Analysis of gamma² Velorum photometry from the South Pole

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Title:
Analysis of gamma² Velorum photometry from the South Pole
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Analysis of Gamma 2 Velorum photometry from the South Pole
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vii, 181 leaves : ill. ; 28 cm.
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Taylor, MaryJane, 1961-
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Subjects / Keywords:
Gamma 2 Velorum (Binary star)   ( lcsh )
Gamma 2 Velorum (Binary star) -- Observations   ( lcsh )
Wolf-Rayet stars   ( lcsh )
Wolf-Rayet stars -- Observations -- Technique   ( lcsh )
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1988.
Bibliography:
Includes bibliographical references.
Statement of Responsibility:
by MaryJane Taylor.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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Full Text











ANALYSIS OF -y2 VELORUM PHOTOMETRY FROM
THE SOUTH POLE














BY

MARYJANE TAYLOR


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

UNIVERSITY OF FLORIDA

1988




LIBRARIES
















ACKNOWLEDGEMENTS


At this time, I would like to express my gratitude to

those people without whose contributions this work would

have been far more frustrating.

First, I would like to thank the chairman of my Ph.D.

committee, Dr. John P. Oliver, for his dedication and

expertise in the construction of the South Pole Optical

Telescope (SPOT), and for his knowledge in the development

of the software necessary to automate the SPOT system. I

thank him for the many hours that he has dedicated to this

project and for the endless headaches incurred, especially

near the beginning of each observing season.

I would also like to express my sincere appreciation

to Dr. Kwan-Yu Chen, principal investigator of the SPOT

project, for his contributions to this research. He has

provided valuable advice in various aspects of this

research, and has read this dissertation with a very keen

eye. Dr. Chen has also supplied me with references to

current papers in the literature on Wolf-Rayet stars, and on

y2 Velorum.

Thanks also go to Dr. Frank Bradshaw Wood, principal

investigator of the project in its infancy, for suggesting









the topic of this dissertation. Dr. Wood has also made me

aware of current topics in the literature, and has carefully

read this dissertation.

In addition, I extend my thanks to the two other

members of my Ph.D. committee, Dr. Jerry L. Weinberg and

Dr. Bruce T. Edwards, for reading this work and making

constructive criticisms which have improved its quality.

Thanks also go to Dr. Stephen T. Gottesman, chairman

of the Astronomy Department at the University of Florida,

for taking the time to share his knowledge of the

interpretation of power spectra with me, despite not being a

formal member of my Ph.D. committee.

I would like to express my sincere appreciation to

Dr. John E. Merrill for his devotion to the South Pole

project, and for always keeping the members of the team on

track. His experience and insight into many of the problems

has been extremely useful.

I would like to extend my sincere thanks and

appreciation to Dr. Lance Erickson for the long discussions

on the application of the methods of Fourier Transform and

least-squares analysis as they pertain to this work. I

would also like to thank him for the weekends that never

were and for helping me to maintain my sanity these last few

months.

Finally, warmest thanks go to my father whose never-

ending patience, encouragement, and support for the last


iii









twenty-one years have made me always strive for the best. I

owe my love of astronomy to him. In addition, he is to be

thanked for the long hours devoted to the tedious process of

formatting this dissertation in accordance with Graduate

School regulations, and for the use of his Hewlett-Packard

printer.

The Steller Photometry Program was supported by grants

from the Division of Polar Programs of the National Science

Foundation.





















TABLE OF CONTENTS


ACKNOWLEDGEMENTS . . .

ABSTRACT . . .

CHAPTERS

1 BACKGROUND. . . .

2 INSTRUMENTATION AND DATA ACQUISITION SYSTEM .
Instrumentation . .
Data Acquisition . .

3 DATA REDUCTION TECHNIQUES . .

4 DATA ANALYSIS . .
Spectral Photometry of the Hell and CIII
Emission Lines . .
Data Set I . . .
Data Set II . .
Data Set III . .
Data Set IV . .
Data Set V . . .
Data Set VI . .
Data Set VII . .
B and V Photometry. . .

5 DISCUSSION AND CONCLUSIONS. .

REFERENCES . . .

BIOGRAPHICAL SKETCH . .


1

17
. 17
. 28

. 31

. 52

. 52
. 52
65
76
86
110
. 122
. 146
155

. 165

. 176

179
















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



ANALYSIS OF -y2 VELORUM PHOTOMETRY FROM
THE SOUTH POLE


BY

MARYJANE TAYLOR

DECEMBER, 1988



Chairman: John Parker Oliver
Major Department: Astronomy



Several hundred photometric observations of the Wolf-

Rayet star, y2 Vel, have been obtained with the South Pole

Optical Telescope using filters centered on the Hell and

CIII emission lines at 4686A and 5696A, respectively. The

observations are reduced to intensities using a region of

the continuum centered at 4768A as the comparison source.

Two independent techniques are used to determine

periodic behavior of variations in the strengths of these

emission lines. The first of these methods uses power

spectrum analysis based on Deeming's method of Fast Fourier

Transforms. The second process involves fitting a first-

order sine wave to the data using least-squares analysis.

vi









The results of the analysis of the Hell feature

indicate a "fundamental period" of 1.20 hours with an

amplitude of fluctuation of a few percent. Several

harmonics and subharmonics of this period are also detected.

The presence of a 1.20 hour period of variability has

certain theoretical implications which are discussed in the

context of recent theoretical developments. It is suggested

that these spectral changes are due to radial pulsations of

72 Vel.

An attempt is made to arrive at satisfactory models to

describe intensity variations of the CIII emission line.

Despite the weakness of this feature, periods are determined

which indicate slightly more rapid fluctuations than those

found to describe variations in the corresponding helium

data. It is suggested that this result may provide clues

indicating the relative locations of line formation in the

extended wind.

In addition to the analysis of narrowband photometry,

observations in the visual and blue filters are reduced to

photometric magnitudes using comparison star HR3452. The

analyses of these data do not reveal any evidence of an

optical eclipse in the 72 Vel system, at least within the

limitations of these data.
















CHAPTER 1
BACKGROUND



In 1867, C. Wolf and G. Rayet discovered several stars

which exhibited very unusual spectral characteristics;

namely, numerous broad emission features superimposed on a

faint continuum. At that time, the only star known to have

an emission line in its spectrum was -y Cassiopeia. Normal

stellar spectra consisted of a continuum marked by

absorption rather than emission lines. In fact, the only

astronomical objects which were known to have spectra

dominated by emission features were gaseous nebulae. Wolf

and Rayet both realized that the spectral characteristics of

the stars they had discovered were considerably different

from either those of 7 Cas or gaseous nebulae. Although

originally classified in the Henry-Draper Catalogue as

spectral type 0, these peculiar objects have now been

assigned the separate spectral classification of W and are

called Wolf-Rayet stars.

In general, the spectrum of a star is used as an

indication of the evolutionary state of that star. However,

even today, over a century after their discovery, neither

the evolutionary status, nor many of the physical,

geometrical and chemical properties of Wolf-Rayet objects

1











are well understood. It follows then, that in the case of

Wolf-Rayet stars, an understanding of the nature of the

emission line mechanisms producing such a peculiar spectrum

is needed before establishing an appropriate evolutionary

scenario. It is this unusual emission line spectrum which

is commonly referred to as the "Wolf-Rayet phenomenon." The

most currently accepted interpretations of observations of

such an intriguing class of stellar objects are presented in

the following few paragraphs.

Analysis of spectroscopic observations of Wolf-Rayet

stars allows us to state with considerable confidence, the

characteristics of the spectra. Very succinctly, the

spectra are dominated by emission lines superimposed on a

continuum which is characteristic of an 0 or an early B type

star. Only in a few cases are intrinsic absorption features

observed. Generally, the only absorption features in a

Wolf-Rayet stellar spectrum are the P Cygni absorption

components of certain emission lines in some stars. Such

P Cyg absorptions indicate expansion of material surrounding

the Wolf-Rayet star. The width of the emission lines can be

used to infer the velocities of expansion. Although the

breadth of the emission lines varies for each ion, probably

because different ions are formed at different depths of the

atmosphere, these widths correspond to velocities ranging

between hundreds and thousands of kilometers per second.











Spectral observations have led astronomers to realize

that there are two main sequences of Wolf-Rayet stars. The

WN type Wolf-Rayet star has an optical spectrum dominated by

nitrogen and helium ions. Several of the WN subtypes

exhibit traces of carbon: in particular, the CIV lines at

5801A and 5812A in the optical region of the spectrum and at

1550A in the ultraviolet region. The enhanced abundances of

helium and nitrogen, as well as the lower than "normal"

abundances of carbon and oxygen, may be explained by the

fact that these stars expose material which has been

processed in the CNO cycle. The second sequence of Wolf-

Rayet stars are the WC types. As their nomenclature

indicates, these stars have spectra which are almost

entirely dominated by carbon ions, but which may also

display helium and oxygen lines as well. Unlike the WN

types, the presence of nitrogen in WC stars is very weak.

