A new determination of Jupiter's radio rotation period

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Title:
A new determination of Jupiter's radio rotation period
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xiv, 126 leaves : ill. ; 29 cm.
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Higgins, Charles A., 1964-
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Radio astronomy   ( lcsh )
Jupiter (Planet)   ( lcsh )
Astronomy thesis, Ph. D
Dissertations, Academic -- Astronomy -- UF
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bibliography   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1996.
Bibliography:
Includes bibliographical references (leaves 118-125).
Statement of Responsibility:
by Charles A. Higgins Jr.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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notis - AKS4954
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Full Text












A NEW DETERMINATION OF JUPITER'S RADIO ROTATION PERIOD











By

CHARLES A. HIGGINS JR.


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


1996


/** ^


., -.



















To my family and my friends,
for they are all that matter















ACKNOWLEDGMENTS


First and foremost, I must acknowledge my advisor Dr. George R. Lebo, chairman

of my graduate supervisory committee, for his suggestion of this topic and his support

and guidance throughout my graduate career. I would also like to thank him for his

friendly and fun discussions, as well as some workouts, on the subject of running.

Second, I wish to thank Dr. Thomas D. Carr, cochairman of my graduate supervisory

committee and head of the radio astronomy program at the University of Florida. He

was one of the founders of the radio program in 1957, and still is one of the hardest

working people in the department. He has given me valuable instruction and advice for

this project.

For my other supervisory committee members, Dr. Alex G. Smith, Dr. Kwan Yu

Chen, and Dr. James E. Keesling, I would like to thank them for their helpful suggestions

and support for the completion of this document.

I would also like to acknowledge the engineers, Wesley B. Greenman and Jorge Levy,

for all their patient help with the equipment and the data, and Don McNeil for his help

with the data reduction. In particular, I wish to thank Dr. Francisco Reyes for his insight

and helpful discussions regarding this project. Sincere gratitude to Jim Thieman and Jim

Green as well as Shing Fung and Bob Candey of NASA's Goddard Space Flight Center

for their support and scientific insight on many projects.

Many thanks go to my graduate student friends in radio astronomy, Leonard Garcia

and Dr. Liyun Wang, as well as acknowledgments to all the graduate students, faculty

iii








and staff. There are many great people here. In particular I wish to thank all the

astronomy office personnel, Jeanne Kerrick, Darlene Jeremiah, Suzie Hicks, Ann Elton,

Debra Hunter, and Glenda Smith, for their help in keeping my records, classes and

finances in order. Many thanks go to Kazumasa Imai for help with the ephemeris program

and to Nancy Chanover from New Mexico State University for her help with the Fourier

Analysis programs.

I also wish to recognize the UF astronomy department, Dr. Humberto Campins, the

UF Division of Sponsored Research, the Florida Space Grant consortium, and Universities

Space Research Association's Visiting Science Program at NASA's Goddard Space Flight

Center, along with the National Space Science Data Center, for support and funding

throughout my graduate career.

Finally, I wish to thank the dozens of observers at the UF radio observatory. Without

you, and the countless number of sleepless nights, this project would not be possible.


















TABLE OF CONTENTS

ACKNOWLEDGMENTS .................


. iii


LIST OF TABLES ..................................... vii

LIST OF FIGURES ................................... viii

ABSTRACT ........................................ xiii

CHAPTERS

1. INTRODUCTION ................................... 1
1.1 Overview of Jupiter's Radio Emissions ................... 2

1.2 History of Jupiter's Rotation Period Calculations .............. 7


2. THE UNIVERSITY OF FLORIDA DECAMETER DATA .
2.1 The Radio Telescope System ................

2.2 Data Collection ........................
2.3 Data Reduction and Format ................

3. ROTATIONAL PERIOD CALCULATION ...........
3.1 Cross Correlation Technique ................

3.1.1 Calculation of Occurrence Probabilities ......
3.1.2 Cross Correlation ...................
3.1.3 Rotation Period Calculation ............
3.1.4 Weighting Method ..................

