten times greater than the radio emission at 2 cm, which is in disagreement with the characteristic spectral energy distribution of a non-thermal radio source (Neugebauer et al. 1971). However, there may be two different energy sources, or one might try to construct a model for opacity at infrared wavelengths. In addition, approximately 102 identical sources of Bmin 30 gauss and radius 1012 cm could emit the observed flux. The existence of multiple small sources may not be unreasonable considering the strong evidence of almost continuous activity in some galactic nuclei.





61




Extragalactic Infrared Radiation

Estimates of the infrared luminosities from extragalactic variables are tentative to unreliable because of the lack of observations between 50 to 300 P. However, extragalactic variables are characterized by infrared luminosities of 1010 to 1011 LO (Neugebauer et al. 1971 and Telesco et al. 1976) and total Seyfert emission in the infrared may be
44 47
as high as 10 to 10 ergs/sec (Rees et al. 1969). In addition, a sample of infrared spectra from Seyfert nuclei indicates that they can be characterized by a power law of index a = -1.5 to -2.0. In this wavelength range, NGC 1068 may have a more negative power law index, and a correspondingly steeper spectrum. In particular, between 28 and 320 y', NGC 1068 has a luminosity equal to 3.7 x 10 L It should be noted that while some members of the specific class of compact galaxies (as distinct from the general class of EGV) have infrared excesses similar to Seyfert galaxies, others do not show any conspicious infrared excess. A sample of 30 QSO's show spectra that can generally be characterized by indices of a = -0.2 to -1.6 from 0.32 to 2.2 p, although some clearly show curvature. Stein (1975) observes that the infrared spectra of OJ 287 and BL Lac are generally flatter (a '\ -1) than the infrared spectrum of sources such as NGC 1068 (a s -2), and he then speculates that some sources may emit both thermal and non-thermal infrared radiation. Not all Lacertids have been detected or even observed in the near-infrared.

Variations of the 2.2-n infrared flux on a time scale comparable to the measured optical variations have been observed for 3C 279, 3C 345, 3C 446, and 3C 454.3, which are among those sources having the steepest





62



rise in their energy distributions at infrared wavelengths and which exhibit short duration large amplitude optical variations (Oke et al. 1970). In addition, it is argued on the basis of the infrared and visual spectral distributions in Figure 12, that to within the limitations of simultaneous measurement, the infrared and visual variations follow one another. If this is true, it would indicate that for these sources the same mechanism is probably responsible for the production of radiation from the infrared to the ultraviolet.

Rieke (1972) and Kinman et al. (1974) have provided evidence for both long-term (years) and short-term (months) variations in OJ 287 between 2.2 and 10 j. Rieke contends that these short-term infrared variations correspond in extent and time with B-magnitude and millimeter observations made at the same time. Kinman et al. established a very strong correspondence in long-term activity over the same wavelength range. Rieke also observed possible evidence for infrared variations of BL Lac in the 2 to 20-p range but the data are sketchy. Significant short-term variability of BL Lac at 2.2 is believed to exist (Neugebauer et al. 1971).

No satisfactory explanation of the infrared emission from extragalactic sources has yet been found. Thus far, observations of some sources provide evidence that both thermal and non-thermal radiation is present. Neugebauer et al. have observed that knowledge of the energy distribution between 20 and 500 V is critical to any investigation of the radiation mechanism. While any discussion of detailed models is probably premature until that data is available, I will briefly review the speculations.

Of course there are two possible radiation mechanisms; thermal





63



re-radiation by dust grains and non-thermal radiation by incoherent synchrotron or inverse Compton scattering. It is generally agreed that very short-term (less than a few weeks) variability of the infrared radiation or significant as well as variable infrared polarization would imply a non-thermal source. However, to date there has not been conclusive evidence of either of these characteristics.

The proponents of thermal radiation argue that small grains may

condense during the expansion phase following a violent outburst and that the observed energy distribution is obtained by the superposition of several different blackbody curves corresponding to shells of dust at different distances from the source. As noted earlier, there is evidence for the existence of dust in or near Seyfert nuclei and quasars (Burbudge and Stein 1970). While the amount of dust required for such emission appears physically reasonable, its required size does place lower limits of a few weeks to a month on the allowed time scale of variations at wavelengths a 10 v. Variations on a shorter time scale have not yet been conclusively established. The discovery of slight polarization could be explained by emission from magnetically aligned grains.

The proponents of a non-thermal mechanism argue that while there is evidence of dust near active sources, it is too far removed and of too little quantity to cause the observed infrared flux. The main difficulties in the case for non-thermal emission are the need for a sharp cutoff at low frequencies and the condition that inverse Compton scattering losses not exceed synchrotron losses. Burbidge and Stein (1970) conclude that the energetics of a synchrotron model are physically reasonable because total required energies are less than those required to explain the compact radio sources or to explain non-thermal optical radiation,





64



but require magnetic fields of '1 1 to 100 gauss. They also point out that in some cases, the data support the hypothesis of nuclei consisting of a large number of separate components. Cavaliere et al. (1970) propose a model which emits both synchrotron and inverse Compton radiation.

During the writing of this summary of research efforts, I was struck by the analogy to an earlier attempt to explain a troublesome spectrum, that of the blackbody. If we can explain the spectrum, most likely we can explain the source. However, we must first have the whole spectrum!
















CHAPTER III
ANALYSIS OF THE LONG-TERM OPTICAL AND RADIO RECORDS


The Research Problem

Up to ten years of observations of the sometimes violent optical and radio variations of extragalactic variables have compelled many to ask the potentially important question, Are the optical and radio variations for a given source correlated? The gap in the observable spectrum between millimeter radio radiation and optical radiation makes it impossible to follow an event through the intervening spectral range and necessitates attempts to correlate radio and optical variability before one can test a model against data taken at these separated wavelengths. If a relationship exists, then what are its characteristics and its implications with respect to the emission mechanisms just summarized? At the same time, if no relationship exists, what are the implications? As I have indicated by the summaries in Chapter II, the answers to these questions are very important for defining the radiation mechanisms and modeling the source of radiation. In addition, such information is necessary for the planning of cooperative multi-wavelength observing programs. For the first time, collections of observations are reaching the point where meaningful investigations of such correlations on a time scale of many years can be made.

A visual inspection of the optical, millimeter, and centimeter data for a few extragalactic variables reveals variations that are comparable




65





66



in time and, in some cases, amplitude. This is both promising and hazardous, because one must be careful to avoid chance correlations between random events that are not really related. Most searches for correlations have examined the short-term variations of 3C 120 (Usher 1972), OJ 287 and BL Lac (Kinman and Conklin 1971; Andrew et al. 1971; Epstein et al. 1972; Andrew et al. 1974; Kinman et al. 1974; Miller et al. 1974) and the long-term activity of BL Lac (Hackney et al. 1972), and OJ 287 (Lyutyi 1973).



The Radio and Optical Data Records

The Rosemary Hill Observatory of the University of Florida, the

Algonquin Radio Observatory, the University of Massachusetts, the Royal Greenwich Observatory, and the Yale University Observatory have monitored extragalactic variables at radio or optical wavelengths for a number of years. The present study examines these long-term records in an attempt to discover correlated activity for sources common to the monitoring programs. It makes use of Rosemary Hill blue or photographic magnitudes (McGimsey et al. 1975; Scott et al. 1976), Algonquin 2.8-cm (10.7 GHz) data (Medd et al. 1972; MacLeod et al. 1975), University of Massachusetts

1.9-cm (15.5 GHz) data (Dent et al. 1974; Dent 1976), Royal Greenwich Observatory optical magnitudes (Tritton and Brett 1970; Cannon et al. 1971; Tritton and Selmes 1971; Selmes et al. 1975), and Yale Observatory photographic magnitudes (Lu 1972). In addition, blue magnitudes from the Goethe Link Observatory were used for 3C 273 (Burkhead and Parvey 1968; Burkhead 1969; Burkhead and Lee 1970; Burkhead and Stein 1971; Burkhead and Rettig 1972; Burkhead and Hill 1975).





67



For the first time, the extensive records from the above observatories have been integrated and presented together in figures accompanying the textual presentation for each source. Thus, these figures represent a relatively complete documentation of the available observed long-term radio and optical variations (or lack thereof). The raw data have been plotted with one-rms error bars. In several cases, data from different observatories were combined to obtain a longer data record. I acknowledge that this is a potentially hazardous procedure for any quantitative analysis for three reasons. First, different optical observatories may use different comparison sequences; and while Rosemary Hill B magnitudes are filtered (GG-13) exposures taken with a reflector, Royal Greenwich B-magnitude plates are unfiltered exposures taken with a refractor. Second, there is often a time delay and an amplitude difference between the Dent 1.9-cm data and the Algonquin 2.8-cm data, as one might expect from the expanding source model. Third, the calibration of the absolute flux density scale may differ between two radio observatories.

However, for visual presentation of long-term trends in the data, the effects of the second factor are generally negligible. To minimize the effects of all three factors, in most cases where different sets of data were combined to form a single radio or light curve there was sufficient overlap between the sets to establish that the variability information was essentially identical for both sets (to within less than one rms error) and to measure the zero-point offset between the two sets if such an offset existed. The empirically determined offset was then applied to the shorter of the two sets to create a consistent long-term record.





68




Cross-Correlation Analysis

The long-term optical and radio data records have been examined visually with great care to search for evidence of correlation. This was accomplished by plotting the two data records on different sheets, literally laying one curve on top of the other, and sliding one with respect to the other in search of coincidences between the two records. Then, as a first attempt to search analytically for correlations, the optical magnitudes and radio fluxes were linearly cross-correlated. Unfortunately, long-term astronomical measurements are almost invariably spaced unevenly in time because of the monthly and annual cycles imposed by the moon and the sun, with additional interruptions being created by equipment failure, weather, and scheduling.

Because of the mathematical difficulties associated with treating

unevenly spaced time series, it is common practice to fit a curve to the data, thus creating a continuous function which can be used directly or sampled evenly for analytical study. However, this requires the choice of a fitting function, thus introducing a certain bias into the data. This is particularly important in studies of rapid, large-amplitude, random variables where two or more outbursts may be superimposed, the character of each individual outburst is not known, and the data lost in observation gaps are unpredictable.

For these reasons, in an attempt to avoid biasing the raw data, I chose to synthesize evenly spaced time series by stepping through the radio and optical data records for a given source by an increment of time Atl, averaging all data falling within that increment, and either linearly interpolating or leaving a "hole" for those time increments in





69



which no data were taken. Next the total record of radio data was shifted backwards in time relative to the optical by an amount At2' The radio record was then moved forward in time by steps of At3, (At3 & At) while a normalized linear cross-correlation coefficient, R, was calculated for all overlapping data for each increment of At3. For any value of the time shift At (At = nAt3 At2), coincidences between radio data and optical holes, or vice versa, were not used in the calculation of the correlation coefficient. This procedure was followed until the radio data had undergone a total time shift of 2At2.

For this study, the following formula. was used to calculate the normalized cross-correlation coefficient, R, for each value of At,




Z (xiYi) (Ex ) (Ey i)
R(At) = 1 y (32)
2 1 2 2 1 2 1/2 i N ( x i) I [Eyi N (Eyi)21/2



where x and y are functions of time and N is the number of coincidences between radio and optical data increments. This can be shown to be exactly equivalent to the more classical formula for R (Harnett 1970), E (xi x) (yi y)
R = 11(33) 1/2
2 2
[E(xi x) E(yi y) ]


by the use of the following identity:



E(xi ) = (xl x) + (x2 x) + ... (xN x)


= (Exi) Nx (34)





70



The technique just outlined has a number of characteristics that should be noted.

a) The original optical and radio data records resulted from

irregularly sampling two continuous functions of time. The correlation coefficients are calculated for synthesized, evenly spaced

time series which are assumed to represent the long-term functions

of time.

b) Observational errors are not considered in the calculation of

the time averages or the correlation coefficients.

c) The calculated correlation coefficients are partly a function

of the choice of At, which is itself dependent on the time resolution of the data and the time scale of the observed activity.

d) Attempts to correlate too small a data sample result in spurious coefficients which, when plotted as a function of At, form a scatter

diagram. When this occurs for the overlap of the beginning of one

data set with the end of the other set it is referred to as an

"edge effect".

e) When each of the two records has only a singly significant peak

or "bump", the records will be strongly correlated for some value

of At even though there may be no physical relation between the two

events. Great caution must be exercised in the consideration of

such "one-event" correlations.

f) Because I am cross-correlating unevenly space time series and

examining a population of cross-correlation coefficients, the

classical test of significance is at best questionable and at worst

simply not applicable. It is included in Table 4 only for lack of a better statistical method, and it should be used in conjunction





71


with a careful and skeptical examination of the data records

themselves.

g) The precision of At is limited by the choice of Atl'

h) The statistical technique used, equation (32), calculates a

normalized linear cross-correlation coefficient between two

functions which are represented by time series; however, radio flux

is linearly proportional to the emitted energy while an optical

magnitude is proportional to the log of the emitted energy. Thus

strictly speaking this technique measures the relation between

emitted radio energy and the log of the emitted optical energy as

a function of time shift At. This was done because of the

following:

1) Most investigations involving optical data are both conducted and published using a magnitude scale to represent the

data.

2) Presentation of the optical and radio data on the same

graph in a form that is easy to examine necessitated the use

of both radio flux and optical magnitudes.

When a potentially significant cross-correlation was found, a

regression plot of radio flux vs optical magnitude was made to illustrate and investigate the functional relationship between the two sets of data. The regression plots were obtained by shifting the synthesized time series by the value of At that gave the maximum correlation coefficient.

It is difficult to justify the use of linear interpolation to fill observational gaps in the data records because we have no knowledge of the emission intensity during that gap. Thus the interpolated data





72



records must be used cautiously, and the validity of results from the interpolated data records must be examined for each source independently. In general, for any given source the hole technique and the interpolation technique yielded similar results. Thus, because the hole technique more nearly approximates the original record, the results of this technique alone are summarized in Table 4 (Chapter IV).



Choice of Correlation Parameters

As noted previously, the value of the correlation coefficient and its distribution as a function of At do depend on AtI, which is determined by the character of both the optical and radio data records. Thus a trial and error method of using different values for AtI and At3 was employed to find the "best" values.

Obviously it makes no sense to use a At3 smaller than Atl because this oversamples the resolution of the data introduced by Atl. However, ome might use a At3 larger than At1 to accentuate long-term effects when working with high time resolution data sets. In general At3 should equal Atl. The choice of At2 of course depends on the relative coverage of the optical and radio data records.' If correlation coefficients are calculated when the extent of the overlap between the optical and radio data is less than 10%, and in some cases 20%, of either the entire optical record or the entire radio record, then edge effects or spurious "one-event" correlations arise. Therefore At2 was usually chosen to calculate the correlation coefficient for all overlaps involving more than 10 to 20% of the whole of both data records.

The choice of the "best" values for At1 and At3 was of course a subjective judgement based roughly on the following criteria.





73



For the cross-correlation calculation, a) What was the smallest value of At1 for which R vs At remained a smoothly varying function? b) Secondarily, what was the value of At1 that yielded the maximum correlation coefficient? For the regression plots, a value of At was chosen which yielded a "sufficient" number of points to suggest a possible relationship.

In the following presentation of the results, graphical summaries of R vs At for more than one value of At1 are sometimes presented to illustrate the effects of the choice of At.
















CHAPTER IV
RESULTS OF THE CORRELATION ANALYSIS


The results of the analytical study are summarized in Table 4, where column one gives the source name; column two the maximum cross-correlation coefficient, R, corresponding to the time shift At listed in column three; column four lists the number N of increments in the synthesized time series that contained data and were used to calculate the maximum cross-correlation coefficient; and column five gives the confidence level for the maximum value of R calculated from the two-tailed Student's t-distribution. In column two, an "NC" indicates the absence of any distinct maximum in the population of calculated cross-correlation coefficients; an asterisk indicates a "one-event" correlation, in which there is minimal confidence of physical reality. The error estimate in this column is a subjective figure derived from the fact that a number of coefficients for adjacent values of At have nearly the same value. In column three, a negative value for At indicates that the optical events lead the radio events, while a positive value indicates that the radio events precede the optical. The error estimate here is derived by estimating the half-amplitude width of the distribution of correlation coefficients about the maximum value.

In all the plots of R vs At that follow in this chapter, the top

curve illustrates the relation for the raw data or "hole technique" while the bottom curve illustrates the relation for interpolation across holes




74





75



TABLE 4

SUMMARY OF RESULTS OF THE LINEAR CROSS-CORRELATION ANALYSIS

Source R At in years N Confidence OJ 287 0.85+.02 -0.875+1.0 24 >99% OJ 287 Pt I 0.90+.03 -0.60+0.85 13 >99% OJ 287 Pt II 0.92+.04 0.0+0.70 15 >99% 3C 454.3 0.79+.01 -1.2+1.2 31 >99% BL Lac NC(?) -0.5 (?) CTA 26 0.82+.08* -1.1+0.9 16 >99% PKS 0405-12 NC PKS 0420-01 0.65+.10* -0.2+0.8 16 >98% 3C 120 NC NRAO 190 NC PKS 0458-02 NC 3C 138 NC PKS 0735+17 0.71+.02* +0.88+0.9 13 >99% PKS 0736+01 NC OI 363 NC OK 290 NC 3C 273 NC PKS 1354+19 NC OQ 208 NC 1510-08 NC NRAO 512 0.66+0.1* 0.0+0.3 27 >99% 3C 371 0.55+0.1 0.5+0.8 29 >99% 3C 446 NC PKS 2345-16 NC





76



in the raw data. Except for this difference, all parameters used in obtaining the top and bottom curves are identical. While both curves are included for completeness, all quoted values of R and At refer to the top curve unless explicitly stated otherwise.



OJ 287

This object provided the best visual correlation of all the sources studied in this work, a result that was strongly reinforced by the analytical study. Despite gaps in the optical record, there is a strong suggestion that the optical and radio curves shown in Figure 16 follow each other quite closely through a number of distinct details defined by each record; and in fact, there is no question that both records show a long-term rise and fall from 1970.0 to 1974.0 and a short-term burst centered at about 1975.0. Despite violent short-term optical flickering this visual correlation is supported both by the cross-correlation coefficient of 0.85 indicated in Figure 17, and by the relationship between radio flux and optical magnitude revealed in Figure 18. (The anticorrelations occuring in Figure 17, for large positive and negative values of At result naturally from the superposition of the ascending radio curve on the descending optical curve and vice versa.)

Close examination of the data shows that after the gap in both

records at 1972.75, there is more complete optical coverage and a different separation between the optical and radio curves than before that date, implying that some shift in the relationship may have occurred. This perception suggested a separation of the data into two segments, Part I containing the data prior 1972.75 and Part II containing the data after 1972.75. While the application of the cross-correlation technique















13.0

OPTICAL

uJ 14.0
t
I-
z
<+ I 5.0 -t 12.0 t

16.0 + 9.0







t + + + + + 3.0



1970.0 71.0 72.0 73.0 74.0 75.0 0.0 DATE




Figure 16. OJ 2817. Rosemary Hill optical and Algonquin 2.8-cm observe :iions. Rosemary iill points aftLer mi d-1971 are B inagnitludes; earl] icr points are phloLogralphic (i ) lmagnlituicldes corrected to ma lgnllltllides.,






78








1.0
0*
**" OJ 287


0.5




R 0.0

.
50



-0.5 .
*. ..

sOo

-1.0

1.0
09*



0.5




R 0.0




-0.5 *"

*
0 *

-1.0

-4.0 -2.0 0.0 2.0 4.0
At (years)
Figure 17. OJ 287. Normalized cross-correlation coefficient (R) vs
time shift (At) for the radio and optical data presented in Figure 16,
using actual data (top) and interpolated data (bottom), with
t At3 0.125 year.






79









10.0

OJ 287
0
0
o 0


8.0 o.

0*
O *
-* *
0
* O O *
**O 00
6.0 oo
* o
X O *
o o* OO *

0000

4.0 o .. o


O




2.0







0.0
16.0 14.0 12.0

MAGNITUDE



Figure 18. OJ 287. Radio flux vs optical magnitude for It = -0.875 year, At 0.05 year. Open circles represent actual data; filled
circles represent points for which the flux or the magnitude, or both, have been obtained by linear interpolation across gaps in the data.





80



yielded R values of 0.90 and 0.92 for Parts I and II (Figures 19 and 20) respectively, the smaller number of data points used in the calculations combined with significant edge effects, cause one to view the results from Parts I and II with caution. In spite of these reservations, the regression plots of flux vs magnitude for Parts I and II shown in Figures 21 and 22 display considerably less scatter than Figure 18, tending to support the validity of the separation of the data at 1972.75. Moreover, the reader should not be misled by the apparently much broader peaks illustrated in Figures 19 and 20 relative to the peak in Figure 17; for Figure 17 has a compressed time scale on the x-axis.



3C 454.3

Although optical data from the Rosemary Hill, Yale, and Royal

Greenwich Observatories were used to study this source, the overlapping records reinforced one another when appropriate zero-level offsets were applied. The correspondence and mutual reinforcement are illustrated in Figure 23, where the three data records are displayed independently with no zero-level offsets. This reinforcement justifies the deletion of the Yale data record from Figure 24 where the density of Yale data points would have obscured the long-term optical trends.

Visual inspection of the radio and composite optical data illustrated in Figure 24 indicates that while there is not as obvious a correspondence between radio and optical activity as there is for OJ 287, the radio and optical records show comparable variations which may be correlated. Application of both the "hole" and the interpolation techniques, using all three optical data records, yielded maximum correlation coefficients of 0.79 and 0.83, respectively, for the optical leading the radio by






81












1.0

*.. . OJ 287
0.5
** 'e
F9. OJ cen R 0 0 ."



-0.5


-1.0 *. ..

1.0-


05




9.9





-1.0













0.05 year.






82













.* ...* .. OJ 287





-0.. .

-1.0
-0.5 .


0.0 I
-0.5







-1.0








-2.0 -10 0.0 1.0 2.0 1t (years)





Figure 20. OJ 287. Normalized cross-correlation coefficient (R)
vs time shift (At) for radio and optical data after 1972.75, using
actual data (top) and interpolated data (bottom), with
t1 = At3 = 0.05 year.
-0.






83










10.0


OJ 287




8.0





O *
0
0 0


0 0
*





*4.0
00












0.0.0
6.16.0 14.0 12.0













MAGNITUDE 0 0* *



4.0



0


2.0







16.0 14.0 12.0 MAGNITUDE



Figure 21. OJ 287. Radio flux vs optical magnitude prior to 1972.75 for it = -0.06 year, At1 = 0.05 year. Open circles represent actual
data; filled circles represent linearly interpolated data.






84












10.0


OJ 287
0
0


8.0 o
0






6.0 *

0x
0 0




.-1 O* O 0


*e
O@




2.0







0.0
16.0 14.0 12.0 MAGNITUDE


Figure 22. OJ 287. Radio flux vs optical magnitude after 1972.75 for At = 0.0 year, At1 = 0.05 year. Open circles represent actual
data; filled circles represent linearly interpolated data.




Full Text

PAGE 1

mj n-VBHTm SEARCH FOR CORRELATED RADIO AND OPTICAL EVENTS IN LONG-TERM STUDIES OF EXTRAGALACTIC SOURCES by RICIiARD BRYAJ^I POMPHREY A DISSERTATION PRESENTED TO THE GRADUATE COU'NCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLl-IENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY LTn^IVERSITY of FLORIDA 1977

PAGE 2

< Jwj .^i^jm ^ *i^g f H^ 't i^ ACKNOWLEDGEMENTS I wish to express my appreciation to my committee chairman, Dr. A. G. Sm.ith, not only for his assistance, but in particular for his support and direction when the future was uncertain; to my committee co-chairman, Dr, C. N. Olsson, for being a true friend who said things that needed to be said, and for his support and advice through both favorable and adverse situations. I also wish to thank Drs. T. L. Bailey, G. R. Lebo, and S. T. Gottesman for their assistance and contributions to my research experience. The study documented in this dissertation makes use of data from many observatories. I am indebted to Drs. J. M. MacLeod, G. A. Har'/ey, and B, H. Andrew of the Algonquin Radio Observatory, and to Drs. K. ?, Tritton, M, V. Penston, and R. A. Selmes of the Royal Greenwich Observatory for permitting me to make extensive use of their previously unpublished data. The Rosemary Hill observations were made by Drs. A. G. Smith, G. H. Folsom, K, R. Hackney, R. L. Hackney, R. J. Leacock, B. Q. McGimsey, and R. L. Scott, and by J T. Pollock and Patricia Edwards. In addition Dr. J. D. G. Rather graciously made his data bank available while it was still in preparation. Much of the initial analysis was supported by a Research Corporation grant and was carried out at the Electronics Research Laboratory of The Aerospace Corporation. Ifnile there I received the generous assistance of )\ manv of the staff to whom I am grateful: G. G. Berry, H. Dyson, I .;ii X

PAGE 3

z^\ 'f*' m>t ^^ f' ir'j _.j ^oiss^!!^jfnvmtirril^mit%t=m^f}^*m': n ttmt fi^ Dr. E. E. Epstein, W. A. Johnson, H. E. King, J. W. Montgomer}-, T. T. Mori, Dr. J. Mottmann, now at the California Polytechnic Institute at San Luis Obispo, Ms. J. D. White, and Dr. W. J. Wilson, now at the Uhiverity of Texas at Austin. In addition, Mrs. Suzanne Hansen typed much of the manuscript and J. Petersen assisted in the preparation of the illustrations During my graduate career, I have been supported by the Research Corporation grant, a University of Florida Graduate School research assistantship, a University of Florida teaching assistantship, part-time emplojTnent at The Aerospace Corporation, and full-time employment at the Jet Propulsion Laboratory. I am grateful to D. J. Lynn, R. M. Ruiz, and Dr. D. A. Elliott of JPL for their support, patience, and understanding while I was finishing this work. The analysis was also aided by funds from the Northeast Regional Data Center of the State University System of Florida. I also wish to thank Dr. W. G. Fogarty of Universidade Mackenzie, Dr. J. T. McClave of the Department of Statistics and Dr. M. A. Lynch of the Department of Physics and Astronomy, University of Florida, for helpful discussions; and W. W. Richardson and H. W. Schrader of the University of Florida for extensive technical assistance. Annual Reviews of Astronomy and Astrophysics, Springer-Verlag New York, Reviews of Modern Physics, The Astronomical Journal and The Astrophysical Journal generously granted permission to reproduce illustrations from their publications. The Astrophysical Journal required that the identical copyright notice as it appears in the Journal be included in the manuscript. This copyright notice follows: Xll