The possible blends of NIII ions with strong carbon features

have been identified (Underhill 1959, Bappu 1973) at optical

wavelengths and blends of NIV and NV ions with other carbon

emissions may be present also at ultraviolet wavelengths

(Willis 1980). The (WC) class of Wolf-Rayet stars exposes

material which has probably been processed by a helium-

burning convective core. In this case, however, the

presence of carbon and oxygen is enhanced at the expense of

nitrogen and helium. Recently, Barlow and Hummer (1982)

have identified a third class of Wolf-Rayet stars, WO. The











WO types represent stars which exhibit strong amounts of

oxygen rather than carbon and are probably a result of

extreme helium burning.

The ratio of hydrogen to helium in Wolf-Rayet stars

remains a controversial topic. Based on analyses of optical

spectra, the H/He ratios are quite low; generally

significantly less than unity. It is not yet known if this

is a reflection of the true chemical composition of these

stars. The ratio of abundances of these elements is often

determined by using measurements of the Hell Pickering

series. Since even quantum number Hell lines occur at

nearly the same wavelength as the hydrogen Balmer lines,

significant amounts of hydrogen could be inferred from an

increase in the strength of the Hell line intensities which

produces a non-smooth Pickering decrement. According to

Smith (1973), an analysis carried out in this manner

resulted in N(H)/N(He) =1-2 for late WN Wolf-Rayet stars

(WNL): namely, WN7 and WN8. She found considerably lower

ratios, N(H)/N(He) =0 for earlier WN types (WNE). These

results indicate that stars which exhibit the Wolf-Rayet

phenomenon may indeed be chemically evolved stars with WNE

types more evolved than WNL types. A similar study was

carried out for WC stars by Rublev (1972) who concluded,

N(H)/N(He) < 0.08. This result must be regarded with a

little more caution than those results for WN types, because

of the severe blending effects of the Hell Pickering lines











with several carbon and oxygen transitions. However, it is

the apparent position of this class of stars on the

Hertzsprung-Russell diagram which contradicts the

observational evidence for low hydrogen abundances. In

fact, this is the primary reason that Underhill (1982) is

still of the opinion that the low H/He ratios do not

necessarily indicate a true absence of hydrogen: it is still

her assertion that Wolf-Rayet stars are chemically similar

to our Sun with 3 < H/He < 10. The temperatures and

luminosities which have been derived for these stars place

them in the hydrogen-burning band of the Hertzsprung-Russell

diagram. More specifically, the late type WN stars are

expected to lie near the BO supergiants while the early WN

types and the WC stars seem to reside near the BO giants.

In addition, current stellar models, which have been

calculated for He-rich stars with masses and luminosities

similar to those for Wolf-Rayet stars, indicate considerably

higher effective temperatures than are observed for Wolf-

Rayet stars. One could agree with Underhill, who states

that perhaps certain physical processes occur in the

atmospheres of these complicated stars which may explain the

low amounts of detected hydrogen relative to helium. It is

true that if the temperatures or densities of the atmosphere

are not appropriate, hydrogen emission may not be observed

in the assumed amounts. Hydrogen emission occurs in the

Balmer lines as a result of a recombination event. Such a










6
deionization can occur only if the electron temperatures are

low enough and the density of material is adequate to allow

a sufficient number of recombinations to occur in a small

enough period so that the transitions involved appear in the

Balmer series. Underhill contends that the densities and

temperatures may not be appropriate to allow hydrogen to

emit readily. Additional observational evidence indicates

that this is not the case. Since the x-ray flux is

relatively low, one would infer that the temperatures of

Wolf-Rayet stellar atmospheres are not high enough to allow

hydrogen emissions to occur. Given current theories of the

evolution of hot, massive stars, it is not difficult to

imagine that these objects eject much of the material from

their atmospheres during their long-term evolutionary

development. The spectral observations can be easily

misinterpreted since many of the emission features in the

spectra of Wolf-Rayet objects are either very broad or the

result of blending of several different species.

One representative of the Wolf-Rayet class of stars,

72 Velorum, is located in the southern sky at right ascension

8h09ml2s, and declination -47018' (1988.5). The 7' Vel

system is the brightest Wolf-Rayet star in the sky with a

visual magnitude of 1T76. The star is an intriguing system

for both observational and theoretical astronomers. It has

been the object of many investigations in the last twenty

years or so and is the subject of this dissertation.










7

The -y' Vel system was discovered to be a spectroscopic

binary by Sahade in 1955. The system consists of a Wolf-

Rayet star of spectral classification WC8 and a hot

supergiant component of spectral type 09 (Conti and Smith

1972). Ganesh and Bappu (1967) carried out the first

spectroscopic study in order to determine the orbital

parameters of the -y2 Vel system. Using the CIII-IV blend at

4650A which is assumed to be formed in the envelope of the

Wolf-Rayet component, and the hydrogen absorption line of

the 0 star at 4340A, they found an orbital period of 78-5.

A more accurate estimate of the period was accomplished by

Niemela and Sahade (1980). They determined a radial

velocity curve using the strong violet-shifted absorption

line, Hel at 3888A. The position of this feature was

measured relative to the H8 absorption line of the 09

supergiant. They determined a period of revolution of

7845002 with an eccentricity of 0.40. Moffat et al. (1986)

carried out another radial velocity analysis of the y' Vel

system in an attempt to define the orbital elements of the

system more precisely. They used radial velocity curves

obtained for several emission features but were unable to

improve upon the 7845002 period or the 0.40 eccentricity.

However, their refined ephemeris coupled with the period of

Niemela and Sahade, is given by the following equation:


E0 = JD2445768.96 + 7805002.


(1-1)











With the aid of equation (1-1), the 09 star is found to be

in front of the WC8 star at phase 0.0 and behind the Wolf-

Rayet component near phase 0.5. According to the study by

Moffat et al. (1986) the epoch of periastron passage is

determined to be JD2445802.6. Although an eclipse has been

detected in the ultraviolet region of the spectrum (Willis

and Wilson 1976) at phase 0.65, no definite eclipse effects

have been recorded at optical wavelengths. Gaposchkin (1959)

reported a 1642334 period with an amplitude of variation

ranging between 0!19 and 0O13 using visual and photographic

measurements, but to date no other work has been able to

confirm these results.

The masses of the individual components can be

determined from the simple relation




Kabs MWR
Kem = (1-2)
Kem "09



where Kabs and Kem are the amplitudes of the absorption and

emission radial velocity curves and MWR/M09 represents the

ratio of the mass of the WC8 star to the 09 supergiant.

According to the study by Moffat et al., the best values for

Kabs and Kem are given by



Kabs = 70 2 km/sec, and

Kem = 130 6 km/sec.











These values are in good agreement with independently

determined results by Niemela and Sahade but have smaller

uncertainties. They indicate that the mass of the Wolf-

Rayet companion is approximately 0.54 times that of the 09

star, with minimum masses of 17M for the WC8 component and

32M for the supergiant.

In an attempt to measure the radius of the individual

components of -y Vel as well as the separation distance of

this binary system, Brown et al. (1970) obtained

interferometry measurements with the stellar intensity

interferometer at the Narrabri Observatory. Their

measurements in the continuum at 4430A included the effects

of both -y2 Vel and -y' Vel, which is located 41" away from -y2

However, the analysis is simplified by the fact that the

assumed contribution from -y' Vel is negligible. These data

indicate an angular diameter of the Wolf-Rayet component of

0"44 0705 x 103, and an angular semi-major axis of the

orbit of 4'.'3 0'5 x 10'. Using spectroscopic observations

of Ganesh and Bappu (1967), together with these angular

measurements, the distance modulus for the y Vel system is

7.7 0.3 or about 350pc. A simple trigonometric

computation yields a radius for the WC8 component of 17R A

more conventional method of measuring HB indices of several

stars in the vicinity of Vel results in a distance of

457pc, and hence, a radius for the Wolf-Rayet star of 22R .










10

Since an eclipse in the optical region of the spectrum

has not been detected, the inclination of the system can be

assumed to be approximately 700. Using the angular semi-

major axis of the orbit obtained by Brown et al., the

projected semi-major axis is 2.09 0.05 x 10"cm, or

assuming i=700, 2.22 + 0.13 x 10cm. These measurements

imply a separation distance of approximately 319R .