3.1.5 Final Data Set ....................
3.1.6 Statistical Significance ................

3.2 Statistical Power Spectral Analysis ...........


4. STRUCTURE WITHIN HOM EMISSION .
4.1 Introduction ................
4.2 Data Analysis ...............


4.2.1

4.2.2
4.2.3


Occurrence Probability: Frequency Versus CML

HOM-DAM Relation ................
Polarization Studies .................


. . 20
. . 20

. . 2 1
. . 24

. .. 33
. . 35

. . 35
. . 38
. . 40
. . 4 1

. . 42
. . 47

. . 48


. . 74
. . 74
. . 76

. . 76

. . 80
. . 8 1


4.2.4 Occurrence Probability: Magnetic Latitude Versus Frequency

4.2.5 Solar Wind Interactions ......................
4.2.6 Intensity Profiles ..........................

4.3 D discussion .. ... .. .. ... .. .


. 83

. 84
. .85

. 86


.
.
.









5. DISCUSSION OF VARIABILITY ..............
5.1 Radio Rotation Period ..................
5.2 Variability Measurements ...............
5.2.1 Rotation Period Drift ..............
5.2.2 Cross Correlation Drift ............

6. SUMMARY AND CONCLUSIONS .............
6.1 Rotation Period ......................
6.2 HOM Structure ......................

APPENDICES

A. CALIBRATION OF THE UF ANTENNAS ........
A. 1 UF Radio Antennas Receivers and Calibrator .
A.2 Calculation of Minimum Detectable Flux Density .

B. SUMMARY OF THE EPHEMERIS PROGRAM .....

BIBLIOGRAPHY .........................

BIOGRAPHICAL SKETCH ...................


. . 96
. . 96
. . 98
. . 99
. . 10 1

. . 107
. . 107
. . 109



. . 111
. . 111
. . 112

. . 115

. . 118

. . 126















LIST OF TABLES

Table Page

1.1: Jupiter's radio emission components ..................... 15

2.1: 18 MHz Florida radio observation data . . 26

2.2: 20 MHz Florida radio observation data . . 27

2.3: 22 MHz Florida radio observation data . . 28

2.4: Totals for UF radio observatory decameter data . 29

2.5: Example of a Jupiter data reduction file . . 30

3.1: 18 MHz rotation period information . . ... 50

3.2: 20 MHz rotation period information . . 51

3.3: 22 MHz rotation period information . . 52

3.4: Independent rotation period determinations based on 24-year data 53

3.5: Independent rotation period determinations based on 12-year data 53

3.6: D ata for X2 test .................................. 54

A. 1: Antenna parameters for the UF radio observatory . 114

A.2: Receiver parameters for the UF radio observatory . 114

A.3: Telescope characteristics for data calibration . . 114

B.1: Specific parameters used for the ephemeris program . 116















LIST OF FIGURES


Figure Page

1.1: The average power flux density spectrum of Jupiter's nonthermal
magnetospheric radio emissions. Also shown are the sensitivities of the
telescopes given as minimum detectable flux densities (ASMIN) at the two
extremes of the galactic background emission, the plane and the pole. 16

1.2: Probability of detecting Jupiter radio emission for a given longitude (A)
for the observations from 1957 to 1994 at (a) 18 MHz, (b) 20 MHz, and
(c) 22 MHz. The three most probable regions are designated as source
A (A=2400), source B (A=1300), and source C (A=330). ... 17

1.3: Normalized occurrence probability of Jovian emissions versus longitude
for combined 18, 20, and 22 MHz observations from 1957 to 1994 18

1.4: Shaded surface occurrence probability versus longitude (A) and the
phase of Io (0) for 18, 20, 22 MHz observations from 1957 to 1994.
Overlaid is a contour plot to the same scale. The (A,4) coordinates of
the lo-A source are (210-250, 240), Io-B (90-180, 900), Io-C
(3000-360, 2400), and non-Io-A (2200-2800, 00-360). ... 19

2.1: Block diagram showing the components of a simple radio telescope. 31

2.2: Sample strip chart recorder output at 22 MHz on May 24, 1986. The
Universal Time is given at the top of the figure. The Jupiter emission,
identified by the observer with "J", begins about 0800 UT and ends at
0930 UT. Note the burstiness of the emission and its quick begin and end.
Calibration data are labeled at the end of the observation at 1030 UT. 32