PAGE 4

H-^ vi .V I* iKJi jr.:. "* ^ '** '' > ^ So that the author and publisher may be protected from the consequences of unauthorized use of the contents of the manuscript, we consider it essential to secure a copyright. Therefore, it is mutually agreed that upon the acceptance of the submitted manuscript for publication by this Journal the author grants and assigns exclusively to the American Astronomical Society for its use any and all rights of whatsoever kind or nature now or hereafter protected by the Copyright Laws (common or statutory) of the United States and all foreign countries in all languages, including all subsidiary rights. The American Astronomical Society, in turn, grants to the author the right of republication without charge in any book or periodical of which he is an author, contributing author, or editor, subject only to his giving proper credit in the book or periodical to the original Journal publication of the paper by The University of Chicago Press for the American A.stronomical Society. I am indebted to many friends for their help throughout my graduate work. The assistance and companionship of Dr. James R. Kennedy and Jack G. Schudel, III were invaluable in the completion of a major portion of this work. Long discussions with Jim Kennedy helped formulate the direction I have taken in this research; the subroutine PPLOT which appears in the Appendix is his, while the subroutine CORREL incorporates many of his ideas. Jack Schudel assisted significantly in the computations and a number of the illustrations. I also wish to thank Dr. Carl Olsson's family, John Young, Eric Van Horn, Al and Isa Adams, Jim and Jerry Hatch, and Jim and Barb Thieman for their help, support, and friendship. There are some individuals who have had a significant influence on my attitudes and my work during my graduate career. I wish to express my sincere gratitude to Ray and Andy Bloomer, Kit Harvel, Jim and Cathy Kennedy, and Joe and Liz Mullen not only for their support and direction, but also for helping me learn hoxj to play the game. In addition I wish to gratefully acknowledge my brother and his family, and the countless relatives and friends of my family who, IV

PAGE 5

^*^^ iy-.^ B e "f< ^ ^ ^|| i ^ ^i r^ ^tK-^ while not able to assist me directly, expressed their concern and support verbally and in prayer. Finally, I dedicate this work to Dr. George Horvat and to my parents for their prayers and support, both that which I am aware of and that which I have not even recognized. V

PAGE 6

•**~ "T ^ 'W ^'' ^ "' — ^ *^ "-J-i^ ** ^ *M > .J3^TO s ff '^ jm w wi ?r li.,c TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ii LIST OF TABLES ix LIST OF FIGURES x ABSTRACT xiv CHAPTER I INTRODUCTION 1 Extragalactic Variables 3 State of Our Knowledge 5 II THEORY APPLIED TO SPECTRAL ENERGY DISTRIBUTIONS 10 Spectral Energy Distributions 10 Radio Frequency Spectra 12 Radiation From a Single Electron 14 Radiation From a Distribution of Electrons 18 Time Variations 23 Expanding Source Model 24 Expanding Source Model Difficulties and Alternatives 27 Inverse Compton Scattering 29 Optical Spectra 36 Galactic Infrared Radiation 55 Extragalactic Infrared Radiation ..... 61 VI

PAGE 7

> :-m' -JW wT UP W L. —^*— Pf^^MLf *< jlt ^ i n pn >y: Page III ANALYSIS OF THE LONG-TERM OPTICAL AJSID RADIO RECORDS. 65 The Research Problem 65 The Radio and Optical Data Records .... 66 Cross-Correlation Analysis 68 Choice of Correlation Parameters 72 IV RESULTS OF THE CORRELATION ANALYSIS 74 OJ 287 76 3G 454.3 80 BL Lac 98 CTA 26 (PKS 0336-01) 102 PKS 0405-12 102 PKS 0420-01 108 3C 120 108 NRAO 190 (PKS 0440-00) 118 PKS 0458-02 118 3C 138 (PKS 0518+16) 124 PKS 0735+17 128 PKS 0736+01 135 01 363 135 OK 290 143 3C 273 147 PKS 1354+19 153 Oq 208 161 PKS 1510-08 161 NRAO 512 161 VI 1

PAGE 8

"I — Mj yT mij. ii p^y'*Wi i*-*J?JSLiB"'*: •
PAGE 9

•z*>i'vr w mi^'m -n^i
PAGE 10

ptn'^i.-mf^ a ^* -i-wm ?' "iiijhi, L^u i j ,j. LIST OF FIGURES Figure Page 1 Spectral Energy Distributions for Five Quasi-Stellar Objects and the Seyfert Galaxy NGC 1068 .... 11 2 Four Classes of Radio Frequency Spectra .... 13 3 Synchrotron Spectrum from a Single Electron as a Function ofx = v/v 16 c 4 Expected Synchrotron and Inverse Compton Spectra for the Galactic Halo 34 5 30 120. Optical and Near-Infrared Spectrum ... 38 6 3L Lac. Optical and Near-Infrared Spectrum ... 40 7 OJ 287. Optical Spectrum 41 8 OJ 28 7. Optical and Near-Infrared Spectrum Extrapolated to Short Radio Wavelengths .... 43 9 BL Lac. Changes in Optical and Near-Infrared Spectrum with Time 45 10 Selected Quasars. Optical and Near-Infrared Spectra 47 11 Selected Quasars. Optical and Near-Infrared Spectra 49 12 Selected Quasars. Optical and Near-Infrared Spectra 51 13 3C 345, 3C 446, 3C 454.3. Changes in Optical Spectral Index with Time 52 14 Spectral Energy Distributions Showing Known Infrared Components 57 15 Schematic Extinction Curve 58 16 OJ 287. Optical and Radio Curves 7 7 17 OJ 287. R vs At for all Data 78 18 OJ 287. Radio Flux vs Optical Magnitude .... 79 s

PAGE 11

• wii TB i^ > w^i I aj i ^M j M Wtr3^.-^nua i _jtj^ J_ K tl tjE ^^ Figure Page 19 OJ 287, Part I. R vs At 81 20 OJ 287, Part II. R vs At 82 21 OJ 287, Part I. Radio Flux vs Optical Magnitude. 83 22 OJ 287, Part II. Radio Flux vs Optical Magnitude 84 23 3C 454.3. Three Independent Optical Data Records 86 24 3C 454.3. Optical and Radio Curves 88 25 3C 454.3. R vs At for all Data 90 26 3C 454.3. R vs At for Part of Optical Data ... 91 27 3C 454.3. Radio Flux vs Optical Magnitude. ... 92 28 3C 454.3. Radio Flux vs Optical Magnitude. ... 93 29 3C 454.3. R vs At for Part of Radio Data .... 95 30 3C 454.3. Tim Independent Radio Data Records. 96 31 3C 454.3. R vs At for I\vo Radio Records .... 97 32 BL Lac. Optical and Radio Curves 99 33 BL Lac. R vs At for all Data • 100 34 BL Lac. R vs At for all Data 101 35 CTA 26. Optical and Radio Curves 103 36 CTA 26. R vs At for all Data 104 37 CTA 26. Radio Flux vs Optical Magnitude .... 105 38 CTA 26, Radio Flux vs Optical Magnitude .... 106 39 PKS 0405-12. Optical and Radio Curves 107 40 PKS 0405-12. R vs At for all Data 109 41 PKS 0420-01. Optical and Radio Curves Ill 42 PKS 0420-01. R vs At for Part of Radio Data ... 112 43 PKS 0420-01, R vs At for all Data 113 44 3C 120. Optical and Radio Curves 115 XI

PAGE 12

"' <| Wit t t\ j > j,^t^ mr%miigo^ -^t-mw^.thbi hl fiu^ Figure Page 45 3C 120. R vs At for all Data 117 A6 NRAO 190. Optical and Radio Curves .' 119 47 NRAO 190. R vs At for Part of Radio Data .... 120 48 NRAO 190. R vs At for all Data 121 49 PKS 0458-02. Optical and Radio Curves 122 50 PKS 0458-02. R vs At for all Data 123 51 3C IBS. Optical and Radio Curves 125 52 3C 138. R vs At for all Data 127 53 PKS 0735+17. l\-70 Independent Radio Data Records. 129 54 PKS 0735+17. R vs At for Two Radio Records ... 130 55 PKS 0735+17. Optical and Radio Curves 131 56 PKS 0735+17. R vs At for Part of Radio Data ... 132 57 PKS 0735+17. R vs At for Part of Radio Data ... 133 58 PKS 0735+17. R vs At for all Data 134 59 PKS 0735+17. Radio Flux vs Optical Magnitude. 136 60 PKS 0735+17. Radio Flux vs Optical Magnitude. 137 61 PKS 0736+01. Optical and Radio Curves 139 62 PKS 0736+01. R vs At for Part of Radio Data ... 140 63 PKS 0736+01. R vs At for all Data 141 64 01 363. Optical and Radio Curves 142 65 01 363. R vs At for all Data 144 66 OK 290. Optical and Radio Curves 145 67 OK 290. R vs At for all Data 146 68 3C 273. Two Independent Radio Data Records 148 69 3C 273. R vs At for Two Radio Records 150 70 3C 273. Optical and Radio Curves 152 XI J

PAGE 13

MJeJj^ ^u i iJWIJ-ftiJB sa Figure Page 71 3C 273. R vs At for Part of Radio Data 154 72 3C 273. R vs At for Part of Radio Data 155 73 3C 273. R vs At for all Data I57 74 PKS 1354+19. Optical and Radio Curves 158 75 PKS 1354+19. R vs At for all Data 160 76 OQ 208. Optical and Radio Curves 162 77 OQ 208. R vs At for all Data 163 78 PKS 1510-08. Optical and Radio Curves 164 79 PKS 1510-08. R vs At for all Data 165 80 NRAO 512, Optical and Radio Curves 167 81 NRAO 512. R vs At for all Data 170 82 NRAO 512. R vs At for Part of Optical Data 172 83 3C 371. Optical and Radio Cun/es 174 84 3C 371, R vs At for all Data I75 85 3C 446. Two Independent Radio Data P.ecords 177 86 3C 446. R vs At for Two Radio Records 179 87 3C 446. Optical and Radio Curves 181 88 3C 446. R vs At for all Data 182 89 PKS 2345-16. Optical and Radio Curves 133 90 PKS 2345-16. R vs At for all Data 185 91 Radio and Infrared Spectra of Selected Extragalactic Sources 193 92 Idealized Spectrum of an Extragalactic Variable 194 93 OJ 287. Monthly Mean Fluxes at Different Wavelengths 201 XI 11

PAGE 14

II II I I 'I I I II "I iir ii>'ii inriT 'm i ijftt ^Mww_^wy OPTICAL EVENTS IN LONG-TERM STUDIES OF EXTRAGALACTIC SOURCES By Richard Bryan Pomphrey March, 1977 Chairman: Dr. Alex G. Smith Major Department: Astronomy Much of the research on extragalactic variables has attempted to determine the radiation mechanisms that cause the observed spectral energy distributions. This knowledge in turn should help to define the source of energy in these variable objects. This work documents the first attempt to assemble the long-term records of optical and radio fluxes of a large sample of variable extragalactic sources in a search for correlated radio and optical events, using a linear cross-correlation analysis to reinforce visual comparisons. The results of such research may help to parameterize either the radiation mechanism involved or the source structure which can then be used in the study of the radiation mechanism. Chapter I presents the general background of this research topic, including the definitions of quasi-stellar objects, Seyfert galaxies, xiv

PAGE 15

-^ ^< ^.^-L I J^ IM W ^ U l h J^ Ji N galaxies, and Lacertids, and the similarities among these objects which are used as the justification for studying these objects as different manifestations of some common basic phenomenon. Soth Chapters I and II address Xvhat is presently known, hypothesized, or speculated about these variables Chapter II gives a brief but extensive overview of the theoretical considerations involved in research on variable extragalactic objects as a reference against which the results of the search for correlations can be studied. This chapter includes reviews of the character of the radio, infrared, and optical spectra, their changes with time and possible causes, with special emphasis on the synchrotron and inverse Compton mechanism.s and the expanding source model. A simple method of synthesizing evenly spaced time series by stepping through the data in given increments of time is discussed in Chapter III, along with the method used to linearly/ cross-correlate optical magnitudes with radio fluxes and the problems of this approach. A relatively complete documentation of the long-term optical and radio variations is presented graphicall:/ in Chapter IV, where optical data from the Rosemary Kill, Royal Greenwich, Yale, and Goethe Link Observatories has been combined with radio data from Algonquin Observatory and the University of Massachusetts. The results of the correlation analysis are presented through discussion and extensive linear correlation and regression plots, which document a significant correlation for OJ 287 and a potential correlation for 3C 454.3. The lack of correlation in most of the sources studied allows a decrease in the energy requirements of events in these sources and carries implications for the source structure, vjhich are discussed in Chapter V. XV

PAGE 16

The possible implications of the correlation for OJ 287 are reviewed, but no fir:n conclusions concerning source structure or radiation mechanism can be drawn without further data. Finally, extensions of the investigation begun in this work are suggested. A sunimary of the correlation analysis results is reported in a paper by R. B. Pomphrey, A. G. Smith, R. J. Leacock, C. N. Olsson, R. L. Scott, J. T, Pollock, Patricia Edwards, and W. A. Dent, "A Search for Correlated Radio and Optical Events in Long-Term Studies of Extragalactic Sources", in The Astronomical Journal 81, 489, (1976), XVI

PAGE 17

, r x i> .iiip ^ -j pi j .'wi Ti'i j3 'i-i g j — ifuj cwnTw r i MtfH i gg i ea-. ?3i -n CHAPTER I INTRODUCTION In the early 1960 's, the discovery that quasi-stellar objects were a unique source of radiation initiated a period of intense observational and theoretical research which still continues. Although a great deal of data has helped define these objects phenomenologically, we are still not able satisfactorily to explain them theoretically. Moreover, the search for OSO's has revealed that there are many classes of sources which are quite similar to quasars: Seyfert, N-type, and compact galaxies, and Lacertids. In this work I will use the term quasi-stellar object (Q30 or quasar) to refer to all objects variously called quasi-stellar radio sources or quasi-stellar sources whether or not they are radio emitters. Tnese objects possess the following general characteristics: a) faint, star-like appearance on a photographic plate; b) an excess of ultraviolet and infrared radiation (relative to stellar spectra) ; c) broad o emission lines (widths of up to 100 A) x^rith absorption lines sometimes present; d) optical spectra exhibiting large emission line redshifts [0.06 $ z ^ 3.53, where z = (,\ Xo) / Ao]. Some quasars exhibit multiple absorption redshifts while a few have m.ultiple emission redshifts. If the spectral redshifts are assumed to be cosmological, they indicate objects which are receding from, us at a significant fraction of the speed of light, up to 0.91c for OQ 172 (z = 3.53). There has been some discussion (Chiu et al 1973) concerning the creation of two classes of

PAGE 18

quasars, one of which would be used to explain the Lacertid phenomenon. Seyfert, N-type, and compact galaxies are often grouped together because they all possess certain characteristics in common, and depending on who is classifying them, the defining criteria are not always mutually exclusive. Morgan (1972) presents an extensive summary of classification criteria. Seyfert galaxies are generally characterized by small, intensely bright nuclei (described as stellar in visual appearance) in which violent activity appears to take place, manifesting itself in broad hydrogen emission lines charactized by Doppler velocity widths of a few thousand km/s; and by an excess of ultraviolet and infrared radiation. 14any Seyfert galaxies are spirals and some exhibit forbidden emission lines which are much narrower than the broad lines and are not normally seen in galactic spectra. N and compact galaxies basically are classifications of form and are thus somewhat a function of the distance and observing instrument. An N galaxy is defined as one having a small, brilliant nucleus containing a considerable fraction of the total luminosity, superimposed on a much fainter main body. A compact gala^cy exhibits .high surface brightness and is only partially resolved on a medium to high resolution photographic plate. BL Lac is the defining source for the Lacertid class of objects, which exhibit (Strittmatter _et al. 1972) a) rapid intensity variations in the radio, infrared, and optical, lasting days to xjeeks; b) an energy distribution which indicates most of the energy is emitted at infrared wavelengths; c) an absence of emission lines, and in many cases an absence of absorption lines; d) a strong and rapidly varying

PAGE 19

*"(fewi mwvvTiiu M*Ma*3Eijh_ I .ycsM polarization; e) in some cases a stellar appearance (OJ 287) while in other cases a non-stellar appearance (BL Lac) In general, N galaxies have been regarded as intermediate in form and luminosity between quasars and Seyfert galaxies. Extragalactic Variables As early as 1963, Burbidge et_ _al. suggested a possible relationship between quasars and Seyfert galaxies; Sandage (1970) and Kristian (1973) have provided evidence that quasars are like N-type galaxies. For the purposes of this study, the most important point is that many quasars, Seyfert and N-type galaxies, and Lacertids are strong radio emitters and exhibit intensity variations in both optical and radio emission. Moreover, apart from differences in absolute luminosity, these classes of objects are generally indistinguishable on the basis of their radio spectra or their time variations (Kellermann and Pauliny-Toth 1968) Because real differences appear to exist among the optical classifications, I will generally note the specific type of object being discussed at any point. However, because of the increasing circumstantial evidence that there is a relationship among all these variable sources with respect to the nature of the radiation mechanism and energy source active in each of them, unless othertNTise noted I will treat all these classes of objects as somewhat different manifestations of the same basic phenomena, and refer to all members of this general class as Extragalactic Variables (EGV) Why are EGV's such an intriguing area of research? Stated simply, they emit far too much energy in too little time from too small a volume to be completely explained by any present theories. If they are at

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45 cosmclogical distances, quasars have optxcal lumxnosities of xO to 46 ^^3 45 10 ergs/sec and radio luminosities of 10 to 10 ergs/sec (Burbidge and Burbidge 1967) The optical intensity of many quasars varies on a time scale which is characteristically on the order of a tenth of a year, which implies that the active region of the quasar must be very compact. If we make the assumption that we can use the Hubble expansion constant to determine the distance of the quasars from their redshift, then we are confronted with a m.ajor scientific problem. Although not theoretically impossible, we are considering the largest masses ever seen in such small volumes, 10 to 10 ~ solar masses in a spherical volume roughly one tenth of a light year in diameter (Morrison 19 73). Making long lasting stable models for such massive and compact systems, and developing highly efficient mechanisms for converting rest mass into radiation energy remain among the most perplexing problems associated with quasars. From another perspective, beyond the basic phenomena used to classify the types of EGV's, one almost immediately enters a labyrinth of controversial if not contradictory observations, explanations, hypotheses, interpretations, and plain speculations which are fed by generally commendable attempts to bring some meaning to this intriguing area of research by using the best data available, which regrettably often suffer from inadequate time or spatial resolution or inadequate signal to noise ratios. It seems that as researchers make every effort to increase time and spatial resolution, there often is that much more structure to be found, structure which is changing! In addition these research efforts follow on the heels of, and in fact act as significant motivation for, better receiving systems all the way from centimeter to X-ray wavelengths,

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i-^-i^iw I II In. i L. iin n[j i w i i .aua jiu iwi jiLLj, Thus whatever I present in this study does not represent incontrovertible truth, but rather that which appears to be most generallyaccepted by its frequency in the literature and which seems reasonable to me. It also represents the most successful effort to date to analyze the available variability data. State of our Knowledge Some of the most basic questions which remain unresolved are the following: a) Are these objects at the cosmclogical distances indicated by the redshift of their spectra, or are they in fact much closer? b) IJhat is the source of energy emitted, which in some cases is awesome even if the source is not at a cosmclogical distance? c) How is the energy converted into radiation? d) What kind of radiation is emitted? Because the radiation emission is what we obser^/e, hopefully by answering (d) we can make progress on the other basic questions. In this work, where necessary, I will assume the extragalactic variables are at cosmological distances. I will not address the question of energy source and energy conversion other than to note that the most popular theories (Kellermann 1974) involve the collisions of stars or galaxies; the collapse of stars, superstars, galaxies, or intergalactic matter; the explosion of stars, superstars, or galaxies, including chain reactions; positron-electron annihilation and creation of matter; quark interactions; and a pulsar-like mechanism referred to as the "spinar" model. What then do we know from the observations of extragalactic variables? a) Ver^' Long Baseline Interf erometry measurements indicate that the variable sources often have multiple, compact components, typically on the order of 1.0 to 0.001 arc seconds; the physical

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g*^t^rsMW ^u _Hi, iii J II .w .Ai w Hk.m^-i*.iJ L!-UML .g Sftt J I -^ IW ,iLj dimensions deduced from these measurements are a function of distance and expansion velocity of the source. In weak radio galaxies which have nuclear structure apparently' identical to quasars, the radio emission is concentrated in a very small region near the nucleus, with dimensions ranging from 100 pc to less than 0.1 pc. b) Radio and optical variations on time scales of a day to a few years have been observed in different sources. Assuming an event cannot occur in a time much shorter than the light travel time across the active region, the duration gives an estimate of the size of the active region which is independent of the distance to the source, but dependent on whether or not a relativistic expansion is taking place. It is possible that the source of energy could be much larger than the active region if there exists some energy coupling or transfer mechanism. c) Tnere are at least two observations at optical frequencies that provide evidence for solid material in or at least near the nuclei of Seyfert galaxies and quasars (Burbidge and Stein 1970) d) Based on observations of variable nuclei, Burbidge (1970) has speculated that activity in galactic nuclei is a widespread and probably quite general phenomenon, taking place in many if not all types of galaxies. In general there is a wide range of power levels observed and activity has been seen over the full range of distance from nearby galaxies to the most distant objects observed. Thus considering light travel time, this activity has been observed over the full range of observed time. This has been reinforced by a recent discovery by Crane et al. (1976) of centimeter

PAGE 23

variations from the nucleus of M81, a nearby spiral galaxy. e) A strong correlation exists between high optical polarization and variability. The radio, optical, and infrared data collected on EGV's all seem to indicate a high probability that what we are observing are different manifestations of some basic phenomenon common to all EGV's and very likely common also to our own galaxy. ""he obvious question, then, is just what is the basic phenomenon? This question has refused to yield to almost 13 years of concerted effort, for the answer is anything but obvious. To begin with, we don't even know what the basic phenomenon is for which we are looking. Most likely it is either a common energy source, or a common mechanism which couples the energy generated to the energy emitted. This then is probably comouflaged by the magnitude of generated energy, the characteristics of the material surrounding the generator, and the number of such generators in a limited region of space. If a basic phenomenon exists in all EGV's, then theories which attempt to address themselves to the phenomenon must be applicable in all cases; however, because of the many differences among observed EGV parameters, any theory which is not applicable to all EGV's is not necessarily completely invalid. It may simply be valid for certain conditions found in only som.e of the EGV's, and may require further refinement to apply more generally. Our approach then must also be basic; what can we observe? Because we are searching for something common to all these variables, what relationships can we find among the varied observations; and finally, •what do these relationships tell us, if anything? This then

PAGE 24

is the basic approach used in carrying out the research described herein. Analysis of intensity variations may provide critical data on the radiation mechanisms involved, their relationship to one another, distribution of radiation energy, and possible source structure. This is particularly true if a correlation between activity at different wavelengths can be established and will become clearer after reviewing the character of the spectral energy distributions of the variable sources, and the attempts made thus far to explain them theoretically. For the study and intercomparision of radio, infrared, and optical data which follows, the use of Table 1 is indispensable. The entries o o o for 3575 A, 4400 A, and 5490 A correspond to Johnson m^ m and m^ respectively, before correction for atmospheric extinction.

PAGE 25

TABLE 1 INTERCOMI^imiSON OF WAVELENGTHS WITH FREQUENCIES (y) WAVELENGTH O (A) INVERSE LOG INVERSE LOG WAVELENGTH WAVELENGTH FREQUENCY FREQUENCY (mm) (cm ') (Hz ) 3.3 X 10^ 4.5 1.0 X < 10^^ 15.0 2.7 4.4 8.2 X 14.9 2.5 4.4 7.5 14.9 2.2 4.4 6.8 14.8 1.8 4.3 5.4 14.7 1.0 10^ 4.0 3.0 14.5 8.3 X 3.9 2.5 14.4 6.2 3.8 1.9 14.3 4.5 3.7 1.4 10^3 14.1 2.9 3.5 8.6 X 13.9 2,1 3.3 6.2 13.8 1.2 3.1 3.5 13.5 1.0 10^ 3.0 3.0 13.5 5.0 X 2.7 1.5 13.2 3.3 2.5 1.0 10^2 13.0 0.1 1.0 10-^ 2.0 3.0 X 12.5 3.3 X 1.5 1.0 ^^10 12.0 1.0 1.0 10 1.0 3.0 X 11 5 3.3 3.0 X 0.5 9.1 X 11.0 9.0 1.1 0,4 3.3 10.5 10.0 1.0 0.0 3.0 10.5 28.0 1.07 10.0 0.3 0.4 0.55 1.0 1.2 1.6 2.2 3.5 4.8 8.5 10.0 20.0 30.0 100.0 300.0 1000.0 3000 3675 4000 4400 5490 10,000

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CHAPTER II THEORY APPLIED TO SPECTRAL ENERGY DISTRIBUTIONS Spectral Energy Distributions Much of the theoretical effort expended on EGV's and also on nonvariable quasars has been devoted to attempts to explain the radiation mechanisms which give rise to the spectral energy distributions of these sources. Knowledge of the radiation mechanisms, the parameters controlling these mechanisms, and the possible relationships between mechanisms (if more than one is responsible) will provide the information necessary to help explain the energy source and coupling mechanisms A number of characteristic energy distributions are portrayed in Figure 1 (Neugebauer et_ al. 1971 and Telesco ^ al 1976) where the log flux density (with vertical offset C) vs the log rest frequency have been plotted for the quasars 3C 273 (C = 31.0), 3C 445 (C = 31.0), 3C 48 (C = 30.0), 4C 29.68 (C = 30.0), 3C 249.1 (C = 29.0), and the Seyfert galaxy NGG 1068 (C = 33.0). The dashed lines simply connect observed portions of the spectra; thus they extend across most of the infrared portion of the spectrum where little data has been collected due to the lack of atm.ospheric observing windows at most of these frequencies. Subsequent data in the near and far infrared now indicate that there are probably two basic types of spectra, one which shows a large increase in the infrared spectrum, as in NGC 1068, and another which follows the dotted line for 3C 273 to within the accuracy of measurement (Simon 1976). Quasars and Seyfert galaxies exhibit both types of 10

PAGE 27

— •vw!r*'.£>,^-_;>_ 11 NGC1068 ^-.\ 10 11 12 Log v^iHi) 13 14 15 16 Figure 1. Log flux density (with zero-level offsets) vs log rest frequency for the quasars 3C 273, 3C 446, 3C 48, 4C 29.58, and 3C 249.1. Reproduced from Neugebauer _e^ _al. (1971) with permission of the authors and the Annual Review of Astronomy and Astrophysics. More recent data obtained from Telesco e_t ad^. (1976) and Rieke and Low (1975) x\rere used to plot the curve for the Seyfert galaxy NGC 1068.