Brown et al. also obtained measurements of the CIII-IV

emission line of -y2 Vel at 4650A. These data include effects

of both components of -y' Vel in addition to the effects from

the material surrounding the Wolf-Rayet component. The

interferometry measurements give an angular diameter of the

region emitting at the CIII-IV frequency of 2"05 0'.'19 x

10 If one assumes the 350pc distance established by

Brown et al., these data indicate that the CIII-IV blend is

formed in a region around the WC8 component, and at a

distance of 76 10R0 from that star. Wood (1941) derived a

relationship between the dimensions of Roche equipotential

surfaces, relative to the semi-major axis, as a function of

the mass ratio. Given the described dimensions for 7' Vel,

the radius of the Roche lobe is 83R Hence, evidence

indicates that this emission feature at 4650A is formed in

the outer regions of the circumstellar material, and in

fact, in material which nearly fills the Roche lobe of the

72 Vel binary system. These and other properties of this

intriguing system are summarized in Table 1-1. In light of










11
the discussion presented earlier, it is interesting to note

that H/He < 0.02 for -y2 Vel; certainly much different from

the chemical composition of the Sun.

The y2 Vel system is a very peculiar binary which has

attracted much attention in the last two decades. One of

the most intriguing features of this system is the

indication of possible variability in some of the emission

lines which are present in the spectrum of the Wolf-Rayet

component. It is this primary characteristic which has made

72 Vel the subject of so many photometric and spectroscopic

studies. As early as 1918, variation in the shapes of

certain emission lines were reported (Perrine 1918). West

(1972) was the first author to assert that variation in line

intensities might also exist. The results of 24 hours of

observation with the Orbiting Astronomical Observatory,

OAO-2, indicated no short term variations in the CIII

emission line at 1909A. Since then however, several authors

have presented evidence of variations in both line profile

and line strength.

Jeffers et al. (1973a), first reported a 6 minute

periodicity in both line intensity and line shape using

photometric measurements of the Hell (4686A) and CIII-IV

(4650A) features. A later re-analysis of their data (1973b)

revealed even more rapid fluctuations on the order of 154

3 seconds with an amplitude of only about 2%.


























Table 1-1
Properties of the -y Velorum System

Spectroscopic binary WC8 + 091


a) P = 7845002

b) V = 176

c) MWR sin3i > 17M1

d) MO9 sin3i > 32Me

e) q 0.54

f) RWR = 17 3Ro

g) R09 = 76 10Ro

h) a sin(i) > 319R

i) H/He = 0.02









13

Austin, Schneider, and Wood (1973) carried out a very

extensive photometric study of -y2 Vel at the Mt. John

Observatory in New Zealand. They used six narrowband

filters with AA = 10A. Three of these filters isolated the

emission lines identified as Hell at 4686A, CIII at 5696A,

and CIV at 5812A; the other three filters were centered on

the continuum at 4804A, 5302A, and 6106A. These authors

found that the continuum remained essentially constant as

did the triply-ionized carbon feature, at least in the time

interval spanned by their observations. Austin et al.

detected definite night-to-night variations in the strengths

of the CIII and Hell features. The amplitude of variation

for the doubly-ionized carbon line amounted to about O012.

Fluctuations of 003 also occurred in a time period of less

than 2 hours. The singly ionized helium feature exhibited an

increase in brightness of O006 in less than 90 minutes, but,

Austin et al. also note that this line appears to remain

quite stable (i.e., within O002) for relatively long time

intervals. Austin et al. carried out a more intensive -y2 Vel

observing program, concentrating only on variations in the

Hell line. Their results were inconclusive; y2 Vel exhibited

no detectable variations in a 20 minute time period on the

first night of observation. On the second night, however,

the ionized Hell line increased in brightness by as much as

0O10 in 20 minutes, and again later that night, brightened

by the same amount in only 2 minutes. In summary, Austin










14

et al. confirmed previous results that rapid variations can

occur, although not with the rapidity of the degree reported

by Jeffers et al. They found these variations to be

temporal and not periodic.

Another photometric study carried out by Lindgren

et al. (1975) did not provide evidence for stable variations

between 1 and 10 minutes in length, in either the CIII-IV

line at 4650A or the Hell line at 4686A. However, Lindgren

et al. did confirm nightly variations in emission line

strength, in particular, a 0Q03 to O005 change in the 4650A

feature. The observations that were utilized for this

investigation covered an interesting phase of y Vel: that is,

when the 0 star was in front of the Wolf-Rayet component.

These results may indicate an eclipse of some part of the

supergiant by a portion of the circumstellar material

associated with the WC8 star.

Bahng presented results of several spectrophotometric

studies of the 72 Vel system, studying the short term

variations in emission line strengths using a photoelectric

spectrum scanner in the spectral range 4600A to 4720A. In

1973, Bahng reported on results of spectrum scans which were

acquired on four different nights. The emission lines of

particular interest were CIII-IV (4650A) and Hell (4686A).

Although a power spectrum analysis did not yield evidence of

a periodic phenomenon, Bahng did find variations in the

equivalent widths of these lines. These changes amounted to










15
a 2% variation for CIII-CIV, and a 4% variation for Hell and

occurred on time scales of 4 to 20 minutes. Later, Bahng

(1974) recorded a 6 hour spectrophotometry observation in

which variations were detected between 10 and 20 minutes.

Again, however, no predominant periodicity was found. In

his 1975 paper, Bahng analyzed spectroscopic scans which

were obtained in 1973 and 1974. He compares the theoretical

rms deviations computed from photon counting statistics with

the rms deviations of the measured equivalent widths of the

emission lines of interest. Since the rms deviations of the

data exceed the theoretical rms deviations by more than a

factor of three, Bahng considers these variations to be

statistically significant, indicating that real short term

variations in the emission lines of the 72 Vel system do

exist. Although there is no predominant periodicity, a

power spectrum analysis indicates considerable power near a

frequency corresponding to a period of about 1 minute.

Using integrated magnitudes, Bahng finds evidence of

variation with a semi-amplitude of 0O01 with a periodicity

of 339.5 seconds. In addition, a significant peak at

16.2 minutes was also present in the data.

We have presented only a brief summary of some of the

more notable observational studies of y2 Vel which have

appeared in the literature over the last few years. As

pointed out by Haefner et al. (1977), ultra-short period

variations (i.e., those on the order of minutes) seem to be










16
detected only in observations which do not exceed much more

than 30 minutes in length. Fluctuations of this nature are

not generally detected in longer runs of continuous data,

but variations in both emission line strength and profile

are almost always detected on a nightly basis.
















CHAPTER 2
INSTRUMENTATION AND DATA ACQUISITION SYSTEM






Instrumentation

The data used for this research were obtained with the

automated optical telescope located at the Amundsen-Scott

South Pole Station on Antarctica. This instrument is a two-

mirror siderostat zenith telescope with an f/6, 7.8cm

achromatic lens (Figure 2-1). As one would expect, certain

special design considerations are necessary to ensure normal

operation in the extremely low-temperature, harsh

environment which prevails at the South Pole. A specially

insulated building measuring 12' x 8' x 8' was constructed

on site by carpenters of ITT Antarctic Services during the

1985 austral summer. The telescope occupies an 8' x 8'

section of the building, while the computer system and

control electronics are housed in an adjacent room measuring

4' x 8'. This smaller room can be completely isolated from

the telescope room and heated when necessary. Under normal

circumstances, the telescope room temperature is main-tained

at approximately -200C.

The optical head of the telescope contains two

optically-flat front-surfaced mirrors which act to redirect

17









AZIMUTH 0 0 ENTRANCE
HEAD --- WINDOW



ALTITUDE
GLASS TUBE---- HEAD
ING AND ALTITUDE STEPPER
ASSEMBLY-- ,,,
R PORT I
UPPER AZ BEARING


AZIMUTH--- AZIMUTH GEAR
STEPPER' -
LOWER AZ BEARING

FOCUS ---- --- .. --7.8 cm OBJECTIVE


STOP
WHEEL----
FILTER
WHEEL
SHUTTER


01


LIGHT SHIELD

EYEPIECE

FIELD LENS

PMT

S--X-Y TILT ADJUST


Figure 2.1 South Pole Optical Telescope.