3.1: Probability of occurrence of Jupiter as a function of Jovian longitude at
18 MHz for the seasons from 1957 to 1968. The probabilities are given
as histograms and are calculated for 50 bins in longitude. Note that the
sources, especially source A (240-2700), move back-and-forth in
position over time showing the cyclical observational effects of
changing latitude. .............................. 55








3.2: Occurrence probability for seasons 1969-1980 at 18 MHz . 56


3.3: Occurrence probability for seasons 1981-1994 at 18 MHz . 57


3.4: Occurrence probability for seasons 1964-1968 at 20 MHz . 58


3.5: Occurrence probability for seasons 1969-1980 at 20 MHz . 59


3.6: Occurrence probability for seasons 1981-1994 at 20 MHz . 60


3.7: Occurrence probability for seasons 1958-1968 at 22 MHz . 61


3.8: Occurrence probability for seasons 1969-1980 at 22 MHz . 62


3.9: Occurrence probability for seasons 1981-1994 at 22 MHz . 63


3.10: The longitudinal position of the source A over time for (a) 18 MHz, (b)
20 MHz, and (c) 22 MHz. The filled points represent the peak
probability point of the source, and the open points represent the
average of the two half-probability points. The 12-year DE effect can
be seen at all frequencies as the sinusoidal component in the curves. 64


3.11: Example of the cross correlation technique to calculate the shift of the
curves over 12 or 24 year intervals. Panel (a) is the smoothed 22 MHz
occurrence probability for the 1963 season, and panel (b) is the 22 MHz
1987 season. Panel (c) is a plot of the cross correlation coefficients that
were calculated for every 20.5 longitude shift of the 1987 occurrence
probability with respect to the 1963 occurrence probability. The
maximum correlation is 0.975 and corresponds to a longitude shift of
-60.8. The thick dashed curve from -30 to +300 represents a
polynomial fit to the peak of the correlation. . . 65


3.12: Overview of the data combination and weighting method. Column 1 is
all the 24-year pairs of seasons used in this study. Column 2 represents
the cross correlated data. Column 3 is the combined frequency data.
Column 4 is the results for the 24-year and 12-year calculations, and
Column 5 is the final result. The calculations done between each
column are labeled A, B, C, and D, and are summarized in the legend. 66


A --








3.13: Rotation period values for each frequency plotted as a function of each
12 year or 24 year mid-date. The legend in the upper right shows the
frequency and station where the data were gathered. Error bars are
inversely proportional to the individual weights. System III (1965) is
plotted as the horizontal dotted line for reference. . ... 67



3.14: The distribution of all the data given in Figure 3.13 plotted as a
histogram with a bin size of 0s.02. The unweighted mean (yp) and
standard deviation (r) are shown, and a normal curve with the same
parameters is overplotted for reference . . 68



3.15: Rotation period values for each mid-date after the frequencies are
combined. Error bars are again inversely proportional to the weights. 69



3.16: The distribution of data after the frequencies are combined shown as a
histogram with a bin size of 0s.02. The unweighted mean (yp) and
standard deviation (ar) are shown, and a normal curve with the same
parameters is overplotted for reference . . 70



3.17: The statistical significance of the final weighed rotation period. The
vertical line is a reference for System 1II (1965), and the normal curve
has the weighted mean and weighted standard deviation of our final
calculation. The statistical significance between the two measurements
(7.4a) is shown by the horizontal arrow. . . .. 71



3.18: Occurrence probability data for 18 MHz, 20 MHz and 22 MHz are
combined into one occurrence probability histogram versus Jovian
longitude for each season. All seasons are then plotted end-to-end in
longitude (0-359, 00-3590, etc.) and then converted from longitude
to time. Note the 12-year DE effect for the seasons. The shorter term
peaks represent the source A peaks for each season. . ... 72



3.19: Spectral power output for the occurrence probability data given in the
previous figure. The frequency representing the maximum power
corresponds to the rotation period of Jupiter and has a period of 9h 55m
29s.72. The other peaks are harmonics of the rotation period.. 73