PAGE 28

rm ig j i —iJgcCigBg 12 spectra. In addition, there is now evidence of a possible near-infrared "dust bump" in the energy distribution of a number of quasi-stellar objects (Becklin 19 76). The bump may be described as a small departure from the otherwise smooth spectra, as opposed to the large infrared contribution in the spectra of NGC 1068. In general, the known spectral energy distributions for any source can be divided into three regions whose boundaries overlap. The radio 11 spectrum extends from about 1 mm (3 x 10 Hz) to all longer wavelengths, 14 The infrared spectrum extends from about 0.7 y (10 Hz) to about 1 mm; o and the optical spectrum encompasses the region from about 3000 A (-10"^^ Hz) to 7000 A. Radio Frequency Spectra With respect to radio spectra, magnetic field strength, or time scale of flux density variations, no distinction can be m.ade between quasars and compact radio galaxies (Kellermann and Pauliny-Toth 1969) ; thus they are grouped together in this section. A detailed study indicates three basic types of radio spectra (Kellermann 1974) : a) Straight (Class S) spectra, where the flux density decreases monotonically over the whole range of observed frequencies, as in Figure 2d; b) Curved (Class C) spectra, which are steeper at shorter wavelengths (C-) as in Figure 2c, or have a sharp cut-off at shorter wavelengths (C ) as in Figure 2b; max c) Complex (CPX) spectra, which have one or more maxima or minima

PAGE 29

100 10 \ \ 4 C 39.25 ., QSS (al 10 (.0 102 103 10 104 1000 1 100 •N 10 3C 1 23 \ (jalaxy \ 1 (c 105 102 103 ,0'' 105 100 10 1934-63 galaxy lOOOr 100 10 3C 2 QSS 1' 10 (d) (I') (ta> 1. 10 102 103 (ci; 10^ 10^ 102 103 io4 105 Figure 2. il 1 us tr;i L i on of three basic grou])s of radio fracjucney specLra: (a) ^iC 39.2'), Class CPX (Comi'.lox) ; (h) IV'i^i-b'i, CMas.s C max (Ciirvuil) ; (c) 'Ul 123, Class C (Curved); (d) 3C 2, Cla-'-.s S (Slrai s;h t) Koriroduced from Calacilc and Kxtjagalact; i(-,__Radio Asl.ronomy, edited Iv/ C. L. Verscliuur and K. I. Ke 1 1 enuaiin (ii. iJZ) Copyrigllt L97A hy Si)rin}',er-Verl.ag New York, Inc. Used wilh (leriii issloii of ])uh] i ::>\iva: and ed i I Drs w

PAGE 30

•^^ni^^Bsg-ff^HiiiF^' -T^ e' ryg iwrfc 14 It is generally accepted that magnetic fields and a flux of high energy relativistic electrons exist in the EGV's. From such physical conditions, energy may be emitted by electrostatic bremsstrahlung scattered from plasma waves, s3mchrotron radiation, inverse Compton scattering, or by plasma shock waves if the source is turbulent. I-Ihile there are other possibilities, these are most often discussed in the literature. The good qualitative and in some cases quantitative agreement between the synchrotron hypothesis and the observations has presently established this as the most likely radiation mechanism, at least at radio wavelengths. Radiation from a Single Electr on In the presence of a magnetic field of strength B, a non-relativistic electron will move in a helical path about a field line and emit radiation at a single gyro or cyclotron frequency (v ) which is given by v 1 eB -,, ,^. V = -z-^ = ^ (Hz) (1) g zttR 2ii mc where R is the perpendicular distance of the electron from the magnetic field line, m is the electron rest mass, v is the electron velocity, e is the electron charge (emu), B is the magnetic flux density, and c is the velocity of light. Blumenthal and Gould (19 70) have shown that a relativistic electron spiraling in a magnetic field emits a total instantaneous power given by

PAGE 31

15 /y e~ P(v) = mc K^^^iOd^ c v/v (2) where the critical frequency is expressed by and where eB 2 \ 2iraic T, = 1.608 X lO-""-^ B eI ,, JGeV = 4.21 B_^ y (MHz) (3) C = eB. Y mc r 1-^ L -1/2 -1/2 = (1 r) (4) K (C) is a modified Bessel function of the 5/3 order, E is the electron energy (E = v mc") and B_^ = B sin9^ where 6^ is the pitch angle, the constant angle between the electron velocity and the magnetic field. The synchrotron spectrum from a single electron as a function of x = v/v^ is illustrated in Figure 3. As can be seen from equations (2) and (3), for a single particle emitting synchrotron radiation in a homogeneous magnetic field, the emission received at a particular frequency is directly related to the energy of the electron producing this radiation, and the strength of the magnetic field.

PAGE 32

*gM^ tj^-* i W fc O l !>'^ 16 Figure 3. S],"nchrotron spectrum from a single electron as a function of X = v/v Reproduced from Blumenthal and Gould (1970) v/ith permission of the authors and the Reviews of Modern Physics.

PAGE 33

* l>' ^ "W ^L W Mfri M WC^ wCii lUl KUa^ 17 The distribution P(v) has a broad peak near v '^ 0.28 v At hio-her c frequencies (v >> V ) the spectrum approaches P(v) ^i 1/2 I e-^B. 1 mc I V c / 1/2 -(v/v^) (5) While at very low frequencies (v << v ) the spectrum can be approximated by P(v) 4iTe Bj_ r(^)mc^ V 2v" ^ 1/3 (6) where r(l/3) is the Gamma function. P(v) varies little over a large range of frequencies, decreasing to half its maximum value at v/v^ = 0.011 and 1.47 (Oort and Walraven 1956). Most of the radiation is concentrated in a narrow cone, the axis of which coincides with the instantaneous velocity vector of the electron. The angle between the axis and the sides of the cone is given by ,2 1/2 1 mc" (7) As a result the radiation is strongly polarized. In the case where the o pitch angle, 6^, is 90 the electric vector is polarized parallel to the plane of the electron orbit. An observer in this plane will receive a pulse of radiation every time the electron completes an orbit, at

PAGE 34

18 intervals t such that 1 Y — r V \ = V 2^Tr \ (8) The duration of the pulse follows from equation (7) and is given by At 9 Y V r g (9) / VJhile it can be seen from equations (1), (2), and (4) that the synchrotron spectrum is made up of discrete frequencies, the radiation is concentrated in the higher-order harmonics of the classical gyrofrequency, V (Kellermann 1974) and thus is often considered continuous. 6 o In the case where 8 = 90 an observer receives all the radiation e o emitted during the time At. For 9^ r 90 the observed spectrum is -2 -1 reduced by a factor of (sin ) because the distance between the electron and the observer changes with time. However, for a distrib^ition of electrons, the emitted and received powers are again equal. Radiation from a Distribution of Electrons Brown (1974) has shown that a homogeneous and isotropic ensenble of electrons having a number density per unit energy of N(E)dE and located in a vacuum in the presence of a uniform magnetic field B of spatial extent L, will radiate a specific intensity I(v) given by I(v) = ''^— ^2"^ |N(E)dE|^) / K5/3 (£)d5 (10)

PAGE 35

19 where N(E)dE is the number of electrons per cm with energies in the inter\^al E to E + dE, If the electrons are characterized by a power law energy distribution between particular limits E and E^, given by dN(E) = N(E)dE = Ke"^ dE (E^ < E < E^) (11) then the specific intensity takes the form I(v) = e_i_L mc" A 3e 4T;mc (Y-l)/2 a(Y)KB (y+l)/2 -(Y-l)/2 (12) where K is a constant, a(Y) is a slowly varying function of y and in general a(Y) =0.1. The specific intensity radiated will be observed as a brightness distribution, and the integral of this brightness distribution over the whole source yields the flux density S. Thus from equations (11) and (12) it can be seen that a power law distribution of electrons of spectral index y emits a power law photon spectrum which is characterized by S = V (13) w here the two indices are related by a = (14) Thus assuming that a power law electron energy distribution is the source of emitted radiation, the index Y can be obtained by measuring the slope a of the observed spectral energy distribution (Figure 1)

PAGE 36

20 The range of electron energies which contribute to synchrotron emission at a given frequency is strongly a function of the electron spectrum and thus of the index y. Table 2 (from Brown 19 74) lists the range of values E to E which is responsible for 90% of the emission at a particular frequency, for a given value of y. TABLE 2 RA.NGE OF ELECTRON ENERGIES FOR A GIVEN POWER LAW INDEX y 1.0 1.5 2.0 2.5 3.0 4.0 5.0 *--^2^^1^90% 1620 117 56 22 15 8.9 6.1 Thus as y Increases, the range of electron energies increasingly narrows, indicating that the assumption or approximation of a power law distribution of electron energies needs to hold only over a narrow energy range. The shape of the electron energy distribution may deviate enormously from a power law outside the specified energy range without significantly affecting the synchrotron emission spectrum. The validit;^ of the assumption of a power law distribution ranges from y > 1.0 (Kellermann 1974) to y $ 5.0 (Brown 1974). Finally, it should be noted from equation (5) that no form of electron energy distribution can give a synchrotron spectrum that rises faster than the low frequency asymp1/3 totic limit of v for a single electron. The straight radio frequency spectrum in Figure 2d is believed to result from synchrotron emission from a power law distribution of electrons as just discussed. Such spectra generally have indices in the range -1.3 < a < -0.6, with a median value of about -0.8, which corresponds to y == 2.6. Deviations from this straight spectra can arise from

PAGE 37

21 numerous causes. To maintain a consistent presentation of the synchrotron hypothesis, I will discuss here only gross spectral changes x-rhich have synchrotron-related causes, and defer discussion of other causes to another investigation. The turnover or low frequency cutoff in Figure 2b can result from synchrotron self -absorption. Theory predicts that as the brightness temperature of the source approaches the equivalent kinetic energy of the electrons, self-absorption will become important, and the source will become completely opaque at a frequency given by (15) where 9 is the angular extent of the source in arc seconds, B is in 2 gauss, the (1 + Z) term accounts for the effect of the redshift, (S^/8 ) is the surface brightness of the source, and S is the maximum flux density at v m A study of the values of v vs surface brightness for sources for m which has been measured, shows that the observed cutoffs in the radio spectra can be accounted for by synchrotron self -absorption with a magnetic field of B = 10 gauss. This corresponds to a maximum bright7-1 12 ness temperature of T ~ 10 to 10* K, It is hypothesized that this m 12 brightness temperature of 10 K corresponds to the case where energy loss by synchrotron radiation is just equal to the energy loss caused by inverse Compton scattering. According to this hypothesis, inverse Compton scattering would cause a rapid "cooling" of a source which has a l'^ T = 10 K. m

PAGE 38

22 According to synchrotron theory, as v (< v^) increases, one receives more radiation from deeper in the source and the fl-oic increases until V = V at which point the source becomes optically thin and the m flux received becomes a function of the electron energy distribution as in Figure 2d. For frequencies \) < v the spectral index is independent of the electron energy distribution and the theory predicts a value of 2.5. Although the apparent effect of synchrotron self-absorption is evident in many sources and values of a = +1.0 are often observed at long wavelengths, no source has been observed with the a = +2.5 value predicted by theory. This might be explained by a gradual rather than an abrupt transition from the transparent to opaque condition, caused by a. range of opacities resulting from different parts of the source becoming opaque at different frequencies. Alternatively, O'Dell and Sartori (1970) have proposed "cyclotron turnover" as the possible low frequency cutoff mechanism. The spectrum shown in Figure 2a is referred to as a "complex" or "peculiar" spectrijm and cannot be explained by a single source of synchrotron radiation. Thus this type is believed to be a superposition of two or more curved or straight spectra, and is generally associated with compact radio sources. Because of their composite nature, such spectra often have relatively small values of spectral index over a portion of the frequency range and are thus sometimes referred to as "flat". A good correlation exists between composite radio spectra and violent optical and radio variability. The frequency at which selfabsorption becomes significant is a function of the surface brightness 2 temperature (S / 9 ) as is shown in equation (15) Thus tor a given m flux, if the angular extent (6) of the active region is large, the

PAGE 39

23 surface brightness temperature will be lower, resulting in a lower value of V m The relatively good agreenent between theory and observations of the self-absorption cutoff frequency v^, the angular size of individual compact components as measured by VLBI, and the observed peak brightness temperature of 10^^ to 10^^^ K pose strong arguments that the radio emission from the very comapct sources is indeed ordinary, incoherent synchrotron emission (Kellermann 19 70) Time Variations We finally come to the purpose of this research, which is to search for a relation between observed optical and radio variations. In general, time variations might be caused by a) changes in the rate of production or acceleration of relativistic particles; b) loss of energy due to synchrotron radiation, inverse Compton scattering, or adiabatic expansion; c) changes in magnetic field; d) (in the opaque region of the spectrum) changes in the angular size of the source as a result of expansion. In addition it should be noted that plasma ejection from a massive rotating body (spinar) could also be the cause of time variations. However, once the plasma has been ejected, any or all of (a) through (d) would apply. In fact it is most likely that all of (a) through (d) contribute to some degree among the different sources and at different periods of time within individual sources.

PAGE 40

24 One unknown factor to keep in mind is that while we have strong evidence (from measured time of variations) that the optical, infrared, and high frequency radio flux come from very small regions, we do not know presently if these regions are one and the same or whether different parts of the spectrum arise from differnt regions. Expanding Source Model Based on short wavelength (2 to 10 cm) radio observations, the initial expanding source model assumed that radio emission from a variable extragalactic object is due to synchrotron radiation from a spherical cloud of relativistic electrons moving in a magnetic field while the cloud expands adiabatically Shklovsky (1960) originally hypothesized the expanding source model, using it to predict decreases in radio flux from supernovae remnants. If we assume a) the electron energy distribution is a power law of the form given in equation (11) ; b) the magnetic field is fixed in the expanding cloud, so that magnetic flux is conserved, B^ = S (r /r^) ; c) each electron loses energy due to cloud expansion at a rate proportional to its energy, so that the form of the energy distribution is unchanged, that is E^ = E (r^ /r ) for each electron; d) no additional particles enter or leave the region, so that

PAGE 41

then for an optically thin source 2y ^2 = ^1 7 (15) 1 I where r is the radius at time t^ and r^ is the expanded radius at time t„However, examination of the radio spectra indicates that for a given frequency if we extrapolate back in time, at some point the density of relativistic electrons is such that the source is no longer completely transparent to its own radiation. At this point, from equation (15) the brightness temperature depends only on the value of the magnetic field, and the flux density is given by -1/2 2 5/2 S(v,t) B "-^^(t) 0^(t) v''^^ (17) If the expansion is constant in time and if the magnetic flux is conserved during expansion, then t. can be substituted for r^ in assiomption (b) and equation (17) can be used to derive r,.-3 S(t„) = S(t,) _^. (18) If the magnetic flux is constant, such that B(t^) = B(t^) then S(t2) = S(t^) (19) In either case, the race of change of the flux density is independent of the electron energy distribution, because as long as the source is

PAGE 42

25 optically thick, the observed radiation comes from only a fraction of the electrons. From expressions for the frequency v at which the synchrotron self-absorption ceases, it can be shown that 'ly + 3' S(v J m/ S(-:nl> Y + 4 ^ -.11 ml 4y + 6 (20) Again it can be shotvn that the complete expression for flux density as a function of frequency v and time t is given by r S(v,t ) = S 2 ml V 5/2 3/2 ml/ 1exp Y+4 -(2y+3)' M v^ m V V m -T m where S ml 1-exp is the flux density corresponding to any frequency > (21) V ^ at time t, ; ml 1 t„ is the time of observation at frequency v; T is the optical depth of any frequency v m "1 Ttius the model suggests that the varying components are sources of synchrotron radiation which initially are optically thick but become optically thin at progressively longer xi'avelengths as they expand (van der Laan 1966). The simple model predicts that outbursts will be seen earlier, and will have greater flux amplitude and a shorter outburst duration at higher frequencies. In principle, a measure of the radio spectrum at any time and its time rate of change miay be used to predict the future behavior of the

PAGE 43

27 spectrum at all frequencies. In practice this is difficult because many variable source show multiple overlapping outbursts over short periods of time. In fact, long-term observations have shovm that repeated outbursts of relativistic particles over time periods of a year or less are not uncommon in EGV's especially in the Lacertids. If one assumes that the expanding source model is valid, flares will be separated and better defined at higher frequencies due to shorter duration and less overlap. Extending this knowledge to lower frequencies can help identify the possible location in time of individual flares, from which the relative flare amplitude and duration may be estimated, within the constraints of the recorded flux level as a function of time. If this data can be obtained successfully, it allows one to study how a given event propagates in the frequency domain, and thus how it affects the spectral energy distribution. However, estimates of absolute amplitude and duration of a flare are almost impossible due to the difficulty in finding the quiescent radiation level. Expanding Source Model Difficulties and Alternatives While the model has been successful in quantitatively explaining centimeter variations from certain sources including 3C 120 (Dent 1968, Pauliny-Toth and Kellermann 1966, Seielstad 1974), discrepancies exist between 11.0 and 2.8 cm, and the theory appears to break down at short centimeter to millimeter wavelengths (Medd et al 1968, Kellermann and Pauliny-Toth 1968, Lock et al. 1969, Kinman et al. 1974). The discrepancies include incorrect form of the outbursts, lack of time delay and/or lack of amplitude change between events seen at different freauencies. The latter two discrepancies could be caused by the source

PAGE 44

28 becoming optically thin, or by continuous injection of relativlstic electrons. Peterson and Dent (19 73) proposed a continuous injection version of the expanding source model with some limited success. Some of the additional modifications or combinations of parameters which might be tried include: variable expansion of the cloud; a mechanism to accelerate particles after an explosive event; possible escape of particles from the cloud; lack of conservation of magnetic flux; an expanding shell rather than a spherical cloud, introduced by van der Laan (1962) and Lequeux (1962); multiple interacting sources; relativlstic expansion (Ryle and Longair 1967, Rees and Simon 1968); non-isotropic radiation; coherent rather than incoherent radiation; changing electron energy distribution due to loss of energy by inverse Compton scattering, ordinary bremsstrahlung, and ionization. Thus there exists myriad possible combinations of parameters. Because the simple model does have basic qualitative validity despite slgnigicant discrepancies, work is proceeding on revisions of the simple model. In particular, Peterson and Dent's limited success Xirith the obvious possibility of extended injection has motivated continuing investigations in that area. Peterson and King (1975) have attempted to extend the application of the continuous injection model into the optical wavelengths. Because of the gap in the observable spectrum between centimeter and optical wavelengths, it is not even known if a relationship exists between the activity observed at these two different frequencies. However, the limited observations at millimeter wavelengths indicate that the large and rapid variations predicted by the simple expanding rnxdel at these short wavelengths do not. occur.

PAGE 45

29 Inverse Compton Scattering Inverse Compton scattering will take place in a region with a sufficiently large radiation density and a sufficiently strong magnetic field. Thus while this radiation mechanisin most likely functions in the types of sources under discussion, the main question that must be answered is how significant a role does this process play? The inverse Compton mechanism is highly inefficient and if a significant amount of the observed radiation is caused by the inverse Compton mechanism, the already awesome energy requirement increases much further. Inverse Compton scattering refers to the collision of a fast electron with a low energy photon and the resulting production of a high energy recoil photon and a corresponding decrease in electron energy. The solution for the total spectrum of inverse Compton photons scattered per unit time and volume by a distribution of relativistic electrons passing through a photon gas is very complicated in the completely general case, and thus has not been attempted. However, simplifications result in limiting cases which have astrophysical applications. In the rest frame of the electron, if the energy of the photon before scattering 2 is much less than mc the incident and scattered photons will have roughly the same energy and the scattering corresponds to the Thompson limit in which the Compton cross section is independent of the energy of the incoming photon. While in the laboratory frame, the characteristic energy of the scattered photon is large relative to the incident photon energy, it is still small compared with the electon energy and thus the electron loses a small fraction of its energy in any single inverse Compton scattering. However, in the limiting case where the 2 energy of the photon before scattering is much greater than mc the

PAGE 46

30 scattered photon carried ax^ay a large fraction of the electron energy, and thus the electron does not lose its energy continuously. Felten and Morrison (1966) present inverse Compton scattering in a manner that stresses its relationship with synchrotron radiation. Given a power law energy distribution of electrons as in equation (11), as long as the energy spectrum is not too steep, the distribution of recoil photon energies will be determined primarily by equation (11) and will in fact be a power law distribution itself. The electron lifetime against synchrotron radiation loss is given by -312 -1/2 ,^^. t "^ V (22) s m where t is in years, B in gauss, and v in GHz; while the electron lifetime against energy loss to inverse Compton scattering (in the Thompson limit) is given by 6 X 10 r9o>, t % : (23) where t is in years and p is the energy density of the surrounding c 3 radiation field (photon distribution) in eV/cm To give an example of the significance of the radiation energy density on inverse Compton losses, consider a 5 GeV electron (y ^^ 10 ) trapped in the galaxy where p '^^ 10 eV/cm compared to one trapped near the solar surface where 12 3 p "^ 2 X 10 eV/cm In the galaxy, the electron will have a lifetime TO 3 t -^^ 10"^ years, whereas near the solar surface, t '^^ 10 sec.

PAGE 47

31 The total instantaneous power scattered by an electron is given by 4 Q n where a is the Thompson cross section (a = T^^o ); whereas the instantaneous synchrotron power radiated by an electron is given by 7 2 2 2 P (y H) = ^ r ^ cy B^ (25) s r 3 o r where r^ is the classical electron radius and c is the velocity of light. Thus the ratio of the two powers for a single electron is given 2 2 "> P (y ,B) r cy (H sinO ) s r o r e P (y >P) /Tc /ON 2 2 c r (16iT/3)r cy p or 3 B /8tt ] 2. ,.,. sm (28) 2 ^ p I e Then assuming that the electron velocity is randomly oriented V7ith respect to the magnetic field, the time or ensemble average gives 2 ^ < sin 6 > = ^ ; and thus e J P „2 P s a /8iT ^27) c where (B /Sir) is the energy density of the magnetic field. Thus the ratio of losses from synchrotron radiation and from inverse Compton scattering is equal to the ratio of the energy densities. (Note that in some notation H is substituted for B, but as long as consideration is limited to vacuum, B = H.) The assumption of equipartition of energy

PAGE 48

32 between the energy density of the magnetic field and the energy density of the radiation field requires the least total energy from a source. If the energy of the radiation field exceeds twice the energy density of the magnetic field, catastrophic inverse Compton losses result, Kellermann and Pauliny-Toth (1969) have expressed these conditions in terms of the maximum brightness temperature (T ) observed in compact sources. According to their development, for a homogeneous and isotropic source, the intensity of the radiation from inverse Compton scattering relative to the intensity of radiation from synchrotron em.ission (L^/L^) is given by c s c „ 1 m 2 i 12 ^ 10 1 + m 10 12 m (28) 11 where v is the cutoff frequency in ^ffiz due to synchrotron self-absorpm tion. Assuming a roughly typical value of v '>^ 100 GHz, if T^ < 10 K, L /L 1 and inverse Compton scattering is insignificant. But if c s T > 10 K, the bracketed term., which represents the effect of secona m order scattering, becomes important and L /L 'v (T /lO ) Thus it c s m is argued that the catastrophic energy losses due to inverse Compton scattering "cool" the source, causing a decrease of T to between 10 to 10 K, where losses to both processes are roughly the same. As an 11 example, assume that v '\> 1 GHz. Then for T -v10 K, the half-life of m m / 12 an electron is '^^ 10 years, whereas if T '^ 10 K, the half -life drops to about a day. Felten and Morrison developed still another expression relating the radiation intensities, which may prove useful.

PAGE 49

33 ^ v^s s „ B /8tt r\j — — — '\j (I ) K V c c 2 X 10 T ( 3-y ) 2 (29) where K and K represent the constants and parameters entering the s c respective coefficients. They then use that expression neglecting inverse Compton scattering from the 3 K background radiation to compute the expected spectra from synchrotron and inverse Compton radiation for the galactic halo with an imposed high frequency cutoff, as shown in Figure 4. Conditions in the galactic halo are far different from conditions in compact variable sources; the point is that if both synchrotron and inverse Compton components exist and can be resolved in an observed spectral energy distribution, equation (29) will provide a useful estimate of physical conditions in the source. Finally, a relation between the characteristic synchrotron frequency (v ) emitted by an electron at a given energy, and the characteristic energy (e ) of the Compton scattered photon is given by <£,> ^ 0.9 X 10^ ^ V (30) 1 ^1 *^ where e is in eV, B, in y-gauss, and v^ in l>fflz. From this it can be seen that for a given brightness temperature T, the characteristic Compton scattering energy, and therefore frequency, decreases for increasing magnetic field strength. (It should be noted that in my notation, Y Y, 9 and v correspond to Felten and Morrison's y m, 're c ^, and V .) In summary, it should be em.phasized that values of the magnetic fields and electron half-lives against inverse Compton scattering can be estimated using equations (15) and (28), without assuming a distance

PAGE 50

34 2 2 (siiun AjDJ(iqjD) M jj 0) -d u-i 0) M ^ C O c s-j cu n q 0) OJ fj >i o > n CO i-i P S C "3 JJ -H CL ct -H O O M £ ^ Sj ^ J-( O &0 C-U 0) a 'H c cj D > OJ -H C5 rt -H GJ S u C woo CD S jj a 0) • ^ OJ rH d -l-J flJ > CO tC /= C GJ T-i 1-^ 4-1 •H C C ^ O 5^ ,-J s^ JJ <^ .. -H C rJlJ o M-i -d o M 03 -H -d m :3 CO >J M QJ 0) !-i rC M ^ Sj +J -G -H M 3 U O C 6 -rH iJ OJ -H 3 Vj t-i ca p., 4-1 o 0) ^ OJ m u s-i cu 3 1^ cs ac & c i-H -a: ^ 0) C Co O J-J M > -H bO cd -H -H •H 4-1 ^ S J-i CC CU J nj -H ^ t=i /-^ o JJ 'd iJ k£) -H •H rt rn ix) ^ ,-1 !_i C O 13 Cd -H QJ tH 3 3 -3 ^"— ^ '^ cr c M 4-1 ^ MS c ci; 73 4-J O g 3 0) Mi M !-i 4-1 M 4-1 '-I -H 3 o -3 a u-i !-i dl O 0) i-J 1-) pH 3 ^ M O !;< >> QJ S S '-^ OJ M -H cd u-i M t; 0) -o C OJ 3 -H ^3 4-1 CO m en Eh Cu 3 4-1 >, en O ct3 3 ^ QJ or -H cj 0) aM 3 ^ en 4J o P^
PAGE 51

35 to the source or equipartition of energy. Possibly large uncertainties do exist in the determination of the angular size (6) and cutoff freQuencies (v ) especially in sources possessing complex brightness m distributions which are characteristic of EGV's. If the distance to the source is knoxro, the energy content of the relativistic electrons, E and the magnetic field, E^, can be uniquely determined (Kellermann and Pauliny-Toth 1969). However, for typical spectral indices (y '^^ 2.5) the ratio E^/E^ depends on the 'V'20th power of the cutoff frequency, v and the angular extent 8; thus departures m from energy equipartition are difficult to detect. The major controversy centered around synchrotron radiation versus inverse Compton scattering is based on the lifetimes of electrons against energy loss. If one assumes, based on an "average" outburst duration, a typical size of ^10"''^ cm (one light month) for an active region, this implies lifetimes of the relativistic electrons of approximately that same length. Thus some argue that it is unlikely that any significant portion of the emitted radiation could be due to inverse Compton scattering, because that would imply electron lifetimes as short as one day. From this point, Hoyle, Burbidge, and Sargent (1966) calculated the ratio of magnetic to radiation density assuming synchrotron radiation was the dominant process and the source 3C 273 was at a cosmological distance. The resulting ratio of energy densities indicated catastrophic inverse Compton losses, from which they concluded that the source was not at a cosmological distance. However, Woltjer (1966) countered by assuming a non-isotropic radiation field, explained away the energy density problem and put 3C 273 back at cosmological distances. This presents a specific example of the controversial

PAGE 52

36 nature of this research. The considerations listed here have prompted some to develop radiation models which include both synchrotron and inverse Compton radiation (Takarada 1968, Cavaliere et al. 1970, Rees 1971, Blanford and Rees 1972). Optical Spectra To study the absolute energy distributions of EGV's at optical wavelengths, data recorded as stellar magnitudes are converted to an energy scale using the absolute energy distribution of aLyra as a reference. This source was calibrated by Oke and Shild (1970), who formulated a conversion expression m = -2.5 log F C (31) where m is the magnitude, F is the corresponding energy flux in units of 10^^ Janskys (1 Jansky = 10~^^ Watts/m /Hz) and C is a constant. For all conversions made in this study, C = 56.04. Extragalactic variables that exhibit large amplitude optical variations are usually those that have significant optical polarization, steep power law optical spectra, and that tend to be associated with compact radio sources having flat radio spectra at gigahertz frequencies (Kinman 1975). The non-thermal continuum of the Seyfert galaxy 3C 120 is relatively flat in the UV, increases towards the red in the visual range and turns up sharply in the IR (Shields et al 1972), as shown in Figure 5. This appears roughly similar to the energy distribution of the QSO 3C 273.