FIBEF
SLIP F
BRUSH
DRY AI


I~


II










19

incoming light onto the objective lens and eventually to the

photometer. It is this section of the telescope which

protrudes from the roof of the building and is therefore

exposed to ambient conditions. In order to prevent blowing

snow and other sources of moisture from entering the optical

head, a transparent window is used to completely seal the

interior of the telescope. During the 1986 observing

season, the formation of frost on this window and on the

mirrors in the optical head interfered with some of the

observations. Since this time, however, upgrades to the

system have been installed and all of the optics are

maintained frost-free. This was accomplished by pumping

existing dry polar air (the absolute humidity is equivalent

to about 0.15mm of precipitable water vapor) through a

cylindrical tube containing a desiccant, and into the

optical head of the telescope. Here, the air is heated so

that a temperature gradient of about 50C is maintained

between the air in the optical head and the air immediately

outside of the entrance window, with the inside air being

the warmer.

Of the entire design of the telescope, the only moving

part which is directly exposed to ambient conditions is the

elevation axle. The gear system which moves the telescope in

the east to west direction, also moves the entire telescope

tube in both azimuthal directions. The azimuth-motion

resides well within the telescope room, and a worm gear











drive is controlled by a stepper motor assembly. This same

technique provides motion to the field stop and filter

wheels. With the siderostat design, the elevation motor

must move only the optical head in the north to south

direction, and it is therefore necessarily mounted outside

on the optical head assembly. The elevation axis joint is

located between the two portions of the optical head which

house the two optically-flat mirrors. This "up and down"

motion of the telescope is provided with an assembly of

teflon ball bearings.

The optical design of the telescope (Figure 2-1) is

straight forward. Incoming light rays strike the objective

after being deflected by the two front-surfaced mirrors in

the optical head; each is positioned at about 450 with

respect to the normal. As the photons emerge from the lens,

they pass through a diaphragm, a filter, and a fabry lens

which images the objective of the telescope onto the

photomultiplier. It is the photometer which measures the

signal and converts it into an equivalent number of photons.

The South Pole Optical Telescope (SPOT) is equipped

with several diaphragms and filters allowing the selection

of any one of a number of combinations depending upon the

brightness of the source, the tracking rate of the

telescope, and the type of observation desired. The current

system has diaphragms which restrict the field of view to

1, 5', 2', or 1' regions of the sky. The l1 field of view











is used only in the initial star pointing procedure while

the 5', 2', and 1' diaphragms are used in the star centering

procedure and for the actual measurement of the object's

brightness; the smaller the diaphragm, the smaller the

contribution from sky background, and the fainter the

limiting magnitude of the telescope. The filters which are

currently mounted in the filter wheel include the Johnson

standard B and V filters, a neutral density filter, and four

narrowband filters. The neutral density filter is a ND5 and

is used in the star find procedure. This filter's sole

purpose is to prevent the telescope from observing a source

which is too bright: that is, one which could saturate, and

subsequently damage the photomultiplier. Of the narrowband

filters, one is used to monitor auroral and/or sky

variations. This filter is centered on the very strong 01

emission line at 5577A. The remaining three narrowband

filters were chosen specifically for our research on the

Wolf-Rayet star, -y2 Vel. Two of these filters isolate

emission features in the spectrum of -y' Vel; the Hell

emission line at 4686A and the CIII emission line at 5696A.

The third filter isolates the continuum region at 4768A.

More specific details of each of these filters are presented

in Table 2-1. Also, the response curves for six of the

filters are presented in Figures 2-2 through 2-6. In

addition to the filters, one position on the filter wheel

contains a mirror which directs the light beam perpendicular






























Table 2-1
Filter Specifications


Peak
Wavelength
(A)


Half-Power
band-width
(A)


Integration
time
secss)


B

V

Hell

CIII

Continuum

0I


Purpose


4400

5500

4686

5696

4768

5577


900

900

32

32

92

100




















III I I I I--


4
4


4















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0


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C


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<


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0 bo



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aOUDVIPWSUDJI











to the optical axis where it can be viewed through an

eyepiece. This section of the telescope is maintained at a

temperature below -200C in an effort to reduce the dark

current in the system. During the three years in which the

telescope has been operating, this level has remained nearly

constant at 3.7 counts/sec. Other regions of the telescope

are also maintained at optimum temperatures according to a

thermal design analysis carried out by Esper (1986). These

temperatures are achieved with thermal insulation, heaters,

and residual heat generated by stepping motors and other

electronic components. The entire thermal design of the

telescope works in concert with ambient temperatures ranging

from -400C to -80C.



Data Acquisition

The SPOT system is controlled with a modified Dynatem

RM-65 computer system with an 8-bit 6502 microprocessor.

The computer system controls the motions of the telescope in

azimuth and elevation, as well as the motions of the

component parts including the field stop and filter wheels.

The necessary special functions and interfacing of the

telescope are provided by custom built circuits supplied by

the electronics shop at the University of Florida. The

software is written in 6502 assembler language and FORTH.

FORTH is a computer language designed specifically for

instrument control processes. As mentioned previously, the











computer system is located in the SPOT building. However,

in some cases, the telescope can be commanded from a remote

terminal. The data storage media which are currently

employed are 8-inch floppy disks.

During an observing session, photometric and

engineering data are accumulated until a one kilobyte region

of memory is filled. At that time, the buffered data are

written onto a disk file. At the beginning of each hour,

the telescope suspends the acquisition of photometric data

and records the status of various aspects of the telescope.

Such things as the azimuth and elevation positions of the

telescope, the Julian Date and Sidereal Time, and the

temperatures of various sections of the telescope are stored

as engineering records. After these data are obtained, the

telescope resumes its observing program. Observing programs

instruct the telescope with respect to pointing, diaphragm,

appropriate filtering, and number of seconds to integrate

for each filter. In addition, in the case of stellar

photometry, the telescope is given the number of steps and

directional information for sky readings. Observing

programs can be modified, deleted, and added from the remote

terminal. Depending upon the observing program and sky

conditions, a given floppy disk may fill in a week to ten

days. At this time, the winter-over scientist changes the

disks, copies the contents of the filled disk to tape for

archival purposes, and transmits the data to a mainframe










30

computer in Malabar, Florida, via the ATS-3 satellite

communication link. These data are retrieved from the VAX

system in Malabar, and stored on the ATS-VAX at the

University of Florida where the reduction of the data

proceeds.
















CHAPTER 3
DATA REDUCTION TECHNIQUES



During the 1986, 1987, and 1988 observing seasons,

SPOT obtained data for several different research projects.

In order to optimize telescope time and to make the best use

of clear skies, the data for more than one research project

were usually acquired within the same observing program.

The research project that is the subject of this

dissertation has two major objectives: 1) the search for

variations in emission line strengths using the Hell, CIII,

and continuum filters; and, 2) the search for eclipse

effects requiring observations in the B and V filters, as

well as integration on the comparison star, HR3452. In

some observing programs, both 2y Vel and HR3452 were observed

using all available filters. In other cases, an increase in

the time-resolution of the data was accomplished by removing

HR3452 from the observing program and omitting the B and V

filter observations. Therefore, several different observing

sequences were required to obtain the data necessary for

this investigation. Specific details of these programs will

be presented in Chapter 4 where individual data sets are

discussed. In general however, the data acquired for this

project were obtained with the use of the 5' diaphragm in

31












conjunction with the B, V, Hell, CIII, 01, and continuum

filters.

As one would expect, the photometric integration times

necessary to obtain adequate signals for a given star and

filter varies from star to star, and from filter to filter.

The required integration length depends on a particular

star's color and its distance from the zenith. For example,

to obtain comparable deflections in B and V filters for a

red star, it is necessary to integrate for a longer time

period in the blue region than in the yellow. In addition,

the increased scattering of blue light at large zenith

distances requires the use of longer integration times for

the blue filter than for the visual filter. The optimum

integration times for the stars and filters used in this

study are based on this knowledge, as well as experience

that was acquired during the early portions of the 1986

observing season. Integration times are presented in

Table 3-1.

Since a star does not wholly fill the observing

diaphragm, each stellar deflection is actually the sum of

the star and surrounding sky emissions. In order to obtain

a net star-reading, it is necessary to remove an appropriate

value for the sky intensity from each of the stellar

measurements. In the case of a single channel photometer,

this is easily accomplished by integrating on a region of

sky which is devoid of stars within the limitations of the










33


















Table 3-1
Optimum Integration Times for -y2 Vel and HR3452

Star Filter Integration time
secss)


y2 Vel B 2

V 2

Hell 4

CIII 8

Continuum 2

01 8

HR3452 B 10

V 10












telescope but which is reasonably close to the star under

observation. In an automated telescope system, it is

necessary to make certain that both of these criteria are

satisfied. A search of the Palomar Sky Survey (1954) prints

indicates that a displacement of 15' in the positive azimuth

direction from the star is an appropriate displacement for a

typical sky reading. In very general terms, each stellar

deflection is accompanied by a corresponding sky deflection

which is used in the data reduction procedures.