4.1: A frequency versus central meridian longitude (CML) intensity
spectrogram from the planetary radio astronomy (PRA) experiment
onboard Voyager 2 taken during one planetary rotation prior to
encounter with Jupiter. The hectometric radio emission (HOM) is seen
as a diffuse broadband emission extending over a limited CML range.
The lane features are the diagonal regions of low intensity emission at
90 and 330 CM L ................................ 90

4.2: (a) The occurrence probability spectrogram sorted by the wave
frequency and CML. It combines data taken from over 40 planetary
rotations before Voyager 2 encounter and shows that zones of reduced
occurrence probability appear as "lanes". The borders of the lanes are
marked in white in the spectrogram. (b) A similar spectrogram
combining data from over 32 planetary rotations after Jovian encounter.
(c) The magnetic latitude of the Voyager 2 spacecraft during the
observations presented in (a). The lowest occurrence probability for
HOM occurs when the spacecraft is above +100 magnetic latitude. 91

4.3: A summary of the observed emission beaming of HOM is shown
(adapted from Ladreiter and Leblanc [1989]). The overlap of the
right-hand (RH) and left-hand (LH) polarized emissions is shown as the
cross-hatched region. The trajectory of Voyager 2 (at large radial
distances both inbound and outbound) is also shown in magnetic
latitude versus CML. The multiple curves represent periodic spacecraft
positions during the time periods for inbound and outbound data
observations. The lack of HOM emissions from 1200 to 3000 CML (see
Figure 4.2) is found when the spacecraft is above +100. . 92

4.4: The four panels are the HOM occurrence probability plotted as a
function of magnetic latitude and emission frequency for the CML
ranges indicated. Only those data for which the magnetic latitude of the
spacecraft is from 00 to +100 are included. (a) Inbound data for the
CML range 700 to 1300, and (b) for CML 265 to 335. (c) Outbound
data for CML 820 to 142, and (d) for CML 2530 to 3230. All panels
show the lanes or decreases in the occurrence probability. The lanes
start at +100 magnetic latitude at 500 kHz and extend down to the
magnetic equator for HOM frequencies greater than 1 MHz. .. 93

4.5: A contour plot of the local electron plasma frequency to electron
gyrofrequency ratio for the model Jovian magnetosphere used in this
study. It is important to note that the source regions for the R-X
fundamental and the second harmonic emissions are located in regions
where fp / fg < 1. ................................. 94








4.6: A schematic showing the lane structure at two HOM frequencies, 800
kHz and 1200 kHz. The shaded regions represent the equatorial HOM
beam, and the lanes are shown as regions where little or no HOM
emission is seen. Note that the position of the lanes moves closer to the
magnetic equator at the higher frequencies. The sinusoidal curves are
the trajectories of the Voyager 1 and 2 spacecraft on their inbound and
outbound passes .................................. 95

5.1: Longitude shifts from Tables 3.1 3.3 plotted versus time. (a) CML
shifts in System m (1965). (b) CML shifts using the new rotation
period. Note that the weighted average shift is well below the zero
reference in (a), but is well within the error in (b). . ... 103

5.2: 24-year rotation periods plotted as a function of time. Error bars are
inversely proportional to the weights. The dashed line is reference of
our new rotation period, and the solid line is a weighted least squares fit
with the slope and error given. ........................ 104

5.3: Two rotation periods and lor error bars based on splitting the 24-year
data into two groups (Equation 5.4). The slope and error between the
two points is given at the top. The significance between the two points
is indicated at the bottom. ........................... 105

5.4: Longitudinal shifts from cross correlating adjacent seasonal occurrence
probability histograms. Open circles represent the shifts for the 3
individual frequencies, 18, 20, and 22 MHz and filled circles represent
their average. The 12-year cyclical effect is due to DE. The solid line
is a linear least squares fit to the averaged data and shows that the
histograms may be drifting in time. . . ... 106

B.1: Jovian ephemeris program flowchart . . 117














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

A NEW DETERMINATION OF JUPITER'S RADIO ROTATION PERIOD

By

Charles A. Higgins Jr.