PAGE 53

en S tu 3 •H CI QJ O 3 O O C iH O O ^ O 14-1 ^ 0) QJ 4J T-\ 0) CO Cfl CO o a B 1) CD -H cd oj ^ u B o o •H ? 03 •H 13 Qi J2 M a; tn •H ^ 0! C M-l II r^: p>o S !^ 4-1 xi w j-j < •H 13 0) >> H CO TJ QJ T-i CO a Cfl 03 60 ^-1 u o 0) M-l a. w 0) M-l M O CO U 03 o •H -U 03 fX 3 03 CO (2 03 r-H •H 0) r-i 0) CO ,C o •H 03 4J 3 O >^ O CO 0) f-i 3 O •H O I u u 03 OJ J-J 3 03 CO O u m Q) 13 3 CO M-i CO 03 03 > 3 O •r4 6 12 O O U ,3 M-i CO 03 CO •H •H 3 4J 'H 3 H O CO -H -W 13 13 5 OJ (3; 03 •U S^ -^ o tu r^ 13 ^ C^ Cfl CD 0) J-4 P-l c 03 a •H ,3 CJ) M-l O >. 4-1 •H 03 03 > 03 CD cO Ct3 CO O O 13 00 3 !H r-l P. 03
PAGE 54

o C\! CJ) ro c aj f -o £ o c ^ (_ o 1/1 _;! ^ 3 n r r o o o £ o in CO IS) >^ • X o CM CO O c-J "?. <^ "3O CM

PAGE 55

39 The optical and near infrared spectral distribution of BL Lac and OJ 287 are presented in Figures 6, 7, and 8. The Lacertids in general exhibit approxiiaate power law spectra which grow steeper (more negative) between the near infrared and the optical as can be seen from the values in Table 3, from Rieke and Kinman (1974) and Oke and Gunn (1974), Tne somewhat flatter infrared index may be the result of positive curvature in the non-thermal spectrum and inclusion of some stellar radiation at 2.2y. (Note that for BL Lac, the values for the infrared and the optical spectral indices were derived from observations that were separated in time.) TABLE 3 LACERTID OPTICAL AND NEAR-IR SPECTRAL INDICES SOURCE IR (10. 5y 0.44y) OPTICAL (0.55y 0.36u) 0735 + 17 -1.20 + 0.15 -1.9 OJ 287 -0.86 ON 231 -1.13 + 0.12 -2.0 EL Lac -1.15 + 0.2 (10. 5y 2.2y) -1.55 (
PAGE 56

40 ^ -J -H !— XJ C o 'T: r:J •r-' -~-^ i-j 1 i Ci~ u n, a c ro • r-i H ~; 1 r> 1^ n aj 'J1^ K r-IM CM OJ (ZH^^^j/M) AllSN3a XniJ 90"1 G X C o X Cj u ; irj li J '-1 3^ •r-' "^ .— -, ;~: '6 CD f^ ^ |_ •n ; X o :/M c^l '^" ^>^i ^t3 iJ rd /1 pi T O rp J T tfl CD O CM 'T U3 (D N CD CD CD CD CD cn cn (D 01 (D OJ CM CM CM CM CM OJ CM C^J CM CM ^ OD ^ Jj — ; O Jj m JZ — ^ T3" o i_j ;>^ I-J c .il )^ ^-H r~ CD w r" r' *m CJ -'j: •H y: H ij *H • ca o ^ X u OJ J-^ aj 0-1 ^ O Gj O !-( !]~i Oj O 'f^ r^_ rj JZ J2 X 1^ ^^ U : O 2 ^ >

PAGE 57

41 (\! S'Si a vi O! c CM CTj o rc in K >, a 2} o —5 j c 1 > (/I J3 c D jC H C C 'h £ < 03 O O trt OJ .a 00 § ^ -r> o •H H o O •— o a > c a w. S (i> tf 0' ^ o tn — > c ^ rr <. o ^ a -U r: o CD O CD — CJ rO T in O! ^ t ^ ^ ^ ^ 1 i 1 1 i CM 1 (l-ZH 2_^3v_3SS 6js) ^-j 90'1 i. G' r^ C5 H S _J lb •r-i •H ^ K cj !^ M 50 G Cj G !>, u_ ^ •• ^ 'Cj r^ c tn' 3 r. ^ ',^ !JZ 1) U CC

PAGE 58

m e 3 w S-i ri (D CN M-l -H U r~> r-~rt iH CTs 13 Q) tH 0) i-( X >. O 3 4J S-l C P O ra O ^ H) Xi i-: O 4-1 p C u iH •H Xi 0) a 03 & 0) ^ OJ O p^ nj Prf •H TJ 4J to cu Cvj >, !-i r^ Cfl • -C fl CN 4J r-c &'-' 03 ^ B T3 u o c ?^ 4J a o 4-1 u cc C 03 <; S r;; 0) D 0) w ^ 0) iH t-^ rQ x; M-l C3 !-i Hi H 4-1 C, P:^ • rH ttJ 13 M Oj tC M CN c 03 o 4J r~03 0) •H CtJ cn o\ !-i •u T) OJ r-l u Pm & jH Q O 4J G fl s: O c !-l o 4-1 SO 13 01 •H 3 03 d M O (1) 03 o cd tU T3 •H }-i T3 D , M-) iH TJ 1 G 4J C O c; > O •H •H >-l iH H CO •H O cn M *\ O f-i r{ OT 0) !-l •H 4J •H > OJ T3 U P •H 4J OJ C o M r^ 0) iH 0) 4-1 0) P e rH ft p •r) TD T3 OJ iH PH C CD j: j:: H ca rH 4-! 4-1 •H 03 •H • ^— V a S >^ C CM W rCS o r~. ^-N -H cr. i X Td r^ iJ i—i I — i c-\ 0) 00 cfl CN r^ x Oi 3 • ON M a^i-J. Tj rH •W '-I H O cd ,13 xi 4-J C! 3 0) 0) 1^ 03 Ph • T3 I — i ^ 00 s r^ 4-1 cn fH •H P-. 03 •H 0) U OJ !-4 s J-i a 4J 2 03 ,x3 3 •H M D > a Ml a c 'Xj •H •H <4H w 03 •H J3 ptH O w^ -: > ^

PAGE 59

4^ -ZH Das 6j3) 4 901

PAGE 60

44 wavelengths
PAGE 61

45 BL _AC — — 1 1 1— 1 1 .^ 1 -24.6 \ • \ \ -24,8 \ \ -25.0 \^ -25.2 \ \ \ \ \ -25.4 \ \ OCT 20, 1968 ^ JULY 16, 1969 \ -25.6 a = 2.85 + 0.09 \ ; a = 2.92 + 0.03 ^ -24.4 \ • \ O — -24.6 \ \. \ -24. o \ \ -25.0 \ -25.2 \ \ -2 5-.4 \ \ \ • \ -25,6 AUG 19, 1969 • DEC 5, 1969 \ a = 3.17 + 0.06 a-2 93 0.04 \ -9S S L — i i_ 1 1 '. \ 1 1 1 ; ^ 14.5 14.7 14.9 14.5 log ly 14.7 14.9 Figure 9. BL Lac: continuum measurements of the optical spectrum, on different days, indicating change of power law index. Straight lines are least squares fits for alj. the continuum points. Reproduced from Visvanathan (197 3a) with permiission of the author and The Astrophy sical Journal, which is published by the University of Chicago Press.

PAGE 62

53 immediately associated with them, whose character or nature changes with time. Kinman (1975) argues that in the case of the Lacertids, variations of the optical spectral index do not merely consist of changes in the slope of a power law relation, but also consist of variable curvature in the energy distribution. However, observations by Rieke and Kinman (1974) and by Smith _et al. (1975) indicate that the UBV color of OJ 287 remained constant during a long-term decline of three magnitudes in its mean brightness, with short-term changes in the color which have not yet shown any relationship to the short-term changes in brightness. In addition, the observations of Smith et_ al. contain some evidence for a slower rate of decline in the infrared, in contradiction to the 10.5-y observations of Rieke and Kinman, However, Kinman (1975) states that the spectral index becomes flatter tox^ards the infrared. All classes of extragalactic variables, especially the Lacertids, exhibit significant linear optical polarization (Kinman et al. 1974); in addition, 3C 279, 3C 345, 3C 446, 3C 454.3 and BL Lac have shown changes in the polarization position angle during bursts as compared with the position angles before and after activity. This has been interpreted as an indication that changes in the magnetic field configuration of the region emitting the continuum is a characteristic feature of the burst phase of these sources (Visvanathan 1973a) Moreover, observations of both radio and optical polarization in 3C 345 and 3C 454.3, for 2 and 1 years respectively, indicated agreement in the measured position angles in 3C 345, but disagreement in 3C 454.3. In the case of 3C 345, this can be interpreted to mean the optical and radio emission came from the same region. This is vital information if

PAGE 63

54 one is trying to correlate activity at different wavelengths from a multiple-component source. In the case of 3C 454.3, one interpretation is that the radio and optical continua originate from different volumes of space, but this may come about in two different ways. If a correlation exists between optical and radio observations, a single source may emit the optical radiation observed at time t then undergo an expansion and a change in magnetic field configuration before emitting the radio radiation observed at time t, + At. On the other hand, the optical and radio emission may arise from two different, spatially separated sources. The non-thermal character of the optical continuum emission from extragalactic variables appears generally accepted. The observations of apparent power law spectra at optical xjavelengths rapid variability/, and linear polarization which appears to be independent of wavelength, leads to a conclusion by many that the optical continuum has a synchrotron origin. Inverse Compton scattering has also been suggested, but the lack of detection of an X-ray flux from almost all these sources sets an upper limit to the X-ray flu>: V7hich is apparently incompatible with the X-ray flux expected form inverse Compton scattering. Furthermore, 3500 to 8000 A observations of 3C 345, 3C 446, 3C 454.3, and BL Lac between 1968 and 1969 again indicated that both the degree of polarization and the position angle were independent of wavelength. This strongly suggests that the same mechanism is responsible for the continuum radiation in these sources from ultraviolet to infrared wavelengths.

PAGE 64

55 Galactic Infrared Radiation Infrared astronomy is still in an early stage of development because the atmosphere restricts ground-based observations to roughly the 1 to 20 y range. Observations at longer wavelengths are made from balloons, aircraft, rockets, and high altitude observatories. As previously noted, extragalactic variables in general show as infrared excess and, as shown in Figure 1, some emit the majority of their luminosity in the infrared. Attempts to explain this radiation must be based on what we have learned about sources of infrared radiation in our own and in other galaxies. Figure 14, while dated (Low and Aumarni 1970), gives a summation of the infrared observations of the H II regions Orion A and M 17, the galaxy M82, and the galactic nucleus Sagitarius A. More recent data from Telesco et al (1976) has been included for the Seyfert galaxy NGC 1068. Again dashed lines connect known measurements at the time of publication. A significant amount of the infrared radiation in our galaxy is thermal radiation from dust particles or grains, which both scatter and o absorb incident radiation. Absorption of starlight from 3000 to 10,000 A increases with increasing frequency, causing an extinction or "reddening" as illustrated in Figure 15 (Greenberg 1968). The absorbed radiation heats the grains, thus redistributing higher frequency radiation into the infrared. An infrared excess refers to an amxOunt of radiation within a given infrared radiation interval which is in excess of what would normally be expected from the type of source observed. Such excess infrared radiation in our galaxy arises from H II regions, some hot Be and Of stars,

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Figure 14. Spectral energy distributions of galactic and extragalactic sources. Dashed lines indicate a lack of data for that wavelength interval. Upper limits are indicated for M82 at 70 u and Sgr IRA at 1000 y. Reproduced from Low and Aumann (1970) with permission of the authors and The Astrophysical Journal, which is published by the University of Chicago Press. More recent data obtained from Telesco et al (1975) and Rieke and Low (1975) were used to plot the curve for NC-C 1068.

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3 J 3cm 3mm 300/1 M CVJ I CD LU X o o .^\ 30/x Sqr IRA 3fM 11 12 13 LOG FREQUENCY (Hz) M17 RA AND !RB Sgr IRA NG 1068 14

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58 X(^ hX Figure l!). Schematic diagram illustrating extinction or "reddening" as a function of frequency and xvavelengtb.

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59 protostars which are believed to exist in dense gas and dust regions, circumstellar grains surrounding stars, and the galactic nucleus, which is a highly luminous infrared source whatever its nature is. Observations indicate that a significant fraction of both interstellar and circumstellar grains are silicate particles similar to material returned from the moon, thus indicating a possible relationship between the material found in galactic interstellar space and that from which the bodies of the solar system may have formed. In addition, infrared obser>/ations of early hot stars can be interpreted as arising from free-free emission of ionized hydrogen; observations of planetary nebulae may indicate that grains can condense in high velocity fields within destructive ultraviolet radiation fields, that is in almost any environment where the grain temperature is maintained below its evaporation temperature; and limited observations of novae indicate that material ejected during stellar mass loss can condense into dust particles (Stein 1975, and Neugebauer et al. 1971). Furthermore, infrared observations of H II regions have provided evidence that grains can exist in ionized regions and that the emission can arise from grains at different temperatures (Wynn-Williams and Becklin 1974). The galactic nucleus is complex but can be represented by three main components defined by their spatial and wavelength distributions o as follows: an extended source measured over a 1 region and observed o o between 1 and 5 y; a 2 x 4 source which has fine structure and is found at 100 u; a 15" source coincident with the non-thermal radio source Sgr A. The galactic center up to 100 y has an estimated infrared 9 luminosity of 10 L x^hich is much less than the infrared emission irom extragalactic variables. Most of the 1 to 5 p emission is believed to

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60 be stellar radiation, altered by about 30 magnitudes of visual absorption, from a high spatial density of stars. Observations of the nucleus of M31 show similar characteristics. Tae origin of the 100-vi flux is unkno^^ra, although a significant portion again may be thermal re-radiation of starlight. Of most interest here is the 15" (0.7 pc) source which radiates between 3 and 20 y with an energy distribution that can be approximated by a power law of slope a -2. Thus it resembles the spectra of the nuclei of several extragalactic variables and leads to obvious speculation about similar physical processes involved. The radiation from this source could be due to a reasonably sized dust cloud 3 of mass > 3 X 10 M surrounding a concentration of stars or some other source of energy. It might also be non-thermal but this is unclear for a number of reasons. While the 15" source is coincident with Sgr A, the nonthermal radio emission from the latter comes from an area five times the diameter of the infrared source. In addition, the flux density at 20 y is ten times greater than the radio emission at 2 cm, which is in disagreement with the characteristic spectral energy distribution of a non-thermal radio source (Neugebauer et aJ 1971). However, there may be two different energy sources, or one might trj^ to construct a model 2 for opacity at infrared wavelengths. In addition, approxim.ately 10 12 identical sources of B 'v. 30 gauss and radius 10 cm could emit the mm observed flux. The existence of multiple small sources may not be unreasonable considering the strong evidence of almost continuous activity in som.e galactic nuclei.

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61 Extragalactic Infrared Hadiation Estimates of the infrared luminosities from extragalactic variables are tentative to unreliable because of the lack of observations between 50 to 300 y. However, extragalactic variables are characterized by 10 11 infrared Iximinosities of 10 to 10 L_ (Neugebauer et al. 1971 and Telesco _et_ al. 1976) and total Seyfert emission in the infrared may be 44 47 as high as 10' to 10 ergs/sec (Rees _et al. 1969). In addition, a sample of infrared spectra from Seyfert nuclei indicates that they can be characterized by a power law of index a = -1.5 to -2.0. In this wavelength range, NGC 1068 may have a more negative power law index, and a correspondingly steeper spectrum. In particular, between 28 and 320 y, NGC 1068 has a luminosity equal to 3,7 x 10 L It should be noted that while some members of the specific class of compact galaxies (as distinct from the general class of EGV) have infrared excesses similar to Seyfert galaxies, others do not show any conspicious infrared excess. A sample of 30 QSO's show spectra that can generally be characterized by indices of a = -0.2 to -1.6 from 0.32 to 2.2 p., although some clearly show curvature. Stein (1975) observes that the infrared spectra of OJ 287 and BL Lac are generally flatter (a ^ -1) than the infrared spectrum of sources such as NGC 1068 (a "^ -2) and he then speculates that some sources may emit both thermal and non-thermal infrared radiation. Not all Lacertids have been detected or even observed in the nearinfrared. Variations of the 2.2-y infrared flux on a time scale comparable to the measured optical variations have been observed for 3C 279, 3C 345, 3C 446, and 3C 454.3, which are among those sources having the steepest

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62 rise in their energy distributions at infrared wavelengths and which exhibit short duration large amplitude optical variations (Oke _et_ al 1970) In addition, it is argued on the basis of the infrared and visual spectral distributions in Figure 12, that to within the limitations of simultaneous measurement, the infrared and visual variations follow one another. If this is true, it would indicate that for these sources the same mechanism is probably responsible for the production of radiation from the infrared to the ultraviolet. Rieke (1972) and Kinman e_t al. (1974) have provided evidence for both long-term (years) and short-term (months) variations in OJ 287 between 2.2 and 10 y. Rieke contends that these short-term infrared variations correspond in extent and time with B-magnitude and millimeter observations made at the same time. Kinman et_ al established a very strong correspondence in long-term activity over the same wavelength range. Rieke also observed possible evidence for infrared variations of BL Lac in the 2 to 20-y range but the data are sketchy. Significant short-term variability of BL Lac at 2.2 y is believed to exist (Neugebauer et_ al. 1971) No satisfactory explanation of the infrared emission from extragalactic sources has yet been found. Thus far, observations of some sources provide evidence that both thermal and non-thermal radiation is present. Neugebauer e_t al^. have observed that knowledge of the energy distribution between 20 and 500 y is critical to any investigation of the radiation mechanism. VThile any discussion of detailed models is probably premature until that data is available, I will briefly review the speculations. Of course there are two possible radiation mechanisms; thermal

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63 re-radiation by dust grains and non-thermal radiation by incoherent synchrotron or inverse Compton scattering. It is generally agreed that very short-term (less than a few weeks) variability of the infrared radiation or significant as well as variable infrared polarization would imply a nonthermal source. However, to date there has not been conclusive evidence of either of these characteristics. The proponents of thermal radiation argue that small grains may condense during the expansion phase following a violent outburst and that the observed energy distribution is obtained by the superposition of several different blackbody curves corresponding to shells of dust at different distances from the source. A.s noted earlier, there is evidence for the existence of dust in or near Seyfert nuclei and quasars (Burbudge and Stein 1970). While the amount of dust required for such emission appears physically reasonable, its required size does place lower limits of a few weeks to a month on the allowed time scale of variations at wavelengths 5 10 y. Variations on a shorter time scale have not yet been conclusively established. The discovery of slight polarization could be explained by emission from magnetically aligned grains. The proponents of a non-thermal mechanism argue that while there is evidence of dust near active sources, it is too far removed and of too little quantity to cause the observed infrared flux. The main difficulties in the case for non-thermal emission are the need for a sharp cutoff at low frequencies and the condition that inverse Compton scattering losses not exceed synchrotron losses. Burbidge and Stein (1970) conclude that the energetics of a synchrotron model are physicallj' reasonable because total required energies are less than those required to explain the compact radio sources or to explain non-thermal optical radiation.

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64 but require magnetic fields of "-1 to 100 gauss. They also point out that in some cases, the data support the hypothesis of nuclei consisting of a large number of separate components. Cavaliere et^ _al • (1970) propose a model which emits both synchrotron and inverse Compton radiation. During the writing of this summary of research efforts, I was struck by the analogy to an earlier attempt to explain a troublesome spectrum, that of the blackbody. If we can explain the spectrum, most likely we can explain the source. However, we must first have the whole spectrum!

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CHAPTER III ANALYSIS OF THE LONG-TERM OPTICAL AND RADIO RECORDS The Research Problem Up to ten years of observations of the sometimes violent optical and radio variations of extragalactic variables have compelled many to ask the potentially important question, Are the optical and radio variations for a given source correlated? The gap in the observable spectrum between millimeter radio radiation and optical radiation makes it impossible to follow an event through the intervening spectral range and necessitates attempts to correlate radio and optical variability before one can test a model against data taken at these separated wavelengths. If a relationship exists, then what are its characteristics and its implications with respect to the emission mechanism.s just summarized? At the same time, if no relationship exists, what are the implications? As I have indicated by the summaries in Chapter II, the answers to these questions are very important for defining the radiation mechanisms and modeling the source of radiation. In addition, such information is necessary for the planning of cooperative multi-wavelength observing programs. For the first time, collections of observations are reaching the point where meaningful investigations of such correlations on a time scale of many years can be made. A visual inspection of the optical, millimeter, and centimeter data for a few extragalactic variables reveals variations that are comparable 65

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66 in time and, in some cases, amplitude. This is both promising and hazardous, because one must be careful to avoid chance correlations between random events that are not really related. Most searches for correlations have examined the short-term variations of 3C 120 (Usher 1972), OJ 287 and BL Lac (Kinman and Conklin 1971; Andrew e^ al 1971; Epstein et_ al. 1972; Andrew et al. 1974; Kinman et al. 1974; Miller et al. 1974) and the long-term activity of 3L Lac (Hackney e_t al. 1972) and OJ 287 (Lyutyi 1973). The Radio and Optical Data Records The Rosemary Hill Observatory of the University of Florida, the Algonquin Radio Observatory, the University of Massachusetts, the Royal Greenwich Observatory, and the Yale University Observatory have monitored extragalactic variables at radio or optical wavelengths for a number of years. The present study examines these long-term records in an attempt to discover correlated activity for sources common to the monitoring programs. It makes use of Rosemary Hill blue or photographic magnitudes (McGimsey et al. 1975; Scott et_ al 1976), Algonquin 2.8-cm (10.7 GHz) data (Medd et al. 1972; MacLeod e^ al 1975), University of Massachusetts 1.9-cm (15.5 GHz) data (Dent e_t al. 1974; Dent 1976), Royal Greenwich Observatory optical m.agnitudes (Tritton and Brett 1970; Cannon et al 1971; Tritton and Selmes 1971; Selmes et_ al 1975), and Yale Observatory photographic magnitudes (Lu 1972). In addition, blue magnitudes from the Goethe Link Observatory were used for 3C 273 (Burkhead and Parvey 1968; Burkhead 1969; Burkhead and Lee 1970; Burkhead and Stein 1971; Burkhead and Rettig 1972; Burkhead and Hill 1975).

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67 For the first time, the extensive records from the above observatories have been integrated and presented together in figures accompanying the textual presentation for each source. Thus, these figures represent a relatively complete documentation of the available observed long-term radio and optical variations (or lack thereof) The raw data have been plotted with one-rms error bars. In several cases, data from different observatories were combined to obtain a longer data record. I acknowledge that this is a potentially hazardous procedure for any quantitative analysis for three reasons. First, different optical observatories may use different comparison sequences: and while Rosemary Hill B magnitudes are filtered (GG-13) exposures taken with a reflector. Royal Greenwich B-magnitude plates are unfiltered exposures taken with a refractor. Second, there is often a time delay and an amplitude difference between the Dent 1.9-cm data and the Algonquin 2.8-cm data, as one might expect from the expanding source model. Third, the calibration of the absolute flux density scale m.ay differ between two radio observatories, Hovrever, for visual presentation of long-term trends in the data, the effects of the second factor are generally negligible. To m.inimize the effects of all three factors, in most cases where different sets of data were combined to form a single radio or light curve there was sufficient overlap between the sets to establish that the variability information was essentially identical for both sets (to within less than one rms error) and to measure the zero-point offset between the two sets if such an offset existed. The empirically determined offset was then applied to the shorter of the two sets to create a consistent long-term record.