During the observing season, data are periodically

transmitted from the South Pole to the VAX 11/750 computer

at the University of Florida. Each of the programs used in

the reduction and analysis of the -y2 Vel photometry was

written in Fortran-77. In order to optimize computer run-

time, the data were initially passed through a program which

unpacked the data from hexadecimal to decimal format and

divided the data into two files: an engineering file

containing information relating to the design and operation

of the telescope, and a separate photometric file containing

the data relating to the stellar deflections. The raw

stellar deflections were then reduced to photometric

magnitudes using standard reduction techniques (Henden and

Kaitchuck 1982). Since each deflection is recorded as a

counts-per-time quantity, and since an integration time

varies from filter to filter, it is necessary to convert all

measurements to the same unit; a counts per second quantity.












Once this is done, the next step is to remove the sky

background from each stellar measurement. This is

accomplished through a simple linear interpolation of the

sky readings to the time of the star reading. The number of

counts (per second) due to the background are then

subtracted from the total counts (per second) due to the

star. In the case of the B and V data, HR3452 was chosen as

the comparison star. HR3452 is very close in color to -y2 Vel

with a spectral classification of BlV and is located only

24' from the variable. For these reasons, and the fact that

HR3452 has not been reported to be variable, it meets the

criteria for a reasonably good comparison star. A second

linear interpolation scheme is then used to determine the

intensity of the comparison star, HR3452, at the time of the

variable star reading. Finally, equation (3-1) is used to

give the differential photometric magnitude



r Dv
Am = -2.5 log --- (3-1)
SD,



where Am is the differential magnitude between -y2 Vel and

HR3452, and Dv and Dc are the deflections (in counts per

second) of y' Vel and of HR3452, respectively.

A major portion of this research is the search for

periodic intensity variations in the Hell and CIII emission

lines of -y' Vel. One technique which is commonly employed in












period determination analyses uses the method of Fourier

transformation of time and intensity measurements. In

particular, Deeming's method (1975) of Fast Fourier

transforms is well suited for data which are unequally

spaced in time. In general, Fourier transform analysis is

used to transform data from the time domain into the

frequency domain, or vice-versa. For instance, a continuous

function of time, f(t), can be transferred into frequency

space according to the formula



F(v) = FTf] = r f(t) exp (-2wivt) dt. (3-2)




The inverse Fourier transform is given by



f(t) = FT[F] F(v) exp (2rivt) dv. (3-3)




In equation (3-2), F(v) represents a spectrum of

frequencies. Each peak in F(u) corresponds to the relative

strength of each frequency in the data, f(t). In most

cases, and in this data, f(t) is not a continuous function,

but rather a sampled-set determined at discrete times, ti.

Hence, equation (3-2) can be re-written as a discrete

transform



N
F(v) = 2 Z [f(t) exp (-2rivt)], (3-4)
1











with N equal to the number of data points in f(t). The

periodic exponential function in equation (3-4) indicates

that the Fourier transform of f(t) has both real and

imaginary components. Since it is the power as a function

of frequency, rather than the Fourier transform that is of

interest, the derivation must be carried one step further.

If f(t) is assumed to be real, then F(v) must satisfy the

relation



F(-v) = F*(i), (3-5)



where F* (v) is the complex conjugate of F(m). Then, according

to Rayleigh's theorem which states:




+- If(t) 2 dt = +00 IF(v)|2 dv, (3-6)



we can define the power, P(v), as the product of F(v) and its

complex conjugate, which leaves only the real quantity



P(v) = IF(v)12 = C2 (v) + S2 (v). (3-7)



C(v) and S(v) in equation (3-7) are the cosine and sine

components, respectively, and are defined as




C(v) = Z [f(t) cos (2rvt)], and (3-8)
N












S(v) = N Z [f(t) sin (2xvt)]. (3-9)




Since the data used in this investigation are acquired

over a finite span of time and are not sampled at equal time

intervals, the Fourier transform is contaminated with the

sampling function. This spectral window or "beam", as it is

frequently referred to, is given by the relation,



W(v) = G2 (v) + H' (v). (3-10)



In (3-10), G(v) and H(v) are defined in the following manner:




G(v) = Z [cos (2rvt)], and (3-11)
N

H(v) = 1 Z [sin (2rvt)]. (3-12)
N



According to equations (3-10) to (3-12), the spectral

window function is normalized so that W(0) = 1. The Fourier

convolution theorem states that the Fourier transform of the

signal, FT[f], is the convolution of the data with the

sampling function (i.e., beam). The fact that the data are

unequally spaced over a finite time interval has seve-ral

consequences. The sampling period of the data puts a

constraint on the lowest frequency which is resolvable in

the data. The frequency resolution in a discrete data set

corresponds to the width of the beam (W) at v = 0 and is











related to the sampling period by equation (3-13)



6v = 1/T, (3-13)



where T is the length of the data set. Therefore, the

minimum frequency which is retrievable from a given data set

is given by the Nyquist frequency



vmin = 1/(2AT). (3-14)



It is the data spacing which puts an upper limit on the

frequency that can be recovered from a given data set. In

the case of a function consisting of points spaced at equal

time intervals At, the maximum frequency is given by the

Nyquist frequency. Since the data used in this study are

unequally spaced in time, At is not a constant. For purposes

of this investigation, it was deemed appropriate to

calculate the average time interval for a given data set and

use that value for At, according to equation (3-15):



vmax = 1/(2At). (3-15)



In addition to upper and lower limits being placed on

the frequencies which can be recovered from the data, the

data are also not represented by a continuous function of

time. The discrete nature of the data contributes several











features to the spectral window (beam) which adds

considerable complexity to the nature of the spectrum.

Since the Fourier transform of the data is a convolution of

the spectrum with the window, the resulting "dirty" spectrum

may be subsequently contaminated with spurious sampling

features. This aliasing can be masked as either a damping

of real features or an enhancement of "false" features,

making interpretation difficult. For this reason, a one-

dimensional deconvolution (CLEAN) algorithm (H6gbom 1974)

has been adopted for use in this study. The CLEAN algorithm

is that used by Roberts, LehAr, and Drehar (1987) which

deconvolves the sampling function from the dirty spectrum to

give a better representation of the true spectrum. This

deconvolution is accomplished in the following manner:

First, the largest peak in the dirty spectrum is located and

stored. The spectral window (beam), is then superimposed

onto the dirty spectrum so that the main peak in the beam

coincides with the largest peak in the dirty spectrum. A

given percentage of the spectral window is subtracted from

the corresponding dirty spectrum. The peak of the spectrum

which is removed from the data spectrum is stored as a CLEAN

component. The spectrum which results after subtracting the

spectral window is also stored in a residual file. This

procedure is repeated for a given number of deconvolutions

(peaks). A gaussian representation of the spectral window

is then convolved with each CLEAN spectra. Finally, in











order to preserve the noise which existed in the original

spectrum, the residual values are added back to the

convolved CLEAN components giving the CLEAN spectrum. The

input parameters for the CLEAN algorithm include the number

of CLEANs to be performed (peaks) and the gain. It is the

gain which governs the percentage of the spectral window

which is removed from the dirty spectrum during each CLEAN

iteration.

The CLEAN procedure is used to improve the strongest

features of a spectrum and is of limited use in data which

may have a small signal-to-noise ratio. In fact, experience

has shown that over-CLEANing data can actually introduce

spurious features in the clean spectrum. Figures 3-1 to 3-6

are used to demonstrate the hazards that can result from the

improper use of this algorithm. Figures 3-1 and 3-2

represent the spectral window, and the dirty spectrum,

respectively, for a sample data set. Figures 3-3 to 3-6

represent the clean spectra after 10, 100, 500, and 1000

iterations of CLEAN. It is quite clear from these graphs

that the peak at v = 40 (cycles per day) in Figure 3-3

decreases in strength as the number of CLEANs increases,

while the peak at v = 235d-' gets progressively stronger.

In fact, in Figure 3-6 this is the only peak which remains

in the spectrum with considerable amplitude. It is likely

that a misinterpretation of the data would result in this

type of over-application. In this study, care has been
















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48

taken to minimize the introduction of such spurious features

into the power spectrum. This has been accomplished by

restricting the CLEAN procedure to data above the 3aN level.

In addition, more stability is provided in the CLEAN

algorithm through use of a smaller gain size and more

iterations. In our case, a gain parameter of 0.25 was

adopted.

Because of the possible uncertainties of the power

spectrum analysis, an independent method of period

determination was also used. This method is based on

fitting models to the data with the aid of the method of

least-squares. The intensity variations which may exist in

the y2 Vel system are probably much more complex than that

which can be described as a simple cosine or sine function.