May, 1996

Chairman: George R. Lebo
Cochairman: Thomas D. Carr
Major Department: Astronomy

New observations of Jovian ground-based decameter (DAM) emission from 1977
to 1994 are added to the University of Florida (UF) database for the determination
of a precise rotation period and for the investigation of long-term effects. We used a
proven technique of cross-correlating occurrence probability histograms separated by 12
or 24 years and calculated 24 independent rotation period values of the inner Jovian
magnetosphere. Our new weighted mean rotation period value is 9h 55m 29s.685, where
the weighted standard deviation is 0s.003. This new rotation period corresponds to a
sidereal rotation rate of Jupiter of 8700.5366 00.0001 per day and would corotate with
the magnetic field of the planet more closely than the International Astronomical Union's
accepted System III (1965) period. The rotation period is not changing linearly at a
rate in excess of 27.1 milliseconds per year. The statistical difference between our new
period and System In (1965) is more than 7 standard deviations and would result in a
drift between the two rotation systems of about 00.2 per year. This is the first evidence
that the IAU System III (1965) rotation period may need revision.








We also found and analyzed persistent spectral features seen within Jovian hectometric
radio emission (HOM) data observed by the Voyager planetary radio astronomy (PRA)
experiment. The features of interest appear as "lanes" of decreased emission intensity
within the amorphous HOM and are apparent in intensity and occurrence probability
spectrograms of frequency versus Jovian longitude. We created occurrence probability
spectrograms of frequency versus magnetic latitude using both inbound and outbound
Voyager 2 data at Jupiter and found that the lane features are at least semipermanent
and are spatially and temporally stable. There is no evidence of changes in intensity or
polarization reversals across the lanes, and there is no correlation of the occurrence of
the lanes with the solar wind density. The lane features appear to be either an intrinsic
property of the emission or the result of a complex propagation effect, further indicating
that HOM is a separate emission component of the Jovian radio emissions. No theory at
this time can explain all the observed features.













CHAPTER 1
INTRODUCTION



Jupiter is a very massive and complex planet orbiting the Sun every 11.9 years

at a distance of 5.2 times the Earth-Sun distance. It also possesses the largest and

strongest overall magnetic field in the solar system. The interaction of this magnetic field

with the surrounding space plasma has provided scientists with perplexing problems to

solve. Some of these problems include the phenomenology of the many and diverse radio

emissions emanating from the Jovian system. While there are many Jovian radio emission

components to be studied, the focus of this dissertation is the decameter (DAM) and

hectometer (HOM) emission. In particular, new ground-based DAM emission data from

1977 to 1994 are added to the University of Florida (UF) database for the determination

of a precise rotation period and for the investigation of long-term effects. Furthermore,

we found and analyzed new spectral features seen in the Jovian HOM observed by the

Voyager spacecraft. These features appear as "lanes" of decreased emission intensity in

the HOM emission and can be used to constrain emission and propagation models for

the HOM emission component.

The collection and reduction of ground-based DAM observational data gathered at

the UF Radio Observatory are discussed in Chapter 2. Chapter 3 is the analysis of these

data and how they are used to recalculate the radio rotation period of Jupiter to a much

higher precision. Analysis of structure within Jovian HOM emissions gathered by the

Voyager spacecraft is the topic and discussion of Chapter 4. In Chapter 5, I discuss the

implications of the rotation period results, and explore the possibility of variability within






2

the Jovian magnetic system. A summary and concluding remarks are given in Chapter

6. First, however, a short overview of the Jovian radio emissions and a history of Jovian

rotation period calculations are presented.


1.1 Overview of Jupiter's Radio Emissions


Jupiter is one of the strongest and most diverse sources of radio emission in the

entire solar system. Jupiter emits in the radio frequency spectrum from 10 kHz to about

300 GHz, corresponding to wavelengths ranging from 30 km down to 1 mm. There

are four well-established band designations corresponding to spectral peaks in the radio

emission: kilometer radiation (KOM), hectometer radiation (HOM), decameter radiation

(DAM), and decimeter radiation (DIM). Table 1.1 is an overview of the frequency and

wavelength components of the four Jovian radio bands, as well as, some of the other

components that have been identified. Figure 1.1 (adapted from Barrow and Carr [1992]

and Kaiser [1993]) is a plot of the average power flux density spectrum of the Jovian

nonthermal radio emissions.