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68 Cross-Correlation Analysis The long-term optical and radio data records have been examined visually with great care to search for evidence of correlation. This was accomplished by plotting the two data records on different sheets, literally laying one curve on top of the other, and sliding one with respect to the other in search of coincidences between the two records. Then, as a first attempt to search analytically for correlations, the optical magnitudes and radio fluxes were linearly cross-correlated. Unf orttmately, long-term astronomical measurements are almost invariably spaced unevenly in time because of the monthly and annual cycles imposed by the moon and the sun, with additional interruptions being created by equipment failure, weather, and scheduling. Because of the mathematical difficulties associated with treating unevenly spaced time series, it is common practice to fit a curve to the data, thus creating a continuous function which can be used directly or sampled evenly for analytical study. However, this requires the choice of a fitting function, thus introducing a certain bias into the data. This is particularly important in studies of rapid, largeam.plitude, random variables where two or more outbursts may be superimposed, the character of each individual outburst is not known, and the data lost in observation gaps are unpredictable. For these reasons, in an attempt to avoid biasing the raw data, I chose to synthesize evenly spaced time series by stepping through the radio and optical data records for a given source hj an increment of time At^ averaging all data falling within that increment, and either linearly interpolating or leaving a "hole" for those time increments in

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69 which no data were taken. Next the total record of radio data was shifted backwards in time relative to the optical by an amount At^^. The radio record was then moved forward in time by steps of At (At„ 5 At ) while a normalized linear cross-correlation coefficient, R, was calculated for all overlapping data for each increment of At • For any value of the time shift At (At = nAt At„), coincidences between radio data and optical holes, or vice versa, were not used in the calculation of the correlation coefficient. This procedure was followed until the radio data had undergone a total time shift of 2At„. For this study, the following formula was used to calculate the normalized cross-correlation coefficient, R, for each value of At, Z (x y ) -y (Zx ) (Zy ) R(At) = rj^ (32) rv 2 1 .n2/^ rv 2 1 .2.1/2 [Zx. (Lx.) ] [Zy. (Z, .) J where x and y are functions of time and N is the number of coincidences between radio and optical data increments. This can be shown to be exactly equivalent to the more classical formula for R (Harnett 1970) Z (x x) (y y) R = ^^ Yn '^^^ [Z(x^ x)^ Z(y^ y)^] by the use of the following identity: Z(x_. x) = (x. x) + (x, x) + ... (x,,^ x) = (Zx.) Nx (34)

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70 The technique just outlined has a number of characteristics that should be noted. a) The original optical and radio data records resulted from irregularly sampling two continuous functions of time. The correlation coefficients are calculated for synthesized, evenly spaced time series which are assumed to represent the long-term functions of time. b) Observational errors are not considered in the calculation of the time averages or the correlation coefficients. c) The calculated correlation coefficients are partly a function of the choice of At, which is itself dependent on the time resolution of the data and the time scale of the observed activity. d) Attempts to correlate too small a data sample result in spurious coefficients which, when plotted as a function of At, form a scatter diagram. l-Tnen this occurs for the overlap of the beginning of one data set with the end of the other set it is referred to as an "edge effect". e) Wlien each of the two records has only a singly significant peak or "bump", the records will be strongly correlated for some value of At even though there may be no physical relation between the two events. Great caution must be exercised in the consideration of such "one-event" correlations. f) Because I am cross-correlating unevenly space time series and examining a population of cross-correlation coefficients, the classical test of significance is at best questionable and at worst simply not applicable. It is included in Table 4 only for lack of a better statistical method, and it should be used in conjunction

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71 with a careful and skeptical examination of the data records themselves g) The precision of At is limited by the choice of At h) The statistical technique used, equation (32), calculates a normalized linear cross-correlation coefficient between two functions which are represented by time series; however, radio flux is linearly proportional to the emitted energy while an optical magnitude is proportional to the log of the emitted energy. Thus strictly speaking this technique measures the relation between emitted radio energy and the log of the emitted optical energy as a function of time shift At. This was done because of the following: 1) Most investigations involving optical data are both conducted and published using a magnitude scale to represent the data. 2) Presentation of the optical and radio data on the same graph in a form that is easy to examine necessitated the use of both radio flux and optical magnitudes. When a potentially significant cross-correlation was found, a regression plot of radio flux vs optical magnitude was made to illustrate and investigate the functional relationship between the two sets of data. The regression plots were obtained by shifting the synthesized time series by the value of At that gave the maximum correlation coefficient. It is difficult to justify the use of linear interpolation to fill observational gaps in the data records because we have no knowledge of the emission intensity during that gap. Thus the interpolated data

PAGE 81

72 records must be used cautiously, and the validity of results from the interpolated data records must be examined for each source independently. In general, for any given source the hole technique and the interpolation technique yielded similar results. Thus, because the hole technique more nearly approximates the original record, the results of this technique alone are summarized in Table 4 (Chapter IV) Choice of Correlation Parameters As noted previously, the value of the correlation coefficient and its distribution as a function of At do depend on At which is determined by the character of both the optical and radio data records. Thus a trial and error method of using different values for At^ and At„ was employed to find the "best" values. Obviously it makes no sense to use a At^ smaller than At because this oversamples the resolution of the data introduced by At However, ome might use a At larger than At to accentuate long-term effects when working with high time resolution data sets. In general At„ should equal At The choice of At„ of course depends on the relative coverage JL ^ of the optical and radio data records. If correlation coefficients are calculated when the extent of the overlap between the optical and radio data is less than 10%, and in some cases 20%, of either the entire optical record or the entire radio record, then edge effects or spurious "one-event" correlations arise. Therefore At^ was usually chosen to calculate the correlation coefficient for all overlaps involving m.ore than 10 to 20% of the whole of both data records. The choice of the "best" values for At and At. x
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73 For the cross-correlation calculation, a) I'Jhat was the smallest value of At for which R vs At remained a smoothly varying function? b) Secondarily, what was the value of At that yielded the maximum correlation coefficient? For the regression plots, a value of At^ was chosen which yielded a "sufficient" number of points to suggest a possible relationship, In the following presentation of the results, graphical summaries o f R vs At for more than one value of At are sometimes presented to 1 illustrate the effects of the choice of At^,

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CHAPTER IV RESULTS OF THE CORRELATION ANALYSIS The results of the analytical study are summarized in Table 4, where column one gives the source name; column two the maximum cross-correlation coefficient, R, corresponding to the time shift At listed in column three; column four lists the number N of increments in the synthesized time series that contained data and were used to calculate the maximum cross-correlation coefficient; and column five gives the confidence level for the maximum value of R calculated from the two-tailed Student's t-distribution. In column two, an "NC" indicates the absence of any distinct maximum in the population of calculated cross-correlation coefficients; an asterisk indicates a "one-event" correlation, in which there is minimal confidence of physical reality. The error estimate in this column is a subjective figure derived from the fact that a number of coefficients for adjacent values of At have nearly the same value. In column three, a negative value for At indicates that the optical events lead the radio events, while a positive value indicates that the radio events precede the optical. The error estimate here is derived by estimating the half-amplitude width of the distribution of correlation coefficients about the maximum value. In all the plots of R vs At that follow in this chapter, the top curve illustrates the relation for the raw data or "hole technique" -while the bottom curve illustrates the relation for interpolation across holes 74

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75 TABLE 4 SUI4M/\RY OF RESULTS OF THE LINEAR CROSS-CORRELATION ANAl.YSIS Source R At in years N Confidence OJ 287 0.85+.02 -0.875+1.0 24 >99% OJ 287 Pt I 0.90+.03 -0.60+0.85 13 >99% OJ 287 Pt II 0.92+.04 0.0+0.70 15 >99% 3C 454.3 0.79+.01 -1.2+1.2 31 >99% BL Lac NC(?) -0.5 (?) CTA 26 0.82+.08* -1.1+0.9 16 >99% PKS 0405-12 NC PKS 0420-01 0.65+.10* -0.2+0.8 16 >98% 3C 120 HC NEAO 190 m PKS 0458-02 NC 3C 138 NC PKS 0735+17 0.71+.02* +0.88+0.9 13 >99% PKS 0736+01 NC 01 363 NC OK 290 NC 3C 273 NC PKS 1354+19 NC OQ 208 NC 1510-08 NC NRAO 512 0.66+O.lA 0.0+0.3 27 >99% 3C 371 0.55+0.1 0.5+0.8 29 >99% 3C 446 NC PKS 2345-16 NC

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in tha raw data. Except for this difference, all parameters used in obtaining the top and bottom curves are identical. I-Jhile both curves are included for completeness, all quoted values of R and At refer to the top curve unless explicitly stated otherwise. OJ 287 This object provided the best visual correlation of all the sources studied in this work, a result that was strongly reinforced by the analytical study. Despite gaps in the optical record, there is a strong suggestion that the optical and radio cur-'/es shown in Figure 16 follow each other quite closely through a number of distinct details defined by each record; and in fact, there is no question that both records show a long-term rise and fall from 1970.0 to 1974.0 and a short-term burst centered at about 1975.0. Despite violent short-term optical flickering this visual correlation is supported both by the cross-correlation coefficient of 0.85 indicated in Figure 17, and by the relationship between radio flux and optical magnitude revealed in Figure 18. (The anticorrelations occuring in Figure 17, for large positive and negative values of At result naturally from the superposition of the ascending radio curve on the descending optical curve and vice versa.) Close examination of the data shows that after the gap in both records at 1972.75, there is more complete optical coverage and a different separation between the optical and radio curves than before that date, implying that some shift in the relationship may have occurred. This perception suggested a separation of the data into two segments. Part 1 containing the data prior 1972.75 and Part II containing the data after 1972.75. While the application of the cross-correlation technique

PAGE 86

77 O cvi O o (X) I o o d O IT) o u "C c u ~ c V -^ef'^^ O < o CL o o -* Q cr o o IT) o 'iC Cj z: 'f. = -^ o p r; ro a = N n 2.8pIric ( UJ *" ^ 1~ t< o&c Q c c c ^ u c O "^ CJ CVJ c: ^j N a. c. — • ._) o >, 'J a; c — ci z: u tc '11 C^ aaniiNOViN

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0.5 OJ 287 R 0.0 9 -0.5 • • • a 0.5 R 0.0 9 iX> -1.0 -4.0 -2.0 0.0 2.0 4.0 At (years) Fissure 17. OJ 287. Normalized cross-correlation coefficient (R) vs time shift (At) for the radio and optical data presented in Figure 16. using actual data (top) and interpolated data (bottom) with At-, = At = 0.12 5 year.

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79 10.0 8.0 6.0 X OJ 287 o o • 9 O • • o o • o • oo 4.0 2.0 0.0 o • o o • o • • o o • • 16.0 14.0 MAGNITUDE 12.0 Figure 18. OJ 287. Radio flux vs optical magnitude for At = -0.875 vear, At = 0.05 year. Open circles represent actual data; filled circles represent points for which the flux or the magnitude, or both, have been obtained bv linear interpolation across gaps in the data.

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80 yielded R values of 0.90 and 0.92 for Parts I and II (Figures 19 and 20) respectively, the smaller number of data points used in the calculations combined with significant edge effects, cause one to view the results from Parts I and II with caution. In spite of these reservations, the regression plots of flux vs magnitude for Parts I and II shotm in Figures 21 and 22 display considerably less scatter than Figure 18, tending to support the validity of the separation of the data at 1972.75. Moreover, the reader should not be misled by the apparently much broader peaks illustrated in Figures 19 and 20 relative to the peak in Figure 17; for Figure 17 has a compressed time scale on the x-axis. 3C 454.3 Although optical data from the Rosemary Hill, Yale, and Royal Greenwich Observatories were used to study this source, the overlapping records reinforced one another when appropriate zero-level offsets were applied. The correspondence and mutual reinforcement are illustrated in Figure 23, where the three data records are displayed independently v;ith no zero-level offsets. This reinforcement justifies the deletion of the Yale data record from Figure 24 where the density of Yale data points xTOuld have obscured the long-term optical trends. Visual inspection of the radio and composite optical data illustrated in Figure 24 indicates that while there is not as obvious a correspondence between radio and optical activity as there is for OJ 287, the radio and optical records show comparable variations which may be correlated. Application of both the "hole" and the interpolation techniques, using all three optical data records, yielded maximum correlation coefficients of 0.79 and 0.83, respectively, for the optical leading the radio by

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81 1.0 0.5 0.0 -0.5 OJ 287 -1.01.0 0.5 0.0 -0.5 -1.0 -2.0 • ••• • 0.0 At (years) 1.0 2.0 Figure 19. OJ 287. Normalized eross-correlation coefficient (R) vs time shift (At) for radio and optical data prior to 1972.75, using actual data (top) and interpolated data (bottom) with At^ = At^^ = 0.05 vear.

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82 1.0 f • I • • • • OJ 287 ).5 R 0.0 -0.5 -1.0 1.0 0.5 I • ••• -0,5-1.0 -2.0 1.0 At (years) 2.0 Figure 20. OJ 287. Normalized cross-correlation coefficient (R) vs time shift (At) for radio and optical data after 1972.75, using actual data (top) and Interpolated data (bottom) V7ith At, = At, = 0.05 year. 1 j>

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83 10.0 OJ 287 8.0 e 6.0 X 4.0 o • • o o o o o 2.0 0.0 16.0 14.0 MAGNITUDE 12.0 Figure 21. OJ 287. Radio flux vs optical magnitude prior to 1972.75 for At = -0.06 year, At = 0.05 year. Open circles represent actual data; filled circles represent linearly interpolated data.

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10.0 X 8.0 6.0 4.0 2.0 0.0 84 OJ 287 o 9 a o o o • o o e • 0 • • • • o 16.0 14.0 MAGNITUDE 12.0 Figure 22. OJ 287. R.adio flux vs optical magnitude after 1972.75 for At = 0.0 year, At]_ = 0.05 year. Open circles represent actual data; filled circles represent linearly interpolated data.

PAGE 94

•^ a s N k! *Ti ^ Hw a> P Ho rt CTQ f-i h-" TO rf j::; 3 o CD C PH1 ii CR (D rt i— t /— s (D H re P ro 3 Pi • 0<; Hfo X) IT) 0) DU) "P* OJ H O. HZ Hn o n O ro 3^ Ml ^— w S n e f-h u o C3 o 3 w era t-i oo ro fl2 J>3 ?-l ro rf 3 Ol H. rD 03 G. -c~ rf o i-ti • C rf hi po LO n Ho o • en o 3 p =? 93 • T3 (D H o .-^ J^ XJ fu O £3O rt CO rr ft> f^ HO m rc O cT cro zr R ta ro i-i ru 3 ^— 1 ro Ca Cb s: 3 Xi HCu [T* 1—' £D 0> i-i. H3^ rt 'O o 3 93 T) tD Q M .-—s cr f-i l-^;r^ Hre ro tD-:5 3 (Ti n pJTO Cu n o v_^ H< f-i rt O ^ a. o 2 (" rr en P3 ft rt a' CJQ 3 0) en >3 1-! CD HO rf a /•~\ s t 3 3^ cr o Cu ni o fs re ro 3 f-f o (a K rt en S S3 O ro (11 rt o a 3 H o en O' (B ^ fD ^ fi td S '< i^ 02 s; H3 i-i Kta M ^ •
PAGE 95

MAGNITUDE CO CD cj:> CD CD CO CD CD CCi CT) CZ3 CD CD CD r~o CO CD -F^ cn CD CD • ~m ^^=^Pi je**" "^s CO on CO CO CD CO cn MAGNITUDE

PAGE 96

Figure 24. 3C 454.3. Optical and Algonquin 2.8-cm observations. The optical record consists of Royal Greenwich B magnitudes (with a -0™47 offset) from 1966 to 1972.75; Rosemary Hill photographic (m„„) magnitudes (with no correction to B magnitudes) from 1968.9 to 1971.5; Rosemary Hill B magnitudes from 1971.6 to 1975.9. Yale B magnitudes (with a +0?125 offset) from 1967.6^ to 1971.0 reinforce the illustrated optical activity but are not included due to the high density of points. The numbering of events does not imply a one-to-one correlation between corresponding numbers (see text)

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15.0 ^16.0 3 CD < SI 7.0 OPTICAL 18.0 |1 t RADIO 2 \i 1... ... II III, 4 H Vf X 1 1* 3 |H| Hj|. 4 i 28.0 22.0 >16.0 10.0 J J_ J L J I L L 1966.0 67.0 68.0 69.0 70.0 71.0 DATE 72.0 73.0 74.0 75.0 76.0 a; 00

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Figure 10. Observed optical and nearinfrared spectra of selected quasai-s plotted as a function of rest frequency Vq = v(l+z). Standard deviation error bars ;ire indicated for the infrared photometry and for all spectral scanner observations where the standard deviation in log f^ is greater than 0.02. Note that Ton 256 and PHL 938 are radio quiet. Reproduced from Oke e_t a_l. (1970) with permission of the authors and The Astr o physical Jo urnal which is published by the University of Chicago Press.

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_0G FLUX DENSITY [\M/U^H1) 03 CD o r^ 0) ~n 71 CJl m t ; c Ol m -< ~>! T M :1 i r „, 1 1 / — — 5" _^* c?" < o O "^ 1 ^ -D ii c^' O on O ~ B 5 o 4 ro _L O Ji J* S A i: ^ 1 J n LOG FLUX DENSITY (WAfHZ) j^' ^ 'j: C:;' o O) '-D SJU o l£ m i^ Irf ID CD CD r:i Jl '0 o X u U3 01 -i 'O O C3 Jl. rNj O 33 CI i — -1 CTl ~ 1 ^ ~ f 1 — X ^ ^ f^_!_ •O 1 C'J~ — T ^ o _.;. 1 T 1 """ o U3 1 ~ 7^ ; / 1?

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Figure 11, A continuation of observed optical and nearinfrared spectra of selected quasars begun in Figure 10. Note that the visual and infrared measurements for both 3C 279 and 3C 345 show variability. The inconsistency betv/een the spectral scanner data and the UBV measurements for PHL 658 is unresolved and probably instrumental. Reproduced from Oke et^ al. (1970) with permission of the authors and The Astrophysical Journal X\fhich is published by the University of Chicago Press.

PAGE 101

LOG FLUX DENSITY ['^•l/l/rHZ] LOG FLUX DENSITY (w/M^HZ) a o O 3,, O 05 -< M — LH o r 1 1 1 • o & [^ % fe 1 'f S ^-o '• rn OT CD CE t; "~. m ? '-— 0-1 :C!l B X W -0" — H rj NJol M Lfl N cn" rs! -s; 6o O 6 c^ >* o^ y o CJ ••i. --^" LH S 2 a ;;;^l J o C=i 1=: L ^^ 1 J 1 LOG FLUX DENSITY {YJ/U^HZ) o m ^ o c: -^ n O CO Nl O K ft^ i^ [y f"^ rv) rb r-j r\: ro hj ro ro ro N> CD CO CD U3 o X) OD CD rn rn m o> Ji ro O & ro o CO CD -t> nj o CD C: > C D B L K 1^ > -^ s s c r-o J. o 1 ^ cr, S^?'^-^ CO rri m C cj, ^ -^ g ^. n R ^1 /',* \ ^ CO oo •5, X S o ^ w I*'"" £=; i o — 1 — g 6^7

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Figure 12. A continuation of Figure 10. Note that while 3C 454.3 and 3C 446 exhibited variations in the visual, infrared photometry was not obtained to check for variability. The UBV measurements of 4C 29.68 were unpublished data from Sandage. The 2.2-y points in 3C 309.1 and 3C 432 are only limiting values. Reproduced from Oke et al(19 70) with permission of the authors and The Astrophysical Journal which is ptiblished by the University of Chicago Press.

PAGE 103

LOG FLUX DENSITY (VV/m2hZ) ^ ^' J^ CO < .. P ^ rn ~" ^ HJ m ~ X a n c3 -^ i^ • y -< n 7^ o 5S M ex; 6 j"' ro o ^ — — ro o CD 01 -& r-o o m -& rj O CD i r— Lr o C) ?: :53., J ^5n o ^~r=. _, S ( ,-]T J -j.'^ -1 T .. ^ oo CjJ :2 -t o H ,." "^ OJ w ro > Sj -Lo 6f M ro o5 • Mb j-i O O) ^5 -g,ro u-1 4 ".• n _0G FLUX DENSITY (W/M^HZ) '^' U^' 1^ o ^0 ii; LD iXJ u? uTj cc CP OD ^ 10 w lO OD _a:' CTi Ji ro o CE-'
PAGE 104

3C 345 3C 446 3C 454.3 -26.0 -26.2 -26.4 -26.0 -26.2 U-26.4 O JULY 16,1969 a=i.20 + o.ii -26.2 -26.4 -26.0 -26. -26.4 o AUG 18, 1969 >..J^^ • 'a=0.820.ll • / APRIL 1, 1970 — "~— -• • a=0. 75 + 0.07 t Mgll 14,8 15.0 -26,2 -26.4 -26.2 -26.4 -26.6 -268 -2 5.4 -2 5.6 ^-25.8 -2 6.0 -262 y / \ ^x V. JUNE 30, 1968 \ Q = 2.200.24 N ^ N : X X.. \ AUG 19, 1969 • N,^ a=2.IO0.08 • \^ / 11 > X. ; \. X -DEC 5, 1969 a = L770.04 ^s> • / 1 CiV 15,0 15.2 log i/o 14.0 16.0 15.2 Fitfui'e 13. 3C 3A.5, 3C X'i6, 3C 454.3. ContinLnim nieasurcmenl:s of Lht; opcic.a.l fXix [iloLted ngaj.usc rest Preqiieucy v.^ = v(.l,4-z) l:"or dif l:eri;nt: days. Indicating ciiange of power .law index. Straiglit Jines reivrpseat least sr[uart'.s fits fLir a.1.1 continnuin |)(i,ints. Circled uo.ints repn-escnt emissi.on Jines. Reproduced from Visvanathan (1973a) w.i.tli perm Ls.s.i en of the author and 'j^il^ As tro[iJiy.siA'^l Jonrna.l wiiicli is iiuhlislnul by tlie University of Cliicagi.i Press. Cn

PAGE 105

89 approximately 1.2 years, as illustrated in Figure 25. As a check, application of the same procedures to the Rosemary Hill Royal Greenwich composites yielded similar correlation coefficients values of 0.78 and 0.83 for approximately the same time delay, as illustrated in Figure 26. Close inspection of the raw data nevertheless necessitates a cautious approach to the physical reality of a cross-correlation, because the optical data show at least four and possibly seven events depending on one's criterion (event 6 of the peaks numbered in Figure 24 is defined by a single point with a large error, and event 7 is a shallow rise and .fall), while the radio record suggests only four events (three major events with a shoulder centered on 1973.25). In addition, superposition of the radio and light curves with a time shift of 1.2 years does not bring about an exact alignment of the radio and optical events. In Figure 25 the extended maximum in R beginning with the radio data leading the optical by about three years starts with the superposition of radio event 1 over optical events 3 to 6, and continues as radio event 1 passes through several optical features. This maximum has doubtful significance because it is a variation of the one-event correlation and the R vs At plot quickly deteriorates into the appearance of an edge effect. The rec-ression plot for At = -1.2 years seems to indicate a weak functional relationship between the optical magnitudes and radio flux, which is illustrated in Figure 27 for At-^ = 0.1667 years, and in Figure 28 for At = 0.1 years. In an attempt to investigate whether or not the dominant radio flare from 1966.5 to 1970.0 is actually the cause of a spurious correlation, all three optical records were correlated with the Algonquin data

PAGE 106

90 0.5 R 3C 454.3 -0.5-1.0 1.0 1.5^ R 0.0 -0.5 -1.0 • •• • • • • • 1 1 1 1 1 1 1 -6.0 -4.0 -2.0 0.0 At (years) 2.0 4.0 6.0 Figure 25. 3C 454.3. Normalized cross-correlation coefficient (R) -vs tirae shift (At) for the optical and radio data presented in Figure 24, including the Yale Observatory data, using actual data (top) and interpolated data (bottom), with At = At = 0.1667 year.

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91 1.0 0.5L R 0. -0.51 1 1 • • a • a • • 1 i 1 1 3C 454.3 • • • • • — • c a 9 o • a 1 1 1 1 R 0.0 At (years! Figure 26. 3C 454.3. Normalized cross-correlation coefficient (R) vs time shift (At) for the optical and radio data presented in Figure 24, excluding Yale Observatory data, using actual data (top) and interDolated data (bottom), with At, = At = 0.1667 vear. 13

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92 19.0 17.0 MAGNITUDE Figure 27. 3C 454.3. Radio flux vs optical magnitude using all the optical and radio data, with At = -1.2 year, At^ = 0.1667 year, Open circles represent actual data; filled circles"^represent linearly interpolated data.

PAGE 109

40.0 30.0 X 20.0 10.0 0.0 3C 454.3 o • •o • *o o oo o O 'O oo o •ooo o oooo o o CO o • 19.0 17.0 MAGNITUDE 15.0 Figure 28. 3C 454.3. Radio flux vs optical magnitude using all the optical and radio data, with At = -1.2 year, At^ =0.1 year. Open circles represent actual data; filled circles represent linearly interoolated data.

PAGE 110

94 obtained after 1970.0. While the resultant R vs At diagram illustrated in Figure 29 has a much narrower peak of R = 0.63 at a At of about -1.2 years than does Figure 25, the two plots are quite similar. Both plots show the same general character for -6.0 < At < +0.0; for At > 3.0 years, Figure 29 deteriorates into the edge effect suggested by the top half of Figure 25 for At > 4.0 years; however, the character of the two plots is quite different for 0.0 < At < 3.0 years. Since both the radio and optical records show comparable activity, the similarity between Figures 25 and 29 is not really surprising. When one considers that by deleting the radio data prior to 1970.0, approximately a third of the radio data have been ignored, the deterioration of the analytical correlation for this case cannot be given much weight As a check of the analytical correlation procedures, the Dent 1.9-cm and Algonquin 2.8~cm radio curves illustrated in Figure 30 were correlated, with the higher-frequency 1.9-cm data assuming the role of the optical record. The results plotted in Figure 31 indicate a 0.97 correlation coefficient for the 1.9-cm data leading the 2.8-cm data by approximately 0.1 year, which is the qualitative result expected from the simple expanding source model. The long decline in the value of R from At = 0.5 to 3.0 years is most likely the result of a combination of the lack of 1.9-cm data corresponding to the first dominant 2.8-cm flare and the varying alignment of that dominant 2.8-cm flare with the smaller 1.9-cm flares from 1970.5 to 1974.-5.

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95 R 0.0 R 0.0 -2.0 0.0 2.0 At (years) Figure 29. 3C 454.3. Normalized cross-correlation coefficient (R) vs time shift (At) for all the optical data but only the radio data obtained after 1970.0, using actual data (top) and interpolated data (bottom) with At = At = 0.1667 year.

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Ar CSD CO CZD CO CO to CO *^ c n3 ^ 1 — 1 CO CLI 31 r-cm obs vat ion CD 1 u cvj 0^ QJ • m r-l ^ r-ij 1 1 1 c e h— 0) u T — CD Q 1 CO r-454.3. qiiin 2 o c CJ C=} en so r-^ < CD aj CTD u ^-. CO 3 a. M c CO CO CO CO CO CnJ LO AP CO CO CO CO CO CO

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97 1.0 .5R 0.0 -0.5 i i 1 •, 1 1 e • 3C 454.3 • • 9 <9 • e e • e o e a e • a e • • • 9 • • 1 1 1 R 0.0 0.0 At (years) Figure 31. 3C 454.3. Normalized cross-correlation coefticient (R) vs time shift (At) for the two radio records of Figure 30, using actual data (top) and interpolated data (bottom), with At = At = 0.1 year.

PAGE 114

93 BL Lac Examination of the optical and radio curves in Figure 32 indicates no obvious overall correlation except that both show numerous, similar rapid events on a time scale of months. The plot of R vs At in Figure 33, for At = At = 0.1667 years, superficially resembles a scatter diagram, but it nevertheless shows a general trend toward a maximum centered at about At = -0.5 year that may be indicative of a long-term correlation that is obscured by the almost incessant flickering. The unusually short time scale of the variability, coupled with the unavoidable gaps in the optical data, make BL Lac difficult to analyze in a definitive manner. It should also be emphasized that the analysis attempted thus far is merely a linear correlation; the trend toward a maximum in Figure 33 may indicate that a different, non-linear relationship exists which would be sharpened by the appropriate type of analysis. Finally, it should be noted that the choice of At^ and At„ used to obtain Figure 33 was not based on the criteria reviewed earlier, but rather on the basis of what values seemed better to illustrate the trend towards a maximum correlation coefficient. The time resolution of the data actually supports values of At^ = At^ = 0.0625 years, which were used to obtain Figure 3A. Vlhile these latter plots have many more points, the general character of the R vs At relation does not differ between Figures 33 and 34.

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99 O CO o o CD ^. .-Ji^E;. -^< O H Q. O < o O O U5 O CD t o ^ tri : — 1 >CU N U-4 ra cn QJ < lO, G •H rC X • U > iJ r^ CO i_) a 'D O -o cn J-i ; j r; -H, cr\ Tj d 4-1 ;-j — a >. c^ r^ QJ > ^ 4_J Tl ci ^ O !^ 5 Vj cu XI a) o .1) U5 CJ Cfi '4-i • P3 P r-. -a -Q sD [^ 0) c 4-) 1^ O 4-J *J g ^ O o ^ 0) r^ aD 1 — i O a^ OJ &. CO ^ •"* *J r^ H H o 'J Oj rH r^ C^i — 1 lO Zj M O5 ro 3 cr QJ 1^ QJ N c c rH 0) U "^ X! >H a r^ CD '4H •^ cu a> ccj c 4-1 cr !-) H tu '11 Q r^ o ^ cti QJ r^ ^ u 4-J J3 M ^ O ca Q) 1 — ^ !-J M T3 cn > < i^ ^ c^ cn CM< ^ c^ rt cn o ij NQ c ^ ^ •H CO CO 'QJ s 'XJ Cvi a o • cn ^ 'O r^ = • O — 1 0) QJ o r-C3 C3 M M o 0) 1 cr\ 4-1 o -U •H ^ 'H • — 1 n •H ;d •H "C O +-1 ""O J_) H ^ (U o CJD C y] !-J t — i C tJ O C r^ >-, cS u •-I u Q !m QJ >, QJ 3 ^ N o s ^ CO •H • s Oi c^ '-1^ ; r^ 'J c CJ S U_J 1 1 £ Cj u cn r\ Q ^ o o Ct! U l^ cJ y K iJ 1) r^ hJ -J 03 > ccj C3 QJ CQ '^ -13 ^ QJ iJ f" O 3 a Cu iJ r-H 5 rH o ^ "TD d • CIj CTJ "^ Cu i+j K O^l a CO U J= rn •H H QJ 'J u o 4-J CJ •H >, i) p ^ r-r~. ^"^ r^ "> 4J S £ .— i •^ ^ V.D 23 0) Od to GJ QJ C^ cr GJ c •H rc ^ T-\ QJ ^ QJ o r^ H u 4J ^-^ CD CI -XJ ci to (J) BaniiNOViAj

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100 0.5 R 0.0 -0.5 1 i 1 1 i 1 BLLAC • • • • • • • a • • •• • 1 • • a 9 t — • • e 9 m • i • 1 1 1 1 R -6.0 -4.0 -2.0 0.0 2.0 At (years) Figure 33. BL Lac, Normalized cross-correlation coefficient (R) vs time shift (At) for the optical and radio data presented in Figure 32, using actual data (top) and interpolated data (bottom), with At, = At = 0.1667 year.