However, the main purpose of this research is to use the

long, continuous observational runs of y' Vel to establish

whether variations in the strengths of the Hell and CIII

emission lines do, in fact, occur. It is not necessarily our

purpose to mathematically describe such variability

precisely. A shift in phase could certainly cause a poor

fit to the data. In any event, the variations which would

exist in such a complicated system are probably periodic at

best. So, for purposes of this investigation, a first-

order sine function of the following form is assumed:



t to (3-1)
D(ti) = Ao + A, sin I (3-16)
I P












In equation (3-16), D(ti) represents the calculated

deflection at time ti, Ao is the baseline in intensity

units, A, is the amplitude of the sine wave expressed in

intensity units, to is the "phase" or time of maximum, and P

is the period. It should be noted at this point that P is

expressed in days divided by 2w radians, a representation

that was chosen so that when one complete cycle had elapsed,

that is, ti to = P, then cos (ti to)/P = 1. In the

least-squares procedure, four parameters are adjusted. They

are: Ao, A to, and P. A first-order Taylor expansion is

computed using the partial derivatives of equation (3-16)

with respect to each of these variables. The routine used

in this context is that of Banachiewicz (1942) and uses

Cracovian calculus. If the errors which were calculated in

the least-squares routine exceed the convergence criteria,

corrections are computed and added to A., Al, to, and P to

give the new quantities:



A0 + AA,,

A, + AA,,

to + At., and

P + AP.


The convergence criteria are the following:












E(AO) < 1 x 10- ,

E(A,) < 1 x 10- ,

E(t0) < 5 x 10-'. and

E(P) < 5 x 10-4.



In these relations, E represents the difference between the

new and old values for each quantity considered.

If all of the parameters do not converge within 30

iterations, it is assumed that a satisfactory model could

not be found within the given input parameters. In the case

of the Hell photometry, an initial intensity-amplitude of

0.01 and a baseline of 0.35 were used. For the CIII data, an

amplitude of 0.01 and a baseline of 0.10 were used as

initial inputs. These two parameters were not as sensitive

to small variations as were the period and phase. To account

for the increased sensitivity in P, an initial and final

period were entered along with a desired incremental step

value. Upper and lower limits on the period assumed two

samples per cycle in accordance with the Fourier transform

analysis. To account for increased sensitivity (to small

perturbations) in the phase parameter, a similar approach is

adopted. That is, a desired increment in the phase is

entered as an input parameter. In every case, the time of

the first observation was used as an initial "guess" of the

value for to. The parameter was incremented from this

initial value to the initial value plus 2w.











Weather reports are recorded at the South Pole every

six hours. Photometric data recorded between two

consecutive periods of reported clear skies were used in

this investigation of -y2 Vel. In addition, since the

telescope does not have the capability to monitor the star

and nearby sky simultaneously, data recorded during times of

auroral activity were omitted from the study. These

omission criteria resulted in the selection of seven

individual data sets obtained during the 1986 austral

winter. Individual observations in each data set were

omitted if the observation in the continuum filter and the

observation in one or more of the emission line filters

deviated by more than 10%. The analysis of the data sets

that resulted is presented in the following chapter.
















CHAPTER 4
DATA ANALYSIS

Spectral Photometry of the Hell and CIII Emission Lines

Data Set I.

This data set includes observations of y2 Vel that

extend from JD2446577.6847 through JD2446577.7792. These

(81) data-points were obtained for each of the helium,

carbon, and continuum filters with an average spacing

between successive readings with a given filter of 00012.

Both -y2 Vel and HR3452, the comparison star used to reduce

the blue and visual photometry, were observed. The exact

sequence of observations is presented in Table 4-1. In the

table, an "X" is used to indicate that an integration was

accomplished with the corresponding filter listed at the top

of the table.

These data were reduced to a ratio of intensities

using methods described in Chapter 3. The data were first

transformed into frequency space using Deeming's method of

Fast Fourier Transforms and assuming a minimum of two

samples per cycle. Given the data spacing of 00012 and the

2.3 hour time interval spanned by this data, the minimum and

maximum frequencies which can be retrieved from the data set

with a reasonable amount of confidence, are vmin = 11d' and

,max = 417d-'. Figure 4-1 represents the sampling

52





















Table 4-1
Observing Program 1


0 Continuum


comparison star
comparison sky
variable star
variable sky


Si-a r


1C*
2 CS
' V*
4 VS


YQta C on t nu-

























i
1


JaMOd aAl:DjaN


/1
I




C
QL)

V)
I-
U-,











function for both the helium and the carbon observations.

The peaks at v = 52, 158, 364, and 470d-' are the odd

harmonics v1, v3, v5, and 17, and the peak at v = 318d-' is the

even harmonic, v6. The convolution of the helium data with

the spectral window function gives the spectrum in Figure

4-2. The noise level is denoted in the lower left-hand

portion of the plot at 5.16 x 10-6. All features to the

right of the arrow satisfy the Nyquist criterion of a

minimum of two samples per cycle. The peaks at v = 170, 323,

and 377d-1 represent statistically significant features at

the 4aN level. A closer look at the spectrum reveals that

the peak at v 377d-' is part alias with that at v = 323d-'

and the peak at v = 170d-' is part alias with a peak at

v = 8d". This last feature is shown in Figure 4-2 but since

it does not satisfy the Nyquist criterion, it is discarded

in this study. Spurious features at or above the 3aN level

are removed from this spectrum with a deconvolution process;

the resulting power spectrum is depicted in Figure 4-3.

Here, we see that the peak at v = 323d' is the only feature

which remains above the 4aN level, at 4.25aN. This

frequency corresponds to a period of 4.5 minutes. According

to the least-squares routine, the best fit to the data,

within the limitations of the Nyquist criterion, occurs for

P = 4.4 minutes, and is described by:







































































i n In n o


o a o o
^- oi


u





C
0)

CT


LL


4-1
0

C
0C




0













0
4-

o





Se4









(42 4 .1
.14





0 CU





4)
l-I
U M


jaMOd aiiopyt9














































































w w w w


6 C 1:


JOMOd aA!4DI;D


I-






O







LL
U
D


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0

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MC

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41 C






<4

0
4 a)

.W





a o
0 c0
0 4-

w 3
43 U




Pli e












ti 0.18518
D(ti) = 0.35099 + 0.00813 sin 0.1850049 (4-1)
1 0.00049



The model computed from this equation is presented in

Figure 4-4 and seems to fit the observations quite well.

However, because there are only an average of 2.5 points per

cycle, one should regard this result with some skepticism.

A visual inspection of a plot of intensity as a function of

time indicates that perhaps the data are changing at a more

gradual rate. The least-squares routine was executed for

periods on the order of the time interval spanned by the

data set; convergence occurred for a period of 2.40 hours.

The model, given by



[ ti 0.10507
D(ti) = 0.34986 + 0.00724 sin 0.10507 (4-2)
1 0.01592



is graphically presented in Figure 4-5. The amplitude of

the variation of this model is only slightly lower than that

for the more rapid fluctuations depicted in Figure 4-4.

The power spectrum for the carbon data obtained in

this time interval is shown in Figure 4-6. Again, the arrow

in the lower left of the plot represents the noise level at

1.287 x 106. It should be noted that the peak at v 70d-1

is part alias with that at v = 20d-' and should, in

principle, be removed with the CLEAN algorithm (Figure 4-7).


































































0 0 0 0 0 0
o o o o o o
1' oocr )l
6 C 6 63 6 ] 66


Wfnnuiluo! : IIaH


+
Ln

r-:
in
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Ct




c
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(0


Q)


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^0


O0


4.- 4 *4




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0 w
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rl C





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'-40 *




o CL O| *
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=U I M


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wnnul!uoo : IIGH










































































I I I I

C1 0 I0 0
*: r- v


1JMOd aIJoiatj


4-4
0

0
C
OC
4-4 (U
td
>0



w
S1
o
0



4.1
C1
o
0
0




Wcu
0 c

O0










0 oB
&< T


-u





U
C
Q)

0l




















































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LL


44




-W C
00
eca

14 0
*cu

0 4



,C
0 0





0


4-4


C4
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kP






0Uc






04 "(B
4Ja~


0
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0 a A a a o
LJ o W o


jaMod 9A!I0198











This is indeed the case, and the only peak which survives

the CLEANing process is that at v 20d-1 corresponding to

04050 (1.20 hours). The signal-to-noise ratio for this peak

is quite large at 8.040N. The least-squares routine

converges to a set of quantities with a similar period,

P = Od0459 (1.10 hours), according to the following

relation:



[ ti 0.45362
D(ti) = 0.11117 + 0.00231 sin 0.00731 (4-3)




The fit to the data using equation (4-3) is presented in

Figure 4-8. Although the amplitude is quite low, this

period may be considered as a satisfactory representation to

the fluctuations since both the power spectrum analysis and

the least-squares routine give similar results.