The discovery of radio emission from Jupiter by Burke and Franklin in 1955 was

serendipitous because Jupiter happened to be in the same region of sky they were

scanning for the Crab Nebula [Burke and Franklin, 1955; Franklin, 1959]. They first

detected Jupiter emission at decameter (DAM) wavelengths, which was later realized to

be the strongest of many radio components (see Section 1.2 for more detail on the early

history of Jovian decametric radio observations). The DAM emission shows a general

bursty characteristic in both ground-based and spacecraft data and shows many different

properties and structures on different timescales [Carr et al., 1983]. It is generally

believed that the source of these emissions are plasma instabilities arising in the inner

magnetosphere near polar latitudes, most probably along the magnetic field lines that






3

run through the Io plasma torus [Leblanc et al., 1994; Kaiser, 1993]. The generation

mechanism of this emission is believed to be the cyclotron maser instability mechanism

where the emission frequency from each region is slightly higher than the electron

cyclotron frequency (fc) in that region [Wu and Lee, 1979]. Since the highest magnetic

field intensity (B) at locations at which radio emission might occur is 14 Gauss, the

relationship fc (in MHz) 2.8B (in Gauss) indicates that the highest possible frequency

of the emitted decametric radiation is about 40 MHz. There is indeed a pronounced cutoff

above 40 MHz in the observed radiation (see Figure 1.1). Ground-based observations

are limited by the Earth's ionosphere to frequencies above 5-20 MHz depending on the

local conditions. Because Jupiter's DAM radio flux is more intense and more likely to

be detected at the lower frequencies, most of the ground-based observations are carried

out between about 18 and 30 MHz. In addition to the cutoff of emission at 40 MHz,

free-escaping radiation is also cut off at the lower frequencies, about 1-10 kHz (see

Figure 1.1). This occurs because the plasma frequency is limited by the local plasma

densities in the Jovian magnetosphere. Below this frequency are the bounded plasma

waves [Carr et al., 1983].

Soon after the discovery of radio emission from Jupiter it was found that the observed

emission probability was correlated with the central meridian longitude of the planet at

the time of observation [Shain, 1956]. Certain longitude regions where the probability of

detection was greater were identified and designated as sources A, B, and C [Carr et al.,

1961]. These source regions are indicated in the latest histograms of absolute occurrence

probabilities plotted against Jovian central meridian longitude given in Figure 1.2. These

graphs represent all years (1957 1994) of observations at 18, 20, and 22 MHz from the

University of Florida Radio Observatory. A combination of the three frequencies plotted

as normalized occurrence probability is shown in Figure 1.3. Figure 1.3 is an extension






4
of Figure 7.14 of Carr et al. [1983] by 17 years to include the 1977 to 1994 seasons.

Over 28,000 hours of observations at each frequency were used to compile these figures!

A second correlation was found in 1964 when it was discovered that the orbital

phase of the Jovian satellite lo had a strong influence on the DAM emission [Bigg, 1964;

Carr et al., 1983]. The orbital phase of Io is the angle of the satellite from superior

geocentric conjunction and is measured positive in the direction of lo's orbit. At the

DAM frequencies of interest here (18-22 MHz), strong emission occurs at the source

B CML ranges only when Io's orbital phase is near 90. This source is now known as

the Io-B source. At source A CML ranges, the strongest and most predictable emission

occurs when the Io phase is near 2400. This source A component is known as the Io-A

source. The other source A component, known as non-lo-A, is uncorrelated with the

phase of lo and thus occurs at all lo phases. Non-lo-A emission is generally less intense

than lo-A, but at times can exhibit a higher occurrence probability. A fourth source is

designated as lo-C because it emits only at source C CML ranges when the phase of Io

is near 2400. The Io-C source usually exhibits the lowest occurrence probability of the

four sources (see Carr and Desch, 1976). Figure 1.4 is a combination shaded surface