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1.0r 0.5 BLLAC R 0.0 -0.5 -1.0 1.0r 0.5 R 0.0 -0.5 -1.0 6.0 -4.0 -2.0 0.0 At (years) 2.0 4.0 6.0 Figure 34. BL Lac. Normalized cross-correlation coefficient (R) vs time shift (At) for the radio and optical data presented in Figure 32, using actual data (top) and interpolated data (bottom), with At = At = 0.0625 year. o

PAGE 118

102 CTA 26 (PKS 0336-01) A preliminary examination of Figure 35 suggests little correspondence between the optical and radio data, but the crosscorrelation analysis results illustrated in Figure 36 show a distinct maximum for a radio time lag of about one year. Closer examination of the optical data reveals that if one averages points, there is a roughly 2.0to 2.5-a bump between 1970.0 and 1972.75 that correlates with a major radio event centered at 1972.2. If the correlation is real it would mean that, although the event happened later at radio wavelengths, both the radio intensity and the optical intensity (not optical magnitude) rose by the same amplitude (a factor of 1.8 above the "base" level), but the radio peak probably had a smaller half-width. This is in contradiction to what one would expect from a naive extrapolation of the simple expanding source model. Regression plots for At = 0.0 and -1.125 years, Figures 37 and 38, indicate that there is a tighter grouping of points and therefore a better defined flux to magnitude relationship for the latter value of At; but this is simply a result of the apparent correlation indicated in Figure 36. The entire correlation is of course a "one-event" correlation and is unimpressive because of the relative lack of activity at optical wavelengths PKS 0405-12 Figure 39 shows little significant optical or radio structure except for the peculiar change in radio level at approximately 1969.6.

PAGE 119

17.0 UJ Q ^18.0 CD 19.0 OPTICAL RADIO J III ll |l H I i,"i'i ir ri 1 J I I I I L I I llll li j_ L ,1 1 i I I I L 1967.0 68.0 5.0 4.0 3.0 2.0 69.0 70.0 71.0 ^„^^ 72.0 73.0 74.0 75.0 76.0 DATE Figure 3.5. CTA 26 (PKS 0336-01). Rosemary Hill photographic magnitudes and Algonquin 2.8-em observations. o

PAGE 120

].5 R 0.0 10^ CTA26 • t> 9 e • -0.5 I ffi -1.0 1.0 0.5 ].5 ) 4 4 O O O 9 A e -4.0 -2.[ 0.0 At (years) 2.0 4.C Figure 36. CTA 26 (PKS 0336-01). Normalized cross-correlation coefficient (R) vs time shift (At) for the optical and radio data presented in Figure 35, using actual data (top) and interpolated data (bottom), with At^ = At^ = 0.125 year. 1 J

PAGE 121

105 MAGNITUDE Figure 37. CTA 26 (PKS 0336-01). Radio flux vs optical magnitude for the data presented in Figure 35, with At = 0.0 years, At]_ = 0.1 year. Open circles represent actual data; represent linearly interpolated data. filled circles

PAGE 122

L06 X u.u — CTA26 — 8.0 6.0 4.0 2.0 nn I • o o o o o e • o 9 • • o •oo •o • •o o 1 1 1 19.0 17.0 15.0 MAGNITUDE Figure 38. CTA 26 (PKS 0336-01). Radio flux vs optical magnitude for the data presented in Figure 35, with At = -1.125 year, At^ =0.1 year. Open circles represent actual data; filled circles represent linearly interpolated data.

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14.0r Q ID tis.o o < OPTICAL 6,0 RADIO I l___™-i19670 68.0 + + + 4i + -fH + + + I M 111 I I It I HI J I 1 L 69.0 70.0 DATE 71.0 72.0 3.0 2.0 >1.0 .J___J73.0 74.0 Figure 39. PKS 0405-12. Royal Greenwich B magnitudes and Algonquin 2.8-cm observa Lions. I--' o

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108 The top half of Figure 40 thus gives a good example of the results of the correlation technique when too small a data sample is used, while the bottom half of the same figure illustrates that the interpolation technique can synthesize an apparently well-behaved R vs At relationship even when there is too little data. PKS 0420-01 There is no apparent visual relationship between the optical and radio records displayed in Figure 41. If the Rosemary Hill optical magnitudes are correlated only with the Dent 1.9-cm record which begins in 1969.7, the results in Figure 42 are rather uninteresting with no clearly defined maximum. However, if the 1-9-cm record is supplemented with the Algonquin 2.8-cm record from 1967.5 to 1969.6, a relatively clearly defined maximum correlation (0.65) is established for the optical leading the radio by 0.2 year, as seen in Figure 43. Superposition of the radio and optical records indicates that this is most likely due to some limited corresponding trends in both records. To date no definite radio counterpart to the conspicious optical flare at the end of 1974 has emerged; however, the latest 9-mm observation by Dent (1976) indicates a possible significant increase. He has not seen any increase at 1.9 cm as of this writing. 3C 120 Figure 44 shows variations on a time scale of approximately onehalf year in both the radio and optical data, but neither visual inspection nor the results of the correlation analysis in Figure 45 yield any significant correlation. The problem here is not dissimilar to that of

PAGE 125

109 1.0 0.5 R 0.0 -0.5 -1.0 1.0 0.5 R 0.0 -0.5 -1.0 i 1 1 I -^ 0405 12 • • • • • • — • • • t • • • • • • I 1 1 1 1 -4.0 -2.0 2.0 4.0 At (years) Figure 40. PKS 0405-12. Normalized cross-correlation coefficient (R) vs time shift (At) for the optical and radio data presented in Figure 39, using actual data (top) and Interpolated data (bottom). with At. At, 0.1 year,

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Figure 41. PKS 0420-01. Rosemary Hill photographic magnitudes and radio flux. The radio record consists of Algonquin 2.8-cm data from 1967.7 to 1969.7 and Dent 1.9-cm data from 1969.7 to 1975.5; the dashed vertical line indicates the transition between the two sets of data.

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17.0 Q 1 18.0 19.0 OPTICAL kki\ \ h 't'||',i; RADIO J__ 1 \ __i„ i 1 I M^Mu^^ l.+ i ^ t I J 1 _1__._L .1 L 3.0 2.0^ .0 1968.0 69.0 70.0 71.0 72.0 73.0 74.0 DATE 75.0 76.0

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112 1.0 0.5-0.51 • • • • • e, • • • • • • • • • 1 1 1 0420 01 • • • • • • • • • • • . • • • • • • • • • • • • 1 t. -i.. o • • • 1 • 1 1 1 0.0 At (years) 4.0 Figure A2, PKS 0420-01. Normalized cross-correlation coefficient (R) vs time shift (At) for all the optical but only the Dent 1.9-cm data in Figure 41, using actual data (top) and interpolated data (bottom), with At, = At = 0.1 year.

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113 1.0 0.5 -0.5 -1.0 R 0.0 -0.5 -1.0 0420 01 •• • 1.0 r 0.5 -4.0 ••••••• -U 0.0 At (years) 2.0 4.0 Figure 43. PKS 0420-01. Normalized cross-correlation coefficient (R) vs time shift (At) for all the optical and radio data presented in Figure 41, using actual data (top) and interpolated data (bottom), with At = At =0.1 year.

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Figure 44. 3C 120. Optical and Algonquin 2.8-cm observations. The optical record consists of Klnman (1968) B magnitudes from 1967.1 to 1968.1; Royal Greenwich B magnitudes from 1967.9 to 1970.2; Rosemary Hill photographic magnitudes (corrected to B magnitudes) from 1969.9 to 1971.7; and Rosemary Hill B magnitudes from 1971.8 to 1975.9. Both the Kinman and the Royal Greenwich B magnitudes were reduced with a Kinman sequence and have been plotted with an offset of -0™125. Rosemary Hill used a combined sequence from Kinman (1968) and Angione (1971)

PAGE 131

!4.0 OPTICAL UJ Q I' CD < 5 *^i n 5.0 + 16.0 + + It H tH: fe fe •f, lit RADIO 1^1 n ^i 11^ i ^^* V^.,^ ..I *^^iHi I ( I +\ H4 f |l%. — -J— i J 1 1 \ 1 I I I I I I 18.0 12.0 >6.0 1967.0 68.0 69.0 70.0 71.0 72.0 73.0 74 75 760" DATE \

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Figure 45. 3C 120. Normalized cross-correlation coefficient (R) vs time shift (At) for the optical and radio data presented in Figure 44, using actual data (top) and interpolated data (bottom), with At = At„ = 0.0833 year.

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R 1.0 0.5 0.0 -0.5 -1,0 1.0 0.5 R 0.0 -0.5 -1.0 1 1 • 1 1 1 1 1 3C 120 • 9 ~ • • •• • 9 • • 1 1 • •• • "... • '. •• .. • • .. ''. • • • • • 1 1 1 1 1 • 999 • -•••••a • a •6.0 4.0 -2.0 0.0 At (years 2.0 4.0 6.0 1-'

PAGE 134

118 BL Lac, in that a multitude of brief events creates so many potential correlations that none is convincing. However, the values of R for 3C 120 do not even show a trend toward a maximum which appears to exist in BL Lac. NRAO 190 (PKS 0440-00) The record of optical and radio data in Figure 46 as yet exhibits no radio counterpart to the approximately 1. 5-magnitude drop and subsequent violent optical flare observed between 1972,75 and 1976.0, nor any obvious visual relationships between the two sets of data. The cross-correlation calculations are similarly uninteresting, exhibiting no significant maxima. This is illustrated in Figure 47 where only the Dent 1.9-cm radio data was used, and in Figure 48 where the 1.9-cm data record was supplemented by Algonquin 2.8-cm data from 1966.9 to 1969.0. Again these last two figures give an indication of how the R vs At olots change as more data are used. Clearly it would be of interest if the 1976 radio observations reflect the unusually sharp optical spike in late 1975, but as of June 28, 1976, Dent (1976) has seen no significant increase in the 1,9-cm flux level, PKS 0458-02 In Figure 49, the relatively sparse and featureless optical data show no counterpart to the double radio flare centered at 1972.75. The R vs At plot for the hole technique, displayed at the top of Figure 50, has the scatter diagram appearance characteristic of an insufficient number of data points; however it is of interest to note that the bottom

PAGE 135

17.0 LiJ Q H o OPTICAL 8.0 19.0 li |l tl' l' (l| RADIO III! '\ I t. \\ i^w ^;* 0^ u M^^ i** i I .0 2.0 ^ .0 J I L J I L J L 1967.0 68.0 690 70.0 71.0 72 DATE 73.0 74.0 750 760 Figure 46. NRAO 190 (PKS 0440-00). Rosemary Hil.l photographic magnitudes and radio flux. The radio record consists of Algonquin 2.8-cm data (offset by -0.3 Jy) from 1966.9 to 1969.8, and Dent 1.9-cm data from 1970.0 to 1975.5; the dashed vertical line indicates the transition between the tv/o sets of data.

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120 0.5 R 0.0 -0.5 -1.0 1.0 0.5 R 0.0 -0.5 -1.0 -6.[ NRAO 190 O 9 9 -4.0 -2.0 0.0 At (years! 2.0 4.0 6.0 Figure 47. NRAO 190 (PKS 0440-00). Normalized cross-correlation coefficient (R) vs time shift (At) for all the optical data but only the 1.9-cm radio data presented in Figure 46, using actual data (top) and interpolated data (bottom), vrith At =At =0.1667 year

PAGE 137

121 1.0 0.5 R 0.0 -0, -1.0 1.0 0.5 h R 0.0 -0.5 -1.0<> — o a NRAO 190 • • -6.0 -4.0 -2.0 0.0 At (years) 2.0 4.0 6.0 Figure 48, NRAO 190 (PKS 0440-00). Normalized cross-correlation coefficient (R) vs time shift (At) for all the optical and radio data presented in Figure 46, using actual data (top) and interpolated data (bottom), with At = At^ = 0.1667 year.

PAGE 138

18.0 UJ Q < 9.0 20.0 OPTICAL t 1 It RADIO il t t^ i I t'l| I HlfVllnl ,i"'„"' 11 It it J... I _jI I I I I I L__ J1 L 1968.0 69.0 70.0 71.0 72.0 73.0 74.0 DATE h I'M 3.0 2.0^ 1.0 75.0 76.0 Figure 49. PKS 0458-02. Rosemary Hill photographic magnitudes and Algonquin 2.8-cm observations.

PAGE 139

I.U 1 1 1 1 0458 02 1 1 ft 0.5 • • • • • • • • ft ft — • ft R 0.0 -0.5 • ft • ft • ft • • • • • • ft • • ft • • ft • • • • • • ft ft • • • ft • • • • • • ft • ft ft • m • -1.0 ""i • 1 1 1 ft — 1 1 I.U 0.5 ft .. ft ft • ft • • • R 0.0 -0.5 ft ft ft • ft • ft ft ft • ft • • ft • •ft ft • • '%• • • ft • • ft • ft • • ft ft ft ft • • ft ft -1.0 1 1 1 1 1 1 1 B.0 -4.0 -2.0 0.0 2.0 4,0 6.0 At (years) Figure 50. PKS 0458-02. Normalized cross-correlation coefficienL (R) vs time shift (At) for all the optical aud radio data presented in Figure 49, using actual data (top) and interpolated data (bottom), with At = At = 0.125 year.

PAGE 140

12.4 half of Figure 50, resulting from the interpolation technique, has molded the sparse data into an apparently well-behaved R vs At relation, with a maximum correlation coefficient of 0.63 at a At of -1.0 years. This is most likely a spurious result caused by the sparse sampling of the optical activity and resultant similar trends between the optical and radio records. While it is possible that the correlation indicated by the interpolation technique is real, it will require a higher timeresolution documentation of optical activity to establish the validity of such a correlation. 3C 138 (PKS 0518+16) An examination of Figure 51 indicates that there is little data overlap for any correlation investigation, except in the highly unlikely case that the radio leads the optical. Moreover, the optical observations show considerable activity xvhile the radio record is nearly featureless. The analytical correlation again shows a scatter diagram for the hole technique and an apparently well-behaved R vs At relation resulting from the interpolation technique, as shown in Figure 52. The maximum correlation coefficient of 0.70 determined from the interpolation technique is based on only seven radio measurements that indicate a slight rise that coincides with the optical event centered at 1972.0, for a At of -1.1 year. This then could be considered a weak one-event correlation. The secondary maximum of 0,60 at a At of +1.0 year uses more radio data, but there is a gap in the radio coverage during the optical flare centered at 1974.0. Thus more radio data will need to be included in the analysis before any significance can be given to the results of the interpolation technique.

PAGE 141

18.0 u a CD 9.0 200 OPTICAL I It i II 111 RADIO (it lH''''t|'l III '|l 11 I 'i „ll I I 'I'll 3,0 2.0 1967.0 68.0 69.0 J I 1 I I 70.0 71.0 72.0 DATE J L 73.0 74.0 75.0 76.0 1.0 Figure 51. 3C 138 (PKS 0518+16). Rosemary HJ 11 photographic magnitudes and Algonquin 2.8-cm observations. ISO

PAGE 142

Figure 52. 3C 138 (PKS 0518+16). Normalized crosscorrelation coefficient (R) vs time shift (At) for the optical and radio data presented in Figure 5]., using actual data (top) and interpolated data (bottom), with At = At = 0.125 year.

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1.0 0.5 R 0.0 -0.5 -1.0i 1 1 1 1 1 1 3C 138 ft ft ft • ft — ft •• ft • ft ft ft ft ft ft • ft • ft ft • • • •• ... ft • ft • ••. ft • • ~ 1 ft ft ft* — 1 1 1 II 1 0.0 At (years)

PAGE 144

128 PKS 0735+17 Figure 53 displays the full 1.9and 2.8-cm data records, which were analytically correlated as a test of the correlation procedures. The resulting R vs At plots are shown in Figure 54, where the correlation coefficient reached a maximum value of 0.91 at At = -0.125 year for both the hole and the interpolation precedures. The optical and composite radio records illustrated in Figure 55 show optical variations on a very short time scale, whereas the radio variations appear more as gentle, long-term undulations. For a complete study, the optical record was analytically correlated first with the 2.8-cm record. The results plotted in Figure 56 are not very convincing due to the scatter, the suggestion of a double maximum, and the relatively low value of the maximum correlation coefficient which reaches a value of 0.52 at At = -rO.5 years and At = -0.4 years for the hole and interpolation procedures respectively. However, it should be noted that the 2.8-cm record stops at the beginning of a long 2-year rise documented in the optical and the 1.9-cm records. Next the 1.9-cm record was correlated with the optical record, with the results plotted in Figure 57. In this case, the maximum correlation coefficient reached a value of approximately 0.71 at At = 0.9 years and 0.59 at At = 0.7 years for the hole and interpolation procedures respectively. Finally, the results from correlating the optical record with the composite 1,9and 2.8-cm record are presented in Figure 58, where the maximum coefficient reaches values of approximately 0,72 ac At = 0.9 years and 0.60 at At = 0.7 years for the two techniques.

PAGE 145

3.0 ^ 2.0 1.0 0735 + 17 ^ ^ Ml S h K S f ^ w ^ t ^ 'f it.? it Ht ti Kk) '* (I ft|i,i,;(\ttt*)r"ts t|'M|fl|H I I I 1) l( 3.0 2.0 1.0 >1967.0" 68.0 69.0 70.0 71.0 72.0 73.0 74.0 75.0 7B.0 DATE Figure 53. PKS 0735+17. Dent 1.9-cm observations (top) and Algonquin 2.8-cm observations (bottom). ho

PAGE 146

130 1.0 0.5 R 0.0 -0.5 1 1 .1 1 1 0735 + 17 • • • • ••• •• • • • • • • • • • • • • • • • • • 1 1 1 1 1 0.0 Atlyears) 2.0 4.0 Figure 54. PKS 0735+17. Normalized cross-correlation coefficient (R) vs time shift (At) for the two radio records in Figure 53, using actual data (top) and interpolated data (bottom), with At = At = 0.125 year.

PAGE 147

I 4 Or UJI50 Q 2 1 6.0 OPTICAL t I i 17.0 RADIO .til 4i,i !' I, "'ii^i 1, 'h'. \ h i^ I /.0 19670 680 69.0 70 710 72 73 74.0 75.0 76.0 DATE Figure 55. PKS 0735+17. Rosemary Hill photographic magnitudes and radio flux. The radio record consists of Algonquin 2.8-cm data from 1966.9 to 1970.2, and Dent 1.9-cm data from 1969.6 to 1975.6. The dashed vertical line indicates the transition to 1.9-cm data alone.

PAGE 148

132 I.U 1 1 1 0735 + 17 0.5 • • • • • • • • • — R 0.0 • • • • • • • • • • • • • • ft -0.5 • • • ft • • • ft • ft ft • 9 • • • • -1.0 1 1 • • 4 *• 1 1 1 1 R 0.0 -4. -2.0 0.0 At (years) 2.0 Figure 56. PKS 0735-M7. Normalized cross-correlation coefficient (R) vs time shift (At) for all the optical data but only the 2.S-cm radio data, using actual data (top) and interpolated data (bottom), with At, = At = 0.125 year.

PAGE 149

133 I.U 0.5 -^ r • • • • • 1 1 0735 + 17 • 0.0 • • • 0 • • • • • • • • • -0.5 — • • • • • — • • -1.0 — • • • a 1 1 a • 1 1 1.0 0.5 R 0.0 -0.5 -1.0 •• •• • • t e • ft V • •• • • •• •• -4.0 -2.0 0.0 At (years) 2.0 4.0 Figure 57. PKS 0735-1-17. Normalized cross-correlation coefficient (R) vs time shift (At) for all the optical data but only the 1.9-cm radio data, using actual data (top) and interpolated data (bottom), with At, = At = 0.125 year.

PAGE 150

134 1.0 0.5 R 0.0 0735 + 17 -0.5 -1.0 L I.Or 0.5 R 0.0 -0.5 -1.0 o • B • • e • -4.0 -2.0 0.0 At (years) 2.0 4.0 Figure 58. PKS 0735-1-17. Normalized cross-correlation coefficient (R) vs time shift (At) for all the optical and radio data in Figure 55, using actual data (top) and interpolated data (bottom), xvith At^ = ^t^ = 0.125 year.

PAGE 151

135 While the last two R vs At plots seem to indicate a potentially significant correlation, it must be remembered that this correlation occurs for the theoretically unlikely condition of the radio leading the optical. This correlation is caused by the 1970.2 to 1975.2 radio "trough" aligning with what could be argued is a similar long-term optical trough about which the optical data flicker. VJhile a plot of 1.9-cm radio flux vs optical magnitude for At = 0.8 year indicates a possible weak functional relationship in Figure 59, the character of the plot does not differ noticeably from the same plot for At = 0.0 shoxm in Figure 60. VJith the present data, this can probably be considered a "one-event" correlation, and thus less than completely convincing. PKS 0736+01 Both the radio and the optical data records plotted in Figure 61 exhibit significant activity with events in both domains on a time scale of the order of a year; however, neither visual nor linear analytic correlations could be found. It is interesting to note the change in character of the S. vs At plots between Figure 62, in which only the 1.9cm data were used, and Figure 63, in which 2,8-cm data from 1967 to 1970.5 were used to supplement the 1.9-cm data. The scatter in the top half of the figures is reduced while the excursions from zero in the bottom half are increased in amplitude. This latter effect is probably due to the greater amplitude radio flares recorded prior to 1970,5. 01 363 Figure 64 shows nearly featureless records for both the optical and the radio data, except for a possible monotic long-term optical rise of

PAGE 152

136 X MAGNITUDE Figure 59. PKS 0735+17. Radio flux vs optical magnitude using all the optical data and the 1.9-cin radio data, with At = 0.8 year, At]_ = 0.1 year. Open circles represent actual data; filled circles represent linearly interpolated data.

PAGE 153

137 X 17.0 15.0 MAGNITUDE Figure 60. PKS 0735+17. Radio flux vs optical magnitude using all the optical data and the 1.9-cra radio data, with At = 0.0 year, At]_ = 0.1 year. Open circles represent actual data; filled circles represent linearly interpolated data.

PAGE 154

Figure 61. PKS 0736+01. Rosemary Hill photographic magnitudes and radio flux. The radio data consists of Algonquin 2.8-cm data from 1966.8 to 1970.5, and Dent 1.9-cm data from 1970.6 to 1975.6, The dashed vertical line indicates the transition between the two sets of data.

PAGE 155

15.0 Q tie.o CD 17.0 OPTICAL Vi *f, H 'I ,f, I 1 RADIO I y 1 1, t" 3.0 2.0 .0 >J L J L__j L 19670 68.0 69.0 70.0 71.0 72.0 DATE 73.0 74.0 75.0 76.0

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140 1.0 0.5 • • 0736+01 R 0.0 -0.5 • • -1.0 1.0 0.5 R 0.0 -0.5 -1.0 -4.0 -2.0 0.0 At (years) 2.0 4.0 Figure 62. PKS 0736+01. Normalized cross-correlation coefficient (R) vs time shift (At) for all the optical data but only the 1.9-cin radio data, using actual data (top) and interpolated data (bottom), with At = At = 0.125 year.

PAGE 157

141 0.5 R 0.0 -0.5 0736+ 01 • • 0.5 R 0.0 -0.5 -1.0 -4.0 -2.0 0.0 At (years) 2.0 4.0 Figure 63. PKS 0736-f-Ol. Normalized cross-correlation coefficient (R) vs time shift (At) for all the optical and radio data presented in Figure 51, using actual data (top) and interpolated data (bottom) with At 1 At^ = 0.125 year,

PAGE 158

15.0 LU Q ID ^16.0 o < 7.0 OPTICAL ^tl A \ RADIO I't'll lllll'll |l'|l"lll I II 1, 1 1 il||i ii|l| 3.0 2.0^ .0 1967.0 68.0 69.0 70.0 71.0 72.0 73.0 74.0 75.0 DATE 76.0 Figure 64. 01 363. Rosemary Hill photographic magnitudes and Algonquin 2.8-cra observations. N3

PAGE 159

143 072 and a small wandering of the radio baseline, both of which are in the formal sense statistically insignificant. The R vs At plot in Figure 65 yields a scatter diagram for the hole technique, but with primarily negative coefficient values that may result from opposed small slopes. OK 290 Visual inspection of the radio and optical records plotted in Figure 66 shows some evidence that the optical events characteristically have a shorter time scale, and reveals a possible correlation for At = -1.25 years that becomes easier to see when the two records are superimposed on one another with that time delay. However, the family of calculated correlation coefficients from the hole technique, seen in Figure 67, x^^anders with some scatter which begins to have the appearance resulting from too little data. The interpolation technique results in clearly defined maxima of approximately R = 0.87 for the optical leading the radio by about 4.0 years and R = 0.62 for the radio leading the optical by about 1.6 years. Superposition of the radio and light curves indicates that the former is caused by the alignment of the 1971.0 1972.0 optical rise with the 1975.0 1976.0 radio rise, while the latter is probably caused by correspondence of random trends. Thus the linear correlation technique offers no support for the suggested visual correlation.

PAGE 160

144 l.U 01 363 0.5 • • • R 0.0 -0.5 • • • • • • •••... • • • • -1.0 • • 1 1 1 1 1 0.5 R 0.[ -0.5 1.0 • • • -4.0 -2.0 0.0 At (years) 2.0 4.0 Figure 65. 01 353. Normalized cross-correlation coefficient (R) vs time shift (At) for the optical and radio data presented in Figure 64, using actual data (top) and interpolated data (bottom) with At. At, 0.125 year

PAGE 161

145 a m CO S 1-4 M "n O iJ J-i rt > ^ n C-^ (U m rH ^ iH o H ffi e a l>i 1 U CO W • s o-i 0) m c n •H Pi ;3 cr > o o &D rr\ ^ CN
PAGE 162

146 1.0 OK 290 0.5 R 0.0 e 9 a -0.5 -1.0 1.0 0.5 R 0.0 -0.5 • -1. -4.0 -2.0 0.0 At (years) 2.0 4.0 Figure 67. OK 290. Normalized cross-correlation coefficient (R) vs time shift (^t) for the optical and radio data presented in Figure 65, using actual data (top) and interpolated data (bottom) with At 1 ii L 0.125 year.