In summary, the helium data seem to follow two

different periods. The shortest period of about 4.4 minutes

represents very rapid fluctuations and was arrived at by

both the power spectrum analysis and the least-squares

solution. In addition, models were computed for periods

corresponding to the length of the data set with the best

fit solution having a period of P = 2.40 hours. Both fits

seem to be quite satisfactory. The intensity variations of

the CIII emission line, although low in amplitude, can be

modeled with a period of 1.10 hours.
























o C
C1 J O |


o a


I .4
0 LO








0 '0 4(O
r. >

N o o 0 co

N C W

0 0 -< -U k) a

o o a o *


0 1 0
o )



o 6o
0* 4
N4 0 d 0"










^0 0 0
6 6 6 6 6 6



wLnnuiluoo : |||o











Data Set II.

One-hundred and eighty-nine observations of

72 Vel were obtained in the helium and carbon filters using

the observing sequence presented in Table 4-2. The time

interval spanned by these data extends from JD2446606.6048

through JD2446606.9553. The average spacing between

successive observations for a given filter is 0-0019. The

decrease in time-resolution of these data relative to the

time-resolution of the data discussed in the previous

section, is an artifact of the new observing program. As

can be seen from Table 4-2, several new objects have been

added to the original observing program (Table 4-1). This

ultimately limits the high frequency components which are

recoverable in the data analysis.

The spectral window for these data is given in Figure

4-9, and includes first, second, third, and fourth harmonics

at v = 23, 43, 64, and 84d-', respectively. In general, as

in this case, spectral windows for unequally sampled data

tend to be more complex at high frequencies. The power

spectrum of the helium data is computed for frequencies

between vmin = 6d' and vmax = 265d-' (Figure 4-10). The

noise level in this figure is denoted in the lower left-hand

portion of this plot at 9.976 x 10'. Given this level of

noise, the peaks at v 16, 22, 42, and 218d-1 might be

classified as statistically significant. However, when one

superimposes the spectral window on the power spectrum, it










66




Table 4-2
Observing Program 2

Star B V He C 0 Continuum

V*1 X X X X X X
V* X X X X X X
V* X X X X X X
V* X X X X X X
V* X X X X
V* X X X X
V* X X X X


V* x x x x
V* X x x x


V* X x x x x x
V* X X X X X X
V* X X X X X X
V* x x x x x x

C*3 X X
CS4 X X
C* X X

V* X x x x x x

C* X X
CS X X
C* X X

V* X x x x x x
V* X X x x x x
V* X X X x x x
V* X X X x x x
V* X x x x

V* x x x x
V* X X X X

VS X X X X X X
V* X x x x
V* x x x x
V* X X X X
V* X X X X
























Table 4-2--continued


O Continuum


Sky B5 X


a Gru
a Gru S6
a Gru

B Gru
B Gru S'
B Gru

Sky A'


'V* variable star
2VS = variable sky
'C* = comparison star
4CS comparison sky
5Sky B = 1 region of sky 1800 from variable star
6 a Gru S = a Gru sky
'B Gru S = B Gru sky
'Sky A = 1 region of sky 1800 from Sky B


St-ar


Star -V Co t -i-





















































o O a o q


JGMOd 9AI!D|9N


O
O




I




C)
C
Q)


O 1






O






0





































































S(0 CD cO


St) 0 U)
rl ui N-


jaMOd 9AflDIat


4-4
0








(0
C C


0
i-, 0



U4



44
0 to
4-4





W W40


3 co
*.-I 0


c



(D3
cr
CT

Q
L.
U-


0



*4
o(
O bO


to
d











is apparent that the peaks at v = 22d-' and v = 62d-' are part

aliases of the considerably stronger peak at v 42d'.

The CLEAN algorithm has been used in an attempt to eliminate

these spurious features, and the results are shown in Figure

4-11. Now, only two peaks have survived the CLEANing

process while remaining statistically significant. They

include the feature at v 42d-' (P 00238) with a signal-

to-noise ratio of 7.7aN and the feature at v = 238d-'

(P = 040042) which has a weaker signal of 4.5aN.

Although the least-squares routine converges for

periods corresponding to each of these frequencies, the

largest amplitude of variation and the lowest observed minus

calculated (0-C) residuals occurs for P = 0O0476 (v = 21d-').

It is interesting to note that this period is exactly twice

the period concluded from the power spectrum analysis and

perhaps this is an indication of the presence of harmonics

of a fundamental period. In order to determine whether or

not one of these periods fits the data more satisfactorily

than another, models are computed for each. Results

indicate that these data are most adequately represented by

P = 0d0476 (Figure 4-12) according to the equation



[ ti 0.48459
D(ti) = 0.34430 + 0.00379 sin 0.48459 (4-4)
S0.00757


Perhaps this period reflects the fundamental mode of















0






0
o0 M
C 5:


o







41


0 wo

o cc
(- -..









o a ao
0^ 09 (d -I








LO to to tO oB


0 i0 0 U)
.M A!i CD


-JMOd 9AIIl01a

































































10 0
0 o e r) en r)
6 6 6 6 d c


+


(6
0
(0
(0
qq^-




V
4,
0
0
CM
0


w m
0
41 P4
40 4J "*
o 0 -*
*O i -4


*.4 U .4
4) w r
.4-i



'44 4bO
o 3
0 ->

0l (a
*i-l


c ,c
> 4j 4- 4





w CL r.
-l 1-4 U

4-4 4) W
(0 0


0 Cd 010.
m 1Ow 00


wnnuiluoo : nIaG










73

variation while the prominent feature in the power spectrum

may represent the first harmonic. The carbon data have also

been analyzed in a manner comparable to that used in the

analysis of the helium data. The dirty and clean spectrums

are presented in Figures 4-13 and 4-14, respectively.

Although the feature at v = 42d-' is considerably weaker than

the corresponding peak in the power spectrum for the helium

data, it still remains the strongest feature in the plot at

5.8aN where aN = 1.680 x 10-'. Three other peaks rise just

above the 4aN level; they occur at

v = 12, 57, and 204d1.

The least-squares routine is executed for periods

ranging between 040038 (v = 263d') and 01759 (v = 6d-1)

Solutions with periods corresponding to each of the

frequencies, found from the power spectrum analysis, result.

Once again, the strongest convergence occurs for a period of

0%0477 (v = 21d'). One must realize that in all of these

models, the amplitude of variation of the CIII emission line

is so small that results cannot be considered to represent

significant intensity changes. The largest variation in

this case is only 1% of the average deflection. It is for

this reason that no specific model is suggested for this

data.

In summary, power spectrum analysis gives a period of

040238 for both helium and carbon data. The least-squares

routine, although still converging for periods on this

















0
I)












o
C 4
0




























_o e)
So ul
CM 0 0







ou

o 0W


s0 r.
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jaMod 9Aip1DaI


I-









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L.
LL.


4.4



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0

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0 p
4-X


4a





M 4















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o44.
Ul (U 4-
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order, give a best-fit with a period equal to twice this

period, or, P = Od0476.

Data Set III.

This data set spans the time interval that extends

from JD2446607.9853 through JD2446608.1921. The set includes

90 observations of -y2 Vel for the helium, carbon, and

continuum filters.

The observing sequence used to obtain these data is

that shown in Table 4-2, with At = 040023. Assuming a

minimum of two samples per cycle and a minimum of two cycles

per data set, frequencies from vmin 10d-' to /max = 217d-'

can be tested. Figure 4-15 shows the sampling function

which results from the acquisition of these data. The peak

at v = 20d-' has considerable power amounting to about one-

third that of the main peak at v Od"1. The second harmonic

at v = 41d'. and the third harmonic at v = 62d-1 are also

identified. In addition, a broad feature centered at

v = 33d-' has a second harmonic at v = 55d-'. The convolution

of the helium data with the beam is determined and presented

in Figure 4-16 in terms of relative power. The noise level

of these data is indicated by an arrow at the bottom left of

the plot at 2.719 x 10-'. The features at v = 11, 73, and

215d-' rise above the 4ao level, but the peak at v = 73d' is

part alias with the stronger feature at v = lld-'. The

CLEANing process leaves two of the three peaks mentioned

above as statistically significant (Figure 4-17). The




























UC'

I-



0 U
'- (
0 C



LL.