and contour plot of the occurrence probabilities of the four sources shown as functions

of CML and Io phase. Again, this figure represents 18, 20, and 22 MHz data taken at

the UF Radio Observatory from 1957 to 1994. The dominant sources are labeled on

the contour plot and on the surface plot. Although observations from the two Voyager

spacecraft provided new information on the DAM emissions, the exact interplay of Io

and the Io plasma torus on the generation of the emission is still unknown. There are

various theories that attempt to explain these observations, but one of the fundamental

unanswered questions is the exact location of the sources (see Carr et al. [1983] and

references therein). As previously stated, it is generally believed that the lo-related






5
emissions originate from source regions along the Io magnetic flux tube between lo and

the Jovian ionosphere near the altitude at which the electron cyclotron frequency nearly

equals the frequency observed. There has also been shown a correlation between DAM

and the solar wind, which gives some evidence of DAM and HOM sources existing near

the auroral zones at higher magnetic latitudes [Stone et al., 1992a; Barrow et al., 1986].

This correlation is slight in the case of DAM, however, and the existence of the effect

needs verification.

The hectometer (HOM) emission is thought to be an extension of the DAM emission

into lower frequencies [Carr et al., 1983; Lecacheux et al., 1980; Boischot et al., 1981].

However, much work has been done to argue that HOM is a separate emission component

with individual characteristics and source locations [Reiner et al., 1993b; Barrow and

Desch, 1989]. HOM was first detected by the Pioneer spacecraft in the early 1970s,

again by the Voyager spacecraft in 1979, and was most recently observed by the Ulysses

spacecraft in 1992 [ Stone et al., 1992a, 1992b; Warwick et al., 1979a, 1979b; Brown,

1974; Desch and Carr, 1974]. The general mechanism of HOM emission is again

believed to be the cyclotron maser instability (CMI) mechanism [Wu and Lee, 1979].

Several models of the HOM emission have been published indicating that the source

locations for the emission are along high L-shells (L = 10-20) [Wang, 1994; Ladreiter and

Leblanc, 1990a, 1990b]. The latest results have come from using the Ulysses spacecraft

observations which indicates that the HOM source location is in the Jovian polar regions

along magnetic field lines that pass through the lo torus (L-shell ~ 6) [Reiner et al.,

1993a, 1993b]. Further analysis of HOM emission structure is presented in Chapter 4.

Decimeter (DIM) emission, now referred to as synchrotron emission, was first

observed in 1958 by Sloanaker [1959] and McClain and Sloanaker [1959], and soon

after it was shown that this emission was synchrotron emission from trapped electrons






6

in the Jovian radiation belts (see reviews by Carr et al., [1983] and Berge and Gulkis

[1976]). Recent radio images show the highest DIM intensities occur near the magnetic

equator at approximately 1.5 Jovian radii (Rj) from the planet [de Pater, 1990]. Figure 1.1

shows that the flux density is smooth and continuous over nearly the entire spectrum. The

DIM radiation shows variability over many different time scales and the most obvious

and significant one is the sidereal rotation of the magnetic field [Carr et al., 1983].

Measurements of the variability of the polarization of the DIM radiation can lead to

very accurate rotation period measurements [Komesaroffet al., 1980]. However we now

believe that the DAM component is more suitable for the measurement of the Jovian

rotation period.

The kilometric (KOM) component is seen as the third peak in figure 1.1 and is broken

into three individual components: broadband, narrowband and smooth. The broadband

(bKOM) and the narrowband (nKOM) components were discovered in the data gathered

by the Voyager I and 2 spacecraft [Scarf et al., 1979; Warwick et al., 1979a, 1979b;

Gurnett et al., 1979]. The bKOM emission shows a bursty structure that extends over

several hundred kHz in frequency while the nKOM is smoother with a frequency range

of less than 100 kHz. The bKOM shows a regular variability over the rotation period,

but nKOM is more sporadic in its appearance and drifts with respect to the accepted

magnetospheric rotation period [Kaiser, 1993]. The source location of the bKOM is

believed to be distinct regions in the northern and southern Jovian inner magnetosphere,

and this question should be resolved once the data from the Ulysses mission are analyzed

[Kaiser and Desch, 1980]. The source location of the nKOM emission, however, is

more confidently known to be in the outer regions of the lo torus [Reiner et al., 1993c].