PAGE 163

147 3C 273 The full 1.9and 2.8-cm data records presented in Figure 68 were linearly correlated as another test of the analytical procedures, with the resultant R vs At plots shown in Figure 69, where the maximum coefficient reaches a value of approximately 0.87 for At -0.125 year for both procedures. The close correspondence in the character of Cent's 1,9-cm variations with the variations recorded by Algonquin's 2,8-cm data led to the inclusion of 1.9-cin data from Alien et al. (1968) to show that this wellknown source had undergone a steep rise in its radio flux in the mid1960' s, as illustrated in Figure 70. Due to the lack of overlap between the Allen data and the other two sets, an offset of -19.0 flux units was applied to this early 1.9~cm data purely for the cosmetic purpose of matching its termination with the beginning of the Algonquin 2,8-cm coverage. After its initial steep rise the radio data shov7 variations that might be interpreted as roughly periodic (a very controversial topic, in particular for the optical record, as the literature demonstrates), and which are similar to the cyclic nature of the optical data. But a number of the later radio cycles occur during what appears to be, within the limits of the observations, a nearly quiescent optical era. The maximum cyclic amplitudes of both the radio and optical intensities are comparable; each increases by a factor of about 1.4. The calculation of the correlation coefficients using only the Algonquin 2.8-cm data, or the Algonquin 2.8-cm data and the Dent 1.9-cm data, yields a spurious one-event maximum due to the alignment of the 1966,7 to 1969.5 radio trough with the 1968,0 to 1971.3 optical trough,

PAGE 164

145 Ar CD CO CD CD CO CsJ CO -^^4;p^ CO LO " ij M 4-1 OJ m r> ^ Vw^ S c o o 1 •H CT> JJ • Cit >H > u J-J 0) H M CU rQ c • U c^ ; t~~ CO c^ CN U ro r^ •H • cr 00 o (K) OJ rH !-i < D M TJ •r-f c f^ nj

PAGE 165

Figure 69. 3C 273. Normalized cross-correlation coefficient (R) vs time shift (At) for the radio data presented in Figure 68, using actual data (top) and interpolated data (bottom), with At^ = At„ = 0,0833 year. iiin-< fti w:i ii

PAGE 166

150 1.0 9 m 9 3C 273 0.5 R 0.0 9 9 -0.5 -1.0 1.0 r0.5 R 0.0 0.5 a e e 9 a e -1.0 -2.0 -1.0 0.0 1.0 2.0 At (years!

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Figure 70. 3C 273. Optical and radio observations. The optical record consists of 100day averages of photoelectric B magnitudes (Kunkel 1967) from 1962.0 to 1967.2, and Burkhead (1968, 1969, 1970, 1971, 1972, 1975) photoelectric B magnitudes from 1968.1 to 1975.3. Royal Greenwich photographic B magnitudes (offset by -0?17) generally allign with these data, but have not been included. The radio record consists of 1.9-cm data from 1964.0 to 1966.3 (Allen e_t al. 1968); Algonquin 2.8-cm data (offset -3.0 Jy) from 1966.5 to 1969.5; and Dent 1.9-cm data from 1969.5 to 1975.5. The dashed vertical lines indicate the transitions between the data sets.

PAGE 168

I2.6ru §12.8 gl3.0 < ^13.2 OPTiCAL '.V ? t *, RADIO 60.0 r'l II l(!il,il!|i^ fi^i ihii ) :.'.' "('Ill'',;' '-S,, < 40.0 >•-3 20.0 1962.0 I I I II I I I 1 — L__ 64.0 66.0 68.0 -L__-J_ JL. J 1 J L DATE 70.0 72.0 __J___l L_ 74.0 76.0 U1 K3

PAGE 169

153 as illustrated by the R vs At plots in Figures 71 and 72. Inclusion of the initial steep radio rise recorded at 1.9 cm obviously invalidates the correlation, as can be seen in Figure 73. The maximum that then appears for the radio leading the optical by about 4.7 years is caused by an approximate alignment of the cyclic trends in the optical and the radio curves. It should be noted that the plotted optical data, prior to 1958.0, represent 100-day averages. These averages maintain a cyclic m character, with a maximum amplitude variation of 0.4 from an average m magnitude of 12.75, that has been traced back to 1887 (Kunkel 1957). Thus there is no optical counterpart to the catastrophic radio outburst between 1964 and 1966.5, and any correlations which arise must be attributed to the approximately cyclic nature of both records unless and until there is a unique correlated event in both the radio and the optical observations. PKS 13544-19 As might be anticipated from the nearly featureless optical record in Figure 74, there is no apparent optical-radio correlation, and the linear correlation procedures produce no results of interest, as can be seen in Figure 75. The only significant radio feature is a raonotonic rise beginning about 1971.0, which aligns with a gradual rise in the optical level between 1969.0 and 1972.0 to cause the broad maximum in the R vs At plots. One might make a weak argument that this is a correlation, but at most it is a one-event correlation.

PAGE 170

1.0 0.5 R 0.0 -0.5-1.01.0 0.5 R 0.0 -0.5 -1.0 1 1 to • 9 3C 273 •• • • • *• • • • • ••• •• • • • ••• *. *. ...... ... ^ • *. 1 1 • 1 III 1 .. -6.0 • ^ • -4.0 -2.0 0.0 Atlyearsl 2.0 4.0 -6.0 Figure 71. 3C 273. Normalized cross-correlation coefficient (R) vs time shift (At) for all the optical data but only the Algonquin 2.8-cm data, using actual data (top) and interpolated data (bottom), with At = At =0.0833 year.

PAGE 171

1.0 0.5 R 0.0 -0.5 -1.0 1.0[ 0.5 R 0.0 -0.5 -1.0 • • • -6.0 .• •••• -4.0 -2.0 • ••• 0.0 At (years! 3C273 • M 2.0 4.0 6.0 Figure 72. 3C 273. Normalized cross-correlation coefficient (R) vs time shift (^t) for all the optical data but only the Algonquin 2 8-cra and the Dent 1.9~cra data, using actual data (top) and interpolated data (bottom), with At = At = 0.0833 year.

PAGE 172

Figure 73. 3C 2 73. Normalized cross-correlation coefficient (R) vs time shift (At) for all the optical and radio data presented in Figure 70, using actual data (top) and interpolated data (bottom), with At = At = 0.0833 year.

PAGE 173

1.0 0.5 R 0.0 -0.5 -1.0 1.0 0.5 3C 273 o • • • • • • • --• R 0.0 -0.5 •••••• 1.0 4.0 2.0 0.0 t (years 2.0 4.0

PAGE 174

1 967.0 68.0 69.0 70.0 ^'• DATE ^2 73.0 74.0 75.0 76.0 Figure 74. PKS 1354+19. Optical and Algonquin 2.8-cm observations. The optical record consists of Yale Observatory B magnitudes from 1969.1 to 1971.0, and Rosemary Hill B magnitudes from 1971.2 to 1975.5. 00

PAGE 175

Figure 75. PKS 1354+19, Normalized cross-correlation coefficient (R) vs time shift (At) for the optical and radio data presented in Figure 74, using actual data (top) and interpolated data (bottom), with At = At^ = 0.1667 year.

PAGE 176

160 1.0 0.5 R 0.0 9 e 1354 + 19 • • -O.b -1.0 1.0 0.5 R 0.0 -0.5 -1.0 • — • e • • • • • • e — — 1 i 1 1 -4.0 -2.0 0.0 At (years) 2.0 4.0

PAGE 177

161 OQ 208 While the optical data in Figure 76 show obvious flare activity, the lack of conspicious features in the radio data precludes the establishment of a correlation, which is borne out by the scatter-diagram appearance of the top of Figure 77. The most convincing radio trend is a gradual rise beginning about 1970.0; there is no evidence of this in the optical record, which is admittedly sparse. PKS 1510-08 Figure 78 reveals abundant radio activity and significant optical activity. However, in view of the short time-scale of the individual radio events (typically about six months), correlation with the somewhat sparse optical record is difficult. This conclusion is supported by the R vs At plot in Figure 79, the top half of Xirhlch resembles a scatter diagram, which is most likely due to the relatively sparse optical data. From 1967.0 to roughly 1973.0, the radio events appear to be superimposed on a long-term decline for which there is no evidence in the optical data. NP.AO 512 Visual inspection of Figure 80 suggests that the radio data follov; the optical data from the beginning of the optical record around 1970.4 to 1972.9. However, after 1972.9 the apparent correspondence deteriorates somewhat for the remaining short run of radio observations. This result is borne out by the correlation coefficients, which reach a maxim\im value of about 0.66 at roughly zero time delay for the total

PAGE 178

Figure 76. OQ 208. Rosemary Hill photographic magnitudes and Algonquin 2.8-cm observations. as

PAGE 179

0.5 R 0.0 163 OQ 208 9 • -0.5 • • S 9 -1.0 1.0,d 0.5 R 0.0 • s -0.5 4 o e 9 -1.0 -4.0 -2.0 0.0 At (years) 2.0 4.0 Figure 77. 00 208. Normalized cross-correlation coefficient (R) vs time shift (At) for the optical and radio data presented in Figure 76, using actual data (top) and interpolated data (bottom), with At^ = At^ = 0.125 year.

PAGE 180

6.0 lij o h17.0 18.0 OPTICAL II ^ RADIO I.H( ,ti*l .,, M/V'i' I I 4 i ".' i li J L J L 5.0 3.0^ .0 1967.0 68.0 69.0 70.0 71.0 72.0 73.0 74.0 75.0 76.0 Figure 78. PKS 1510-08. Rosemary Hill photographic magnitudes and Algonquin 2.8-cm observations. .0

PAGE 181

-4.0 -2.0 0.0 At (years) 2.0 4.0 Figure 79. PKS 1510-08. Normalized cross-correlation coefficient (R) vs time shift ( t) for the optical and radio data presented in Figure 78, using actual data (top) and interpolated data (bottom), with t^ = t^ = 0.1 year. Ul

PAGE 182

Figure 80. NRAO 512. Rosemary Hill photographic ] magnitudes and Algonquin 2.8-cin observations. J t

PAGE 183

6.0 r uj 1 7.0 Q t (3 :ei8.o 19.0 optical RADIO |lMtlt 1968.0 69.0 < y ifl 1 1 1 ft III /"ill, ,iiii'"i'rif^ii^ t X-___J. — i—^ L_ — J — -JJ L ll 70.0 71.0 72.0 DATE A _1 73.0 74.0 75.0 3.0 2.0^ .0 76.0

PAGE 184

optical and radio data records, as shown in Figure 81. However, when 1 optical data only through the end of 1972 are considered, the maximum value of R jumps to 0,8 0.1 for the radio record leading the optical I by 0.03 0.3 year as shown in Figure 82. While a clearly defined maximum in the population of calculated correlation coefficients supports the correlation found by visual inspection of the data, caution must be exercised in the consideration of correlations between two sets of data which show activity on a similar time scale. It is this character of the data records which gives rise to a maximum value of R 0.60 at At = +A.6 years in Figure 81, when the 1968.4 to 1970.2 radio record aligns with a similar optical trend from 1972.6 to 1974.4. Similarly, the same radio feature aligns with the optical data from about 1970.4 to 1971.5 to give a maximum R = 0.7 at At +2,0 in Figure 82 when only part of the optical data are used. 3C 371 Examination of Figure 83 suggests a possible correspondence between the prominent 1969.5 to 19 70.5 optical increase and the 1971 to 1972 radio increase. These events are separated by At -1.5 years. There is also some resemblance in the plateau regions following the increases. Unfortunately these impressions are not supported by the analytical study. The population of cross-correlation coefficients in Figure 84 basically wanders, although it does show a clearly defined, albeit relatively small, correlation coefficient of 0.55 for the radio data leading the optical by 0.5 0.8 year. This results when the 1971-1972 radio rise is superim.posed across the optical data gap around

PAGE 185

Figure 81. NEAO 512. Normalized cross-correlation coefficient (R) vs time shift (At) for all the optical and radio data presented in Figure 80, using actual data (top) and interpolated data (bottom), v^ith At = At = 0.0667 year.

PAGE 186

1.0 NRAO 512 0.5R 0.0 -0.5 -1.0 1.0 0.3t R 0.0 a 0.5 1.0 4.0 a c 2.0 0.0 At (years! 2.0 4.0 o

PAGE 187

Figure 82. NRAO 512. Normalized cross-correlation coefficient (R) vs time shift (At) for all the radio data but only the optical data through 1972.8, using actual data (top) and interpolated data (bottom), with At^ = At^ = 0.0667 year.

PAGE 188

l.Or 0.5R 0.0-0.5-1,01.00.5 R 0.0 -0.5 -1.0 • a • • • m • • • -4.0 -2.0 0.0 Atlyearsl NRAO 512 • 2.0 0.4

PAGE 189

Figure 83. 3C 371. Optical and Algonquin 2.8-cm observations. The optical record consists of Royal Greenwich B magnitudes (offset -0"'25) from 1966.6 to 1969.6, and Rosemary Hill photographic magnitudes from 1969.0 to 19 75,8.

PAGE 190

14.0 ijj Q 3 tl5.0 OPTICAL 16.0 RADIO J L f I i i \ i i 1 I i I I L_ L "II .'I' I ill w l'l,li"l'l'll/l'.\*l' ''•'' l' i*''"l|ll||H||,HtHl||,ii 1966.0 67.0 68.0 69.0 70.0 71.0 72.0 DATE J I-i_ L_ J3.0 2.0 >; 73.0 74.0 75.0 76.0 1.0 4^-

PAGE 191

175 15R 0.0 15-II o • a* • • • .' • • • • • • 1 1 1 1 i 1 -61 -4.[ -2.0 2.0 4.[ 6.0 At (years) Figure 84. 3C 371. Normalized cross-correlation coefficient (R) vs time shift (At) for the optical and radio data presented in Figure 83, using actual data (top) and interpolated data (bottom), with At = At = 0.1667 year.

PAGE 192

176 1972,25. Because the more extensive optical variability contrasts with the relative radio inactivity on either side of the radio rise, this can probably be considered a one-event correlation. It will of course be of interest to see if the particularly well-defined optical flare in mid1975 is reflected in future radio data. 3C 446 As another test of the correlation procedures, the total 1.9and 2.8-cin data records shovm in Figure 85 were correlated, resulting in the RvsAt plots illustrated in Figure 86, which show a maximum value of R = 0.92 for At = -0.3 and -0,25 years for the hole and the interpolation techniques respectively. Although the long-term radio and optical data records in Figure 87 generally follow the same trends, the very violent optical flare at approximately 1974,7 has no obvious radio counterpart to date and is thus probably responsible for the absence of a significant analytical cross-correlation in Figure 88. However, it might be argued that the radio rise beginning near 1974.7 is the event that corresponds to the optical flare. If this were the case, both the value of At and the relative amplitudes would seem to be quite different for the 1970 1971 and the 1974 1975 events, which makes the fit rather _ad hoc PKS 2345-16 Visual examination of the optical and radio records in Figure 89 seems to indicate trends that follow one another rather well for At = -0.9 year. However, the family of calculated cross-correlation coefficients shown in Figure 90 simply oscillates as a function of At,

PAGE 193

6.0 4.0 2.0 if f M* ^^ .; 3C 446 f i^ ^^ t't*,. A 6.0 4.0 >1967.0 68.0 69.0 70.0 71.0 72.0 73.0 74.0 75.0 76.0 DATE 2.0 Figure 85. 3C 446. Dent 1.9-cm observations (top) and Algonquin 2.8-cm observations (bottom).

PAGE 194

Figure 86. 3C 446. Normalized cross-correlation coefficient (R) vs time shift (At) for the two radio records in Figure 85, using actual data (top) and interpolated data (bottom), with At = At„ = 0.125 year. iiiae; -e5jp"&'* —

PAGE 195

179 .5 R 0.0 ].5 1 I 1 3C 446 S • • 9 • • • i I.Or0.5R 0.0 -1. • 9 • • • • • • .5 -2.0 -1. 1.0 2.0 A t (years!

PAGE 196

Figure 87. 3C 446. Rosemary Hill optical magnitudes and Algonquin 2 8~cm observations. The optical record consists of photographic magnitudes corrected to B magnitudes from 1969.0 to 1970.8 and B magnitudes thereafter.

PAGE 197

o CO o to o o cri o O O O UJ I< N O d O CJi < O Q. o o < o CD O CD o o O O o lO U3 CO cr>

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182 1.0 0.5 '• •— 3C 446 R 0.0 -0.5 a • -1.0 -_ inn, 0.5 R 0.0 -0.5-4.0 -2.0 0.0 At (years) 2.0 4.0 Figure 88. 3C 446. Normalized cross-correlation coefficient (R) vs time shift (At) for the optical and radio data presented in Figure 87, using actual data (top) and interpolated data (bottom), with At = At^ = 0.125 year.

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183 O CD O LO o N u •H r^ pu n) M M • o 4-1 Oj c ro ^ O N l-i cfl rH > •H iJ rn n m ;^ .Q o u o c\i e e rOJ a 1 o CO UJ C-; tCM < • c Q O -H .H a o 1 cr 1/1 c
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Figure 90. PKS 2345-16. Normalized cross-correlation coefficient (R) vs time shift (At) for the optical and radio data presented in Figure 89, using actual data (top) and interpolated data (bottom), with At = At = 0.625 year.

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185 0.5 R 0.0 -0.5 -1.0 1.0 0.5 R 0.0 -0.5 -1.0 99 • e e • • -4.0 -2.0 0.0 At (years 2.0 4.0

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186 showing no single significant maximxim for either the hole or the interpolation techniques. This behaviour doubtless results from the successive superposition of the several small peaks in each record, and the analytical method thus fails to support any single value of At, The visual correlation is nevertheless attractive enough to suggest further study. Summary In an attempt to find any relationship that might exist between various types of variability and any real or potential correlations between radio and optical activity as determined by this study, Table 5 lists all the sources studied in this work, together with their activity subclasses and a subjective evaluation of the strength of any correlation found in this investigation (a "No" of course means that no correlation was found) The evaluations result from a weighing of both the formal analysis as summarized earlier in Table 4 and a visual exam.ination of the data. The second column of the table designates the type of object as "Gal" (galaxy), "Lac" (BL Lacertae object), or "Q30" (apparently normal quasar) The activity subclasses, which have been defined previously by Dent _et al. (1974) and more specifically by McGimsey _et _al (1975), include the following. Subclass I consists of objects whose light or radio curves are dominated by rapid, short-term "flickering". Long-term trends are inconspicious and very gradual if present. BL Lac is a classic example. Subclass II is characterized by prominent, long-term variations in mean level, with minor excursions or flickering about the changing mean, as in OJ 287. Subclass III exhibits a mixture of short-

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TABLE 5 Sron-IARY OF CORRELATION ANALYSIS RELATIVE TO OPTICAL AND RADIO VARIABILITY SL^CLASSES 187 Type of Optical Radio Evaluation of Source Obiect Subclass Subclass Correlation OJ 287 Lac II II Strong 3C 454,3 QSO I II Fair BL Lac Lac I I Marginal CTA 25 QSO II III Marginal PKS 0405-12 QSO V V No PKS 0420-01 QSO IV II No 3C 120 Gal III III No NRAO 190 QSO III II No PKS 0458-02 QSO V III No 3C 138 QSO II V No PKS 0735+17 Lac III II Marginal PKS 0736+01 QSO III II No 01 363 QSO V V No OK 290 QSO III II No 3C 273 QSO II II No PKS 1354+19 QSO II II No OQ 208 Gal II III No PKS 1510-08 QSO III III No NRAO 512 QSO III II Fair 3C 371 Gal III II Marginal 3C 446 QSO III II Marginal PKS 2345-16 QSO IV II Marginal

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188 and long-term effects of comparable amplitudes with neither effect dominating, as in the light curves of 3C 120, 3C 371, and NRAO 512. Subclass IV is "episodic", consisting of objects which display long periods of relative quiescence, punctuated by shorter intervals of violent activity, as in the light curves of PKS 0420-01 and PKS 2345-16, Finally, Subclass V has been added for those objects which show little activity at all, such as 01 363. The most striking observation from. Table 5 is that of the nine sources for which some degree of correlation was suspected, seven show radio variation of a character that places them in activity Subclass II, a group that displays relatively smooth, long-term changes in level. It might, in fact, have been suspected in advance that this group would be the easiest in which to find long-term correlations. The optical variations of the nine sources are more uniformly distributed between the subclasses, with two being assigned to each of Subclasses I and II, and four to Subclass III; one of the optical variables was charactered as Subclass IV. The foregoing comments emphasize a significant observation that can be made based on the figures illustrating the combined radio and optical activities as functions of time. The radio and optical variations of a given source may display quite different characteristics. CTA 26, PKS 0458-02, PKS 1354+19, and 3C 273 (at least recently) are clearly more active in the radio region than in the optical. Conversely, 3C 138, Oq 208, PKS 0420-01, and PKS 2345-16 seem to display relatively more activity in the optical spectrum than in the radio. In the cases of 3C 454.3, NRAO 190, PKS 0735+17, and 3C 446 the records suggest that optical activity occurs on a shorter time scale than the radio events.

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189 Of the three galaxies in the table, only 3C 371 showed marginal evidence of correlation. About the same ratio of "normal" QSO's, five out of sixteen, can be described as displaying some evidence of correlation. It is interesting that all three of the objects identified in Table 5 as Lacertids were also identified as displaying at least marginal evidence of correlation between the optical and radio records; the one strong correlation, that of OJ 287, is of course for a Lacertid. While the characteristic violence and short time scale of these objects is conducive to correlation studies, caution must be exercised because the relatively frequent occurence of roughly equal-time-scale activity in both the radio and the optical can lead quite easily to spurious correlations. It should be emphasized that the linear correlation of optical mangitudes with radio flux that is presented here is intended only as a first attempt to search analytically for correlations, and negative results are not necessarily final. In general great care must be exercised in drawing conclusions from unevenly spaced time series which often involve relatively sparse sam.pling and often result in one-event correlations. While such correlations may in fact be real, not infrequently an examination of the entire data racord casts doubt on the validity of such correlations; and in general until further data indicate otherwise, the conservative approach is to regard these one-event correlations as coincidences between random processes. The closeness of the fit between the optical and radio records for OJ 287 for a period of about five years leads to the conclusion that this is indeed a real correlation. In addition, sufficient evidence

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190 exists for possible correlations in several other sources to warrant more concerted obser-^ing efforts at both optical and radio wavelengths. In those cases where no significant visual or analytical crosscorrelation was found, it is still premature to conclude that the optical and radio events are totally uncorrelated. There are at least five possible explanations for such negative results. a) Gaps in coverage have caused optical and/or radio events to go unobserved, (In most cases it is the optical record that is least complete. ) b) The activity may be correlated, but with a time lag so great that data have not been collected over a long enough period of time to establish the correlation. In view of the lengths of some of the records presented here, this becomes increasingly unlikely, c) The activity may be correlated, but with a different functional relationship between optical and radio emission than has been tested analytically here. (This should not, however, preclude the observation of visual correlations.) d) For a given source, some events may be correlated while other events appear in only one of the two spectral regions. Similarly, the time lag At might vary from event to event. In either of these cases, the search for a correlation becomes very challenging indeed. e) No real correlation exists between optical activity and radio activity.

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CHAPTER V CONCLUSIONS Spectral Energy Distributions In considering the theory and results of this study, two points regarding the spectral energy distribution of extragalactic variables need a cautionary clarification. Because this study concerns itself with sources that exhibit both optical and radio emission, the spectral energy distributions of the sources considered are generally of the form sunmarized by most of the distributions in Figure 91; that is, they exhibit a relatively low optical flux that rises into the radio spectral region. However, this is not true for all extragalactic sources; many sources do not show a rise into the radio frequencies and thus are either radio quiet or exhibit a radio flux of amplitude comparable to the optical flux. Also with respect to the spectral energy distributions, some confusion may exist regarding extrapolation of the predictions of the simple expanding source model to optical wavelengths. Figure 92 is an idealized portrayal of the spectrum of an extragalactic variable at a given time t. Curve 1 represents the contribution to the spectral energy distribution from an optically thin, adiabatically expanding cloud of relativistic electrons that has resulted from a flare event that began at some previous time. Curve 2 represents the contribution to the spectral energy distribution from another cloud of relativistic electrons that has resulted from a flare that can be observed at this time at frequencies higher than y, This second cloud is optically thick from v to the frequency v 191

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* 03 m ^3 01 0) S •H CJ c m O 4-i u 0) w 1 •H OJ 3 > rj o en O •H iH ~arj (-. W O'J M O CI. rH 0) •3 3 01 MH O to 01 j3 o H rH •~; N 0) U J-J CO J_) 3 OJ ^ jz; a CO 3 rH > o 4H to TJ m I4H CO •H H CO •H c ,3 cn >> o > c; CO l-i2 60 H •H 01 > Cfi •H k: P T3 e •H 01 s ^ !-) •H C •H iJ 'H !-J 0) i-j cn •H 4-1 CO G 0) rr f^ d +J r^ r^ CO 01 0) rv 0) 3 OJ H T3 cn (— 01 I-* f-* rH TJ ^ U CO cr 4-1 ^ 0) X U QJ 01 •H 3 U 3 M ^-1 k u S ft O rH ^ CO n, m OJ IW s 0) 01 /'-S ra iH H 3 !H 01 LO •H 0) -n 01 > r^ w 0) > ^-1 !h •H CJ\ JZ > CO o OJ 4-1 rH o "^4 p S ^ CO •H o 0) 4-1 u 4-) X M 1-1 CO H 3 • & ^ 0) OJ 01 ^. CO o +J 01 cn CO #\ !-i 01 TJ cn 01 rH J-i M-l s CO ^ u 4H CO a O •H e 4-J 30) 3 01 ^ M 0) iJ & QJ rH OJ 3 'H rH 3 M M •H ^ 0; rH O C e 0) rH 4_1 01 1-3 Tj CO 5 OJ to TS 0) !^ -3 > M -—J u 3 en CO to O 'to 03 01 CO JH S o O a 03 M f-* 3 •H •H 03 14H W M OJ T3 4-1 e w 0) ri 01 6 QJ •H o >. U •H w u 01 !-l cn M x; ft 0) u CO 3 MH ft 13 OJ e 3 J-1 QJ o o C m •ri 03 M-i. TS "3 u to cd cu U CO 3 OJ 4-1 CO !-^ 3 01 •H f, H !>. ij •H ta to 4J o% rH CJ a j-1 r^ • •H CO 3 rH to tu TS 03 U3 IK' O OJ ft > J-I 01 !-i ^f S-( •H 3 !-i 4J O 01 3 iJ cr CU 01 CO 4-J x: > 6C u 0) u M O 4-1 H •H 01 !-l 0) ,J0 u rH 3 3 pq > tw !2 O o ft to :=) p,.-'-^ ff^a^4>;'^i>'^l.^'-^

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19: 1 • i -7—1 o ^ o o CO u f Cvl u 1^^ o m i r ^ 1 1 — 1 • • • •, i 1 1 1 • • 1 i 1 o o o ~ O "^ o ('^D AiiSNBQ xnnj o o o o o o o o

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194 rvl P^ rd U 1 u n] c U 0) +J a. en 0) '> XJ c • n Oi CS 0) 2 iri rH 3 03 o 1 0) C OJ n TS H •H OJ — 1 4-1 tH r^ 0) 3 ^ h ^ ^ cd H •H -H o • m > OI H 1 — i 0-. •H OJ !>! J-J i-l M U 3 S-i 03 6C O i-i H C CO fij OJ 60 Aiisxza xaT^i dot

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195 where it becomes optically thin. For frequencies greater than v curve m 2a represents the case where the slope and thus the spectral index (a) of curve 2 is greater than the spectral index of curve 1; curve 2b represents the case where the two spectral indices are equal; and curve 2c represents the case where the spectral index of curve 2 is less than that of curve 1. Solid curves A, B, and C represent the total spectral energydistribution for the source, and thus reflect the superposition of the contributions from curves 1 and 2 for the three cases just reviewed. Assuming the spectrum results from synchrotron emission and using curve 1 as a reference flux level, as one observes at higher frequencies, at a given time t one expects to observe a higher peak flux (PF in Figure 92) and a higher flare amplitude (FA) only as long as the source remains optically thick (vv the peak flux will decrease, vrhile the flare amplitude xjill be a function of the spectral indices of curves 1 and 2; that is, the flare amplitude will be greater at higher frequencies if conditions support curves 2a and A, but the flare amplitude will be less if conditions support curves 2c and C. The simple expanding source model assumes an instantaneous production of particles, resulting in a source which is initially optically thick at inf initesmally small wavelengths. In a real source, however, (Kellermann 1972) the production of particles must occur over a finite period of time and throughout a finite volume of space. Thus above a frequency v the -^ m source must be always optically/ thin, and the observed intensity variations will reflect the rate of acceleration of relativistic electrons as well as changes in magnetic field strength and electron energy distribution. For V > V there is no expected delay in the time when the peak

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196 amplitude is reached at different wavelengths, and the maximuin flux density reached is less than that predicted by the simple model on the basis of extrapolating an optically thick spectral energy distribution to higher frequencies. Some data at millimeter wavelengths suggest that v ^ 30 GKz ffl (X = 1cm), The extensive Algonquin Observatory data at 2.8 and 4.5 cm indicate a number of sources for which v ^ 6 GHz (A = 4.5cm). Finally it should be recalled that the slope of the spectral energy distribution for an optically thin source will be a function of the electron energy distribution only, Thus in Figure 92 the flare amplitude at v may be less than, equal to, or greater than the flare amplitude at v This is consistent with the results noted in Chapter II, that QSO's sometimes get redder and sometimes bluer during outbursts. Within the limitations imposed by our general ignorance of the infrared spectral energy distribution, and the possible curvature of the optical spectral energy distribution which may im.ply a non-synchrotron component of the radiation, one can come to the following tentative conclusion. If one assumes that the entire spectrum is caused by synchrotron ratiation, then it seems reasonable to conclude from the previous discussion that the optical emission originates from an optically thin source. This is supported by Figures 1 and 91, which indicate that in general there is a long decrease in flux level between radio and optical wavelengths. While changes in the flux level of an .order of magnitude or less are observed at radio frequencies (Kellermcinn and Pauliny-Toth 196S) and at optical frequencies (Figures 11 and 12) there appears to be no evidence of a change in the overall character of the spectral energy distributions, in which the radio flux is often two to three orders of mangitude higher than the optical flux.