0




I'


0 0 0 0 0
0 0 0 0 0
0 00 co 0
ooooo


.iGMOd GA!DIGad





















0
0









-W
0* C0


-o

o4

0 00


















JSM:j 0Apt
>1 4)







LL.
14)

















U) If col o


0 C0 N 0 0



JOMOd aA!lDja8






































































If I) U) (0



n mN


4-4


CC
0

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o)
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0 41
0

0
*-4 o
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8



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41






0
Sca r-
PLV


I
-a]


V


C

30



L


coIt

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0
4


-JMOd aAljoat9











feature at v = lld1 has a relative power of 4.90N while the

peak at v = 215d-' has the slightly lower signal-to-noise

ratio of 4.6aN and represents more-rapid fluctuations in

intensity. The least-squares routine converges to two sets

of parameters with almost the same amplitude in each case.

The first of these models has a period of 2.00 hours and

corresponds to the peak at v lld' in Figure 4-17. The

model for this period is shown in Figure 4.18, and has been

computed with the relation



[ ti 0.50673
D(ti) 0.34410 + 0.00354 sin 0.50673 (4-5)
0.01328



The second set of parameters which results from the least-

squares routine has a period of 2.75 hours and is described

by equation (4-6):



r ti 0.59261
D(ti) 0.34442 + 0.00329 sin 0.5926 (4-6)
1 0.01820



Even though this period does not correspond to any prominent

feature in the power spectrum, the model, pictured in Figure

4-19, seems to fit the data as well as that described by

equation (4-5). Even though the 0-C residuals computed from

equation (4-5) are slightly smaller than the residuals

determined with equation (4-6), gaps in the data make it

































,4 M
o0 P





oD


0u-J
a *






4-4





O 0
0


0
_4

m-4

C4

0.
3






4-4 0
U)
r-4
OC
0 0
4-1
c0 C
T-1


0
-r
Co






4-I


0o








-4
cn b
h* IL

5 f


-4




-4
>-,







U)
41


0
*4)









0
0
4.1







U).

a











C4
*m>


1 I _


wnnuiluoo : 119H



























41 0 *-





( C



4JO
ao
r-4




0 *o
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0 0
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oa c


p-






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(0

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wnnunluoo : 119H










83
difficult to determine which fit is better. Since the first

of the two periods is supported by both methods of analysis,

P = 2.00 hours may be the more appropriate period.

The Fourier transform of the carbon data is converted

to power, and Figures 4-20 and 4-21 show the results before

and after the removal of spurious features. The la noise

level of these data is at 5.685 x 10"'. Since the carbon

emission feature is considerably weaker than the helium

line, it is more difficult to discern intensity variations

in the carbon feature from random noise. In this particular

case, the CLEANing process reduces the strongest peaks in

Figure 4-20 below the 4oN level. The least-squares routine

has the strongest convergence for a period of 34.4 minutes.

However, since the amplitude of variation is only a very

small fraction of the total deflection in that filter, one

cannot regard this result with much confidence.

In summary, the intensity variations of the helium

emission line are probably best described with a period of

2.0 hours. This period was selected by both power spectrum

and least-squares analytic techniques. In addition, the

data have been modeled with a period of 2.75 hours, which

was a solution of the least-squares method only. Relatively

large gaps in the data make it difficult to determine which

period, if either, is the more appropriate. The power

spectrum of the carbon data indicates no strong periodicity.

A least-squares solution with a period of 34.4 minutes is











































































o Co C~o 0
*1~ 6


0
0
N










0





TI








0
oi



u-
0)




mL


0
O





1I


o


4-4
0
(C
BG)
00






(O
41







> 0
4) -1
(a
.0 44












0 0
0 r.



0 0



(U


Q)


0U 1-4

04 a1 to
(fl uo
(a l-
uI >-
Q) 0)
P 4-1 b
O a)r-i
h 'o i


.JOMOd GAIDlpG


































0
In
to



I-






-o






L..
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4-4
0

G C
c0




M4)

0 44
0
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.0


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4-4



2. 4-1
a (







0 CO
5 *P 6
o car-
(UC a


'-4



40


M
-d4


(0 ( (0* 1 0


0 0 0
*


J9MOd aA!1DIba











found, but because of the low amplitude of the variation,

this period is not considered to be a true description of

the variations within this weak feature.

Data Set IV.

This data set consists of 18.8 hours of photometry of

72 Vel extending from JD2446608.7789 through JD2446609.5624.

The observing program displayed in Table 4-2 was used to

obtain a total of 347 observations through each of the

helium, carbon, and continuum filters. The average time

interval between successive observations in any one of these

filters is 040023.

The spectral window is depicted in Figure 4-22 where

peaks at v = 17d-' and v = 35d-' are separated by the same

amount as the peaks at v 38d-' and v 56d-'. The

convolution of the intensity measurements of the helium

emission line with this somewhat more complicated sampling

function gives the power spectrum in Figure 4-23. The loN

noise level at 8.850 x 10' indicates that peaks at v = 11.5,

35, and 166.5d-' are statistically significant features. A

strong feature also occurs at v = 1.5d.', but this frequency

does not satisfy the Nyquist criterion of two samples per

cycle. The peak at v 35d-' is part alias with that at

v = 1.5d-', and should, in principle, be reduced in strength

by the CLEAN algorithm. Figure 4-24 shows the power

spectrum that results after the spurious features are

removed from the dirty spectrum. The only feature which






































C-)


C
Q)

0-


C14





*r4


JQMOd 9Ap!JDI














88





0



ot
O





C4 4




S o(d
wo
0



0 -44



0 0
P





40
@1k
U


o 0





--4
4

(1) '4- 0






oo-
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Ccu
II



a~C VI O
Q )-
o c
C..)

4q)C












0 0 0
cdA4
J~M~d A~1DI0




























4-
0





ulC
0 G
4-4 a






c>
e0

0



0 Ci






0 w
4.)


0z



4-1

3d 0
P) <0


L0




LL


JaMod OAIJr~latl











remains statistically significant is the peak at v = 1.5d-',

but as mentioned previously, the period which corresponds to

this frequency does not satisfy the Nyquist criterion, and

thus cannot be considered in the context of this research.

Although no peaks survive the CLEANing process, the least-

squares routine is still executed. Convergence to a set of

parameters with P = 0208 (5.0 hours) is given by



[ ti 0.22157
D(ti) = 0.34736 + 0.00250 sin 0.03316 (4-7)
0.03316



This fit, depicted in Figure 4-25, has a very low

amplitude of variation and is certainly not a very good

representation of the changes in intensity. This

unsatisfactory fit is confirmed by the low power in the

peaks of the CLEANed power spectrum (Figure 4-24). An

attempt was made to improve the results obtained with these

data by dividing the long data set into two subsets. The

first subset contains observations made between

JD2446608.7789 and JD2446609.1646, and has a time-resolution

which is exactly the same as that for the whole data set.

The shorter span of this subset allows for frequencies

between vmin = 5d-' and vmax = 217d-' to be tested. The

spectral window function for these data, depicted in Figure

4-26, shows similar, but slightly stronger, peaks as those

from Figure 4-22. Dirty and clean spectra are shown in






















44I



O 0c V4





*LO r- 4 3


0 co
00 00

:- U) 0>


-4
( ) a 4c


t o c (

C n>
0 -w
f- 0 1 > D a4)
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Ifl 0
a C
0 0 40 0C0
I-


C'.




o oo
0 CkO




0 0 0



uWnnul!uo3 : I|aH












































































o O O 0 0

o 00 N N
6 6 a 6


I-



V



C-)

Cr



L.


CL


0








0
44













0
l-







44
:u
0





'0
3





U
J
3~-
4-
cu



mm


JGMOd gAIIlD|











Figures 4-27 and 4-28. The noise level in each of these

plots is denoted in the lower left-hand portion of the

figures at 1.737 x 106'. The CLEAN algorithm removes all

spurious features at or below the 3aN level. As can be seen

from Figure 4-28, this process again leaves no statistically

significant features. The least-squares solution for this

data set gives a period of 5.79 hours corresponding in

frequency to the strongest peak in Figures 4-27 and 4-28,

even though these peaks do not meet the statistical

significance criterion. This model is described by



t ti 1.38569
D(ti) 0.34527 + 0.00329 sin -0.03842 (4-8)




and is shown in Figure 4-29. The 0-C residuals computed

with this equation are marginally better than those

determined with equation (4-7).

The second subset of data set IV covers the time range

that extends from JD2446609.1870 through JD2446610.5624.

The minimum and maximum frequencies retrievable from this

subset are the same as for subset 1. Again, the spectral

window (Figure 4-30) is qualitatively similar to the beam

for the entire data set, but is quantitatively different.

Figures 4-31 and 4-32 represent the power spectra before and

after CLEANing the data. The only peaks which remain above

the 4aN level after the CLEANing process are those at