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197 Lack of Correlation After reviewing the results of the correlation analyses presented in Chapter IV, one must separate conclusions into at least two categories. What can be determined from the apparent lack of conclusive correlation between optical and radio activity found for most sources with the observations to date; and what can be concluded from the strong correlation found in the cases of OJ 287 and 3C 454.3? Finally, one must address the question of what further investigations can be made either to test, strengthen, or supplement the results presented herein. The lack of demonstrable correlation for most sources analyzed in this work permits txro important conclusions to be drawn. First, the fact that certain sources have a quite active radio spectrum but a quiescent optical spectrum, or vice-versa, suggests that in those sources the radio and optical emissions may be independent of each other. This may be due either to a physical separation of the regions which emit optical and radio radiation and the accompanying lack of a coupling mechanism, or to the fact that the flare itself may have a limited spectral distribution. Thus the radiation source is stable at some frequencies while it is unstable at others. In addition, the apparently uncorrelated optical and radio activity in other sources is consistent with a Christmas-tree type of model in which localized regions within the source as a whole emit sporadic outbursts with quite different spectral distributions, probably as the result of disparate local conditions. Note that if this model is valid, coupling mechanisms may exist between localized regions which would imply relationships between activity observed from different localized regions, although the activity could not be correlated if localized conditions were of a sufficiently varied character. Thus in

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198 all these cases of non-correlation, the evidence indicates that extrapolation of the simple expanding source model from radio to optical wavelengths is simply not meaningful. Secondly, the lack of radio-optical correlation has a significant impact on the problem of quasar energetics; for if no relationship exists between the radio and optical spectra, the energy associated with any single event is significantly reduced. This is best illustrated by an example, using the expression (Burbidge and Burbidge 1967) 2 2 Aire v Ho ^v F —r. — f 2~ (ergs/sec/Hz) (1 + z") for a cosmology with a deceleration parameter, Or, = + 1, where F is the total radiated energy per unit time per unit frequency interval, f is the observed flux per unit frequency interval at the observational frequency. Ho is the Hubble constant, c is the velocity of light, and z is the redshift of the spectral lines. If Ho = 50 km/sec/Mpc and z = 1, then assuming an idealized step-function flare lasting three months, a radio flare having an amplitude of 20 Jy (20 x 10~^^ watts/m~/Hz) between 9 -2 ""2 10 cm (3 X 10 Hz) and 10 cm (3 x 10"" Hz ) or an optical flare from 13.5 to 12?5 (10 Jy) betV7een 100 nm (3 x lO"'"^ Hz) and 1000 nm (3 x 10 Hz) will emit a total energy on the order of 10 ergs. It is obvious that if such a flare is observed only in the radio or only in the optical spectral region, the source mechanism of the flare will emit much less energy than if a single event is required to radiate in not only the radio and optical spectral regions, but also in the intervening frequencies.

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199 OJ 287, BL Lac, and 3C 454.3 Before discussing the implications of a radio-optical correlation, it is important to review some opinions and important facts regarding sources of particular interest. BL Lac is included although it shows no strong correlation, because it is a source of great interest. There exists important opinion that, assuming there are no infrared or other excursions from the smooth spectra of OJ 287 and BL Lac in Figure 91, the entire continuum spectral energy distribution may be due to synchrotron radiation (Visvanathan 1973b and Stein 1975), In the case of OJ 287 this is supported by the lack of color change in the infrared or L^V observed by Smith et al. (1975) and by Rieke and Kinman (1974). In addition, the general shape of the energy distribution, the amplitude variability, the high variable polarization, and the apparent correlation between infrared and optical activity, as illustrated for OJ 287 in Figure 93, lead to the idea that the infrared and optical radiations originate in the same volume of space (Rieke and Kinman 1974). However, Kinm.an (1975) feels that the fact that the OJ 287 spectrum becomes flatter towards the infrared may indicate that the source becomes optically thick at 20 to 30 p. This lends support to his next speculation, that although the radio and optical radiations have a common particle s-apply, they probably are generated in different localized regions of the source. Finally, it is his opinion that the short-term radio variations are difficult to explain by the simple expanding source model. At least a rough approximation of the overall characteristics of the spectral energy distribution for OJ 287, BL Lac, and 3C 454.3 is given by Figure 91. This figure indicates that for all three sources, there 'A'-ieMi.iawRr>w

PAGE 216

3. 1 1 u U c H o u •H V— ^ IW (U 5-1 CD CO O iH U S CO rt ;-i U r^ tu u 4-J r^ QJ r-l C 4-1 cd CU O C o CC •H 0) 01 g p !-i J2 ti !-i a 4-i •H 0) 0! i^ > S-i cn 6 >^ d Q • c !-i en r>-i •H q-4 ^ 4J 4-1 4-1 0} ta M s > CU d B ^-l o 0) OJ 3 • rH in cn Ta ~j OJ ^ o 'cS > ro o ^j C t;! Cu >-i ;5 'O 2 CD P fi a pa o 4-i cti 1 ^-5 CI 'j-i 01 =1. • rM !^ 4-1 rH c^ id cn •H s < 9J. r^ X N 'S 4J !-i QJ d o CU ^ rH •h .n r^ H l^ QJ Zi 60 o O ^ c a 4J d aj CS CU CO 9:! ^ cn ^ e !-i 4-1 cn >^ a M >.-H M-l MJ o r-l r^ (U ^ Xi 4-1 M 4-J 4-1 C rW 3 c O 4J CJ CC o e 4-( C3 s 0) 0) Q) OJ tH 4= X! O 4-) • iJ & 4-1 r-~ O <+4 00 :3 4-1 Q) O CnI o CJ ^ 4-1 C! d t-) 'en a 01 o o d •H en a) cr* W a 4J OJ M O ce cn •H ro •H c s C^ u •H d !-i CO Td .—( QJ a > 'M a lu (-1 O i-l 3 (1) QJ -d W) cn OJ U-< 4-1 H rQ ^ 0) •H H^ o H 1-1 13

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201 o o o o c o d -^t:o I ^ c 1 m _H o o o o o o o o o < o o o b o o o o SiiNn xmj

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202 is apparentl]/ a long decline in flux density with increaseing frequency all the way into the optical spectrum. VJhile optical and radio spectral distributions are known to change with time, the changes are not more than an order of magnitude change in fltix; thus the basic shape or character has been preserved over the time these objects have been observed. If we assume all the emission is s^mchrotron, then because we have not observed a flux level in the optical spectrum that could be obtained by extrapolating from the radio flux level, we can conclude that to within the accuracy of the present data the radio flux at frequencies less than the turnover frequency, v is emitted from an optically thick region while the radio flux at higher frequencies and the optical flux are emitted from an optically thin region. Thus the optical emission from any correlated activity would appear to originate from either a thick or thin source depending on the turnover frequency, which may change with time. If the radio em.ission originates from the same optically thin source as the optical, there should be no time delay, while if it originates from an optically thick source, a time delay will exist. A visual examination of the sparse data for OJ 287 in Figure 93 indicates a possible time delay from the optical, through the infrared, into the high-frequency radio. This is reinforced by the results of the present correlation analysis for all the available data as summarized in Table 4; however, the analysis of the data subsequent to 1972.75 indicates no time delay, Tvith a rather large error estimate. Of course an important alternative that should not be ignored is that the emitted radiation is not all synchrotron.

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203 Table 6 lists the radio and optical amplitudes for the OJ 287 flare centered at about 1973.1. Column one lists the maximum and minimum flux levels in optical B magnitudes; column two' lists the maximum and minimum flujc levels in fl^sK. units; column three shows the change in stellar magnitudes; and column four lists the linear factor by which the flux levels changed. For a complete presentation of the relative opticalradio flux levels, optical B magnitudes were converted to flux units and radio flux values were converted to a magnitude scale using equation (31) from Chapter II m = -2.5 log F C where m is the magnitude, F is the corresponding energy flux in units of 10" Janskys, and C is a constant equal to 56.04. Table 7 lists the radio and optical amplitudes for the BL Lac flare centered al 1973.5; and Table 8 list the amplitudes for the 3C 454.3 radio flare centered at 1972.5 and the optical flare centered at 1971.0. TABLE 6 RADIO AND OPTICAL AMPLITUDES FOR OJ 287 FLARE Optical Blue Magnitude Flux Change in Stellar -96 2 (10 ~ W/m /Hz) Magnitude Change by Factor of Optical Maximum 13.6 Optical Minimum 16.0 1.4 X 10 1.5 X 10 -2 -3 2.4 9.1 Radio Maximum Radio Minimum 6.57 7.66 9.0 3.3 1.1 .. /

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204 TABLE 7 RADIO AND OPTICAL Ai'EPLITUDES FOR BL LAC FLARE Optical Blue Mamitude Flux Change in Stellar — 9 A 9 (10 VJ/m /Hz) Magnitude Change byFactor of Optical Maximum 15.0 3.8 X 10 Optical Minimum 16.5 9.6 X 10' Radio Maximum 6.36 11.0 Radio Minimum 6.77 7.5 -3 1.5 0.41 4.0 1.5 TABLE 8 RADIO AND OPTICAL AMPLITLT)ES FOR 3C 454.3 FLARE Optical Blue Magnitude Flux Change in Stellar (10 ^ W/m /Hz) Magnitude Change by Factor of Optical Maximum 16.3 1.1 X 10 Optical Minimum 16.9 6.7 X 10 Radio Maximum 6.06 14.5 Radio Minimum 6.46 10.0 -3 0.6 0.4 1.74 1.45 Implications of Correlation Unfortunately, no obvious conclusions can be drawn from a strong ratio-optical correlation, because there are still too many unknown parameters. IvTiile in-depth theoretical investigation of the implications of the data presented lies beyond the scope of the present work, such an investigation could eliminate some of the alternatives and thus lead to a valid conclusion. The primary purpose here will be to review and briefly discuss potential explanations for the correlated activity.

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205 A long-term correlation may be a function of either the source or the intervening medium. If it is a function of the source and if we assume the entire spectral distribution is caused by s3mchrotron radiation, then the spectra in Figure 91 suggest that at the time they were measured, the 2.8-cm (1.07 x lO"" Hz) radiation was emitted from an opaque region of OJ 287 and a transparent region in 3C 454. 3, although in both cases the data are inadequate to determine completely the frequency at which the source becomes optically thin. In the case of OJ 287, one might argue that prior to 1972.5 the source was optically thick, while after 1972.75 the source became transparent at 2.8 cm, thus causing the correlation analysis to indicate a time delay before 1972.75 but no time delay thereafter. However, the spectral energy distribution indicates the source is obviously transparent from optical to Infrared wavelengths, while the curves in Figure 93 suggest a possible time delay. In the case of 3C 454.3, the spectrum in Figure 91 appears to be in conflict with the time delay found between possibly correlated optical and radio activity in this study. Finally, note that all these tentative statements are based on the assumption of a smooth spectral distribution through the infrared wavelengths, for which there is little if any data. If 3C 454.3 were opaque between 20 and 300 y, this could explain the relatively long time delay between optical and radio activity. Also, one could start considering changing opacities as the cause of varying time delays, but this is extremely dangerous because the similarities between radio and optical activity invite spurious correlations. If the intervening medium is the cause of variations, the medium could be either gas or dust or a mixture of the two. In general, optical radiation will be absorbed and scattered by dust, while radio, radiation

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206 will pass through the dust because radio wavelengths are much greater than the dimensions of dust particles. Thus if an intervening dust cloud caused caused variations of a source, the effect would be observed in the optical, but not the radio wavelengths. If the intervening medium were a gas cloud of reasonable density, the gas xTOuld selectively absorb only certain spectral lines, allowing m.ost of the optical radiation to pass through. If the gas were close enough to the source, it would selectively emit at only definite spectral line frequencies. Lyuty and Pronik (1975) have in fact observed variations in the intensity of Ha lines in Seyfert galaxies which copy continuum changes after a delay of 20 to 30 days. In addition, Williams and Weymann (1976) have reported finding a extragalactic gas cloud in front of, but not associated with, the quasar PHL 1222, by the detection of absorption lines in the optical spectrum. uJhile the correlation in OJ 287 is intriguing and compelling for further investigation, it must be remembered that this is the only case of conclusive correlation among the 22 sources studied here, and the hundreds of other sources for which there is insufficient data to search for a correlation. Thus one cannot draw the conclusion that the cause of the correlation in OJ 287 can be extended to other extragalactic variables. The similarity of OJ 287 to other EGV's may bias one towards acknowledging that the correlation must therefore result from something intervening rather than from the source itself. However, OJ 287 is sufficiently unique among EGV's that the correlation may well be a function of this particular source, and involve a mechanism not generally found am.ong extragalactic variables. In addition, the time scale of the long term bump in both the optical and the radio causes one to consider

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207 whether a different kind of process is giving rise to the long-term activity in contrast to the short time-scale variations. Within the meager amount of hard evidence available, a Christmastree type of source would be consistent with the OJ 287 data, with multiple localized source regions having their own spectra and being stimulated by the same source mechanism through some kind of a coupling mechanism acting between the localized emission regions. Thus the overall spectral energy distribution would be the superposition of many separate components. However this would require far different localized conditions to cause individual regions to emit only certain spectral energies. An accurate knowledge of the whole spectral energy distribution and its changes with time is a necessary prerequisite to understanding the nature of the continuum radiation mechanism. A theoretical understanding of the dynamics of these observed flares will probably require an amalgam of the theories of the simple expanding source, prolonged injection of particles, and inverse Compton scattering and synchrotron energy losses (Stein 1975). Further Work To continue the search for answers to the many problems discussed in this work, there are many areas of investigation, both within the framework of the analysis described in this work and exterior to it, which should be followed up. 1) The baseline should be removed from the OJ 287 radio and light curves to determine if a short-term correlation still remains. 2) The optical and radio fluxes should be put on the same scale; then tests for both linear and non-linear functional correlations should

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208 be carried out. This is probably best accomplished through both regression and correlation analyses used iteratively. Correlation analysis will suggest an optimal time delay for a regression analysis, which will suggest the possible functional relationship between the variables, and this can in turn be compared with other functional relationships through correlation analysis. 3) Angione (19 71) suggested a possible correlation between sparse optical and 9.5-iam data for 3C 454.3 between January, 1966 and May, 1968. During this period, the activity reflected in the 9.5-nnn data significantly differs from the Algonquin 2.8-cm data over much of the same period. The short wavelength radio activity and its relation to the optical data could probably be investigated further. 4) VLSI observations using at least three baselines are desirable on a regular basis to determine the source structure, its changes with time, and the possibly localized source (s) of the radio radiation. This kind of regular \TLBI data is highly desirable both for OJ 287 and for other variable sources. 5) Although difficult and time consuming, both optical and radio polarization observations would help to determine if the optical and radio radiations are emitted from the same region of a source, both for OJ 287 and other variables. 6) While certainly difficult, better time resolution at optical wavelengths is highly desirable. 7) The infrared spectrum must be investigated to determine if there is any structure in that portion of the spectral energy distribution for active sources. Such structure could be caused by emission from synchrotron electrons, Compton scattering, or dust.

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109 8) While presently unrealistic, the most important observations that could be made would be to study the whole spectral energy distribution from centimeter-radio to X-ray wavelengths with high signal-tonoise ratios, to watch the evolution of the spectral distribution with time. Finally, the interpretations of this research are obviously biased towards a synchrotron, expanding source emission model for the reasons summarized in Chapters I and II, "Ivhile the meager conclusions I have drawn are scientifically consistent and reasonable, they are obviously colored by many assumptions. Other assumptions and interpretations may contradict what has been presented here, yet may prove to be valid and meaningful.

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APPSM)IX I COtrPUTER PROGRAMS USED IN THE STATISTICAL ANALYSIS Included in this appendix are listings of the programs C0REL2 and LrNREG2 and the accompanying subroutines that were used in the statistical analysis described in Chapters III and IV. To calculate cross-correlation coefficients, the program deck should be ordered in one of the following ways. For noninterpolation use: Program C0REL2 Subroutines DATFUG (Version 1) PPLOT CORREL For interpolation use: Program C0REL2 Subroutines DATFUG (Version 2) LININT SETUPl PPLOT CORREL Similarly, to generate a linear regression plot for the non-interpolation case use: Program LINREG2 Subroutines DATFUG (Version 1) LINREG 210

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211 For interpolation use: Program LINREG2 Subroutines DATFUG (Version 2) LININT SETUPl LINREG Linear regression plots were generated on the printer by executing calls to the subroutines PLOTl, PL0T2, PL0T3, PL0T4. These subroutines are part of the computing system at the Northeast Regional Data Center of the State University System of Florida, and their use is described in in documentation which is available to the user. PLOTl specifies the size of the plot and the separation between tic marks on the axes; PL0T2 specifies the scales of the axes by submitting the maximum and minimum values of the axes; PLOTS plots LCNT points from the txTO specified arrays, assuming that the i-th value from array one corresponds to the i-th value from array two; PL0T4 labels the vertical axis, while the horizontal axis is labeled by a WvITE statement. At the time this analysis was conducted (November, 1975 to February, 1976), all that was required was that the subroutines be called in the proper order, with the correct arguments. The subroutine PPLOT was written by Dr. James Kennedy, who generously gave me the code for my use. It includes the option of performing a Hanning smoothing on a data array by calling a subroutine SMOOTH. However, this smoothing subroutine was not used in the analysis and thus it is not included in this appendix. The programs C0REL2 and LINREG2 will accept data either from cards or from 80-column card images on disc. Data from a number of sources can be input at the same time provided that there is a blank card

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212 separating each data record, that is betvreen the radio data and the optical data for the same source, and between the optical data and the radio data for different sources. The order of the data sets is not important to the actual execution of the programs; however, the convention followed in this work was that for a given source the radio or lower frequency data preceded the optical or higher frequency data. This convention is important in the interpretation of the program output, because it determines whether the radio activity is lagging or leading the optical activity. At the beginning of each data record, both programs expect three header cards. The first header card contains the observatory identification and radio wavelength or frequency, if applicable, in columns 20 to 34 and the source identification and optical frequency (U,B,V, or P) if applicable, in columns 45 to 56. The next two cards are merely headings for columns of data. The programs read only the three fields which are listed under the column READ FORMAT in Table Ai from the data cards. One obvious update of the computer code listed in this appendix would be the creation of a single subroutine DA-TFUG xjhich can either set -99.0 flags to indicated holes for the noninterpolation case or interpolate for the interpolation case. This was not done initially because of restrictions on running time and core size imposed by the priority under which the programs were executed.

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APPENDIX II FURTHER USE OF COMPUTER PROGRAi^IS AKD DATA BANK During the active phase of the statistical analysis, the data bank used for this study existed both on cards and in a partitioned data set which consisted of SO-column card images. Each entry in the data bank had the format listed in Table A-1. TABLE A-1 DATA BANK FORMAT Column Contents Read Format 1-10 Source Identification A4 13-14 Beginning Month 16-17 Beginning Day 19-20 Beginning Year 23-24 Ending Month 26-27 Ending Day 29-30 Ending Year 33-43 Julian Date 46 M for Mangitude or F for Flux 48-52 Magnitude or Flux Value F5.2 54 U, B, V, or P 57-61 Error 64-71 Middate of Observation F8.5 78-80 Observatory Identification At the end of the active statistical analysis, this data bank together with all the programs used in the analysis were copied twice to the 9-track tape named OUASAPv. This tape is stored in the tape :35

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237 library of the Northeast Regional Data Center of the State University System of Florida. In addition to that tape, the following material is kept in the Astronomy Department: 1) a listing of the disc data set that was transferred to the tape QUASAR (this includes both data and programs); 2) the listings from the creation of files 1 and 2 of QUASAR; 3) a listing of a program (lEBUPDTE) that can be used to create a partitioned data set from the tape QUASAR; 4) the card version of the data bank 5) a summary of the materials kept in the department. To begin the kind of analysis summarized in this dissertation, two approaches may be taken: 1) use the listing of the original disc data set as a guide to punch the desired material from the tape QUASAR; or 2) use the listing of lEBUPDTE as a guide to recreate the partitioned data set from the tape QUASA-R; then punch the program PUNCHOOl from the listing of the original disc data set. This program can then be used to dump whatever code or data is desired from the disc data set. Finally note that one change has been made to the code found on the tape QUAS/vR. Tnis change is included in the program listings in Appendix I, and consists of a statement added to the subroutine CORREL between statements 130 and 40. Also note that the program documentation accompanying the listings in Appendix I has been updated relative to the documentation which appears on the archival tape QUASAR.

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BIBLIOGRAPHY A-llen, R. J., Barrett, A. H., and Crowther, P. P. 1968, Ap J jjl, 43. Andrew, B. H,. Harvey, G. A., and Medd, W. J. 1971, Ap Letters 9_, 151. Andrew, B. H. Harvey, G. A., Medd, W. J., Hackney, K. R. Hackney, R. L., Scott, R. L., Smith, A. G. Leacock, R. J., McGimsey, B. Q., Epstein, E. E., Montgomery, J. W. Mottmann, J., and Pomphrey, R. B. 1974, Ap. J ., 191 5. Angione, R. J. 1971, A. J ., 76 412. Becklin, E. E. 1976, (private communication). Bertaud, Ch., DuMortier, B., Vernon, P., Wlerick, G. Adam, G., Bigay, J., Gamier, R. and DuRuy, M. 1969, A. and Ap _3> ^^^6. Blanford, R. D., and Rees, M. J. 1972, Ap. Letters 10 77. Blumenthal, G. R. and Gould, R. J. 1970, Rev. Mod. Phys .,142, 237. Brown, R. L. 19 74, Galactic and Extragalactic Radio Astronom.y ed. Verschuur and K. I. Kellermann (New York: Springer-Verlag New York, Inc ) p 1 Burbidge, G. R. 19 70, Ann. Rev. Astron. Ap ., _8, 359. Burbidge, G. R. Burbidge, E. M. and Sandage, A. R. 1963, Rev. Mod. Phys 35, 947. Burbidge, G. R. and Burbidge, E. M. 1967, Quasi-Stellar Objects (San Francisco: W. H. Freeman and Company), Burbidge, G. R. and Stein, W. A. 1970, Ap. J., 160 573. Burkhead, M. S. 1969, Pub. A.S.P ., 81, 691. Burkhead, M. S. and Parvey, M. I. 1968, Pub. A.S.P 80, 483. Burkhead, M. S. and Lee, V. J. 1970, Pub. A.S.P 82, 1150. Burkhead, M. S. and Stein, W. L. 1971, Pub. A.S.P 83, 830. Burkhead, M. S. and Rettlg, T. W. 1972, P ub. A.S.P 84, 850. 238

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BIOGRAPHICAL SKETCH Richard Bryan Pomphrey was born on May 11, 1946, in St. Louis, Missouri,, He graduated from St. Louis University High School in May, 1964, and began his undergraduate studies as a Chemistry major at Regis College in Denver, Colorado. He transferred to the School of Engineering at Washington University in St. Louis, Missouri, from which he received a Bachelor of Science degree with a major in Physics in May, 1969. In September, 1969, he entered the Graduate School of the University of Florida where he worked as a graduate assistant in the Department of Physics and Astronomy until June, 1973. During that period, he completed the course work leading to the degree of Doctor of Philisophy in Astronomy. From July, 1973, until the present, he has worked at Tne Aerospace Corporation in Los Angeles, California, completing the research requirements for the degrees of Master of Science and Doctor of Philosophy in A.stronomy. In February/, 19 76, he began work in the Image Processing Laboratory of the Jet Propulsion Laboratory and became a member of the Viking Flight Team, working on the Viking '75 Mission to Mars. 243

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosoohv. ^(^X Of \n^k£^ A. G. Smith, Chai^mti/i Professor of PhysicsVazid Astronomy I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. .P7a^ C. N. Olsson, Co-chairman Associate Professor of Physical Sciences and Astronomy I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. /.ift^Uu,^yHJ-fe-H^U"-' 1^-HH S. T. Gottesman A.ssociate Professor of Astronomy

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. /~\ G. R. Lebo Assistant Professor of Astronomy I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. T. L. Bailey ,-/ Professor of Physids This dissertation was submitted to the Graduate Faculty of the Department of Physics and Astronomy in the College of Arts and Sciences and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. March, 19 7 7 Dean, Graduate School


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