Reiner et al. [1994] also found another component of the KOM emission, called sKOM.

This emission occurs in the same frequency band as the bKOM, but it is much weaker,






7

oppositely polarized, and has a smooth profile. The latest observations from the Ulysses

spacecraft show both the HOM and the KOM emissions at a higher sensitivity [Barrow

and Lecacheux, 1993; Kaiser and Desch, 1992; Lecacheux et al., 1992].

The lowest frequency bands of emissions are called the continuum radiation, which

is emitted by most, if not all, of the radio-emitting planets [Kurth, 1992]. The emission

is generally weaker having a smooth profile and a steep spectrum, but Jupiter exhibits

very strong continuum radiation [Kaiser, 1993; Kurth, 1992]. The source location has

been modeled to be near the magnetic equator in the outer regions of the magnetosphere,

but the location is highly dependent on the magnetic field structure model [Kurth, 1992].

The final component of the Jovian radiation is the fast drift and impulsive phenomena

at approximately 10 kHz. They were first seen by Kurth et al. [1989] and exhibit fast

drifting in frequency and bursts that are periodic [Kaiser, 1993]. They exhibit similar

structure to Type III solar bursts. Many other types of bursts exist at the lower Jovian

emission frequencies and show varying periodicities, but these events are not clearly

understood at this time [Kaiser, 1993].


1.2 History of Jupiter's Rotation Period Calculations


Since Jupiter is a gaseous planet, it rotates differentially, and this differential rotation

makes defining a precise rotation rate based on visual observations impossible. A central

meridian longitude system can be defined on the basis of an assumed rotation rate, but no

rotation rate can be found for which any visible Jovian feature remains stationary in that

longitude system. The history of identifying Jupiter's true rotation period and longitude

system is very interesting. There have been a multitude of data collected and many

techniques used in the attempt to solve this problem. I will attempt to give a complete

chronological summary of the Jovian rotation period calculations and results. This will






8

provide an ideal avenue to lead into the major topic addressed in this dissertation: a

Jovian rotation period measurement of unprecedented precision based on the total of the

data collected at the University of Florida Radio Observatory.

One of the first determinations of the Jovian rotation period came from Schroeter

in 1787 using the motions of surface features. During the 1800s many people made

rotation measurements based on particular features on the planet. By 1875, an ephemeris

for physical observations of Jupiter was being published and a longitude of Jupiter's

meridian was established [Marth, 1875]. At that time an arbitrary first meridian was

chosen and a daily rotation rate of 8700.60 was given [Marth, 1875]. Ten years later,

after observations showed features at different latitudes rotating with different rates, two

values of the longitude of the central meridian were published with different daily rotation

rates [Marth, 1885]. The first daily rate corresponded to the motions of the white spots

near the planets equator, and the second corresponded to the observations of the red

spot. The two periods of rotation corresponding to these two systems are, respectively,

System I, 9h 50" 9s.84 and System II, 9h 55m 38s.99 [Marth, 1885]. In 1896, A. Stanley

Williams compiled a list of rotation period measurements based on his judgment of quality

of the observations [Williams, 1896]. He organized the measurements into nine different

zones of latitude and presented a summary of all the zones and the best estimate of the

period for each zone. The convention of rotation period measurements labeled System

I and System II is still in use today. These systems are based on the motions of the

cloud features of the equatorial region and temperate regions, respectively. However the

problem with these systems is that these atmospheric features are not permanently fixed

or connected to the deep interior or core of the planet. Fortunately, in the 1950s radio

astronomy was very popular, and a serendipitous discovery forever changed the way we

observe the planets and how we measure rotation periods.






9

While making observations of the Crab Nebula (Ml) at a frequency of 22.2 MHz

in 1955, Burke and Franklin [1955] found a source of nonterrestrial radio noise that

coincided with the position of the planet Jupiter. Later that year, Shain [1956] confirmed

this discovery at a frequency of 18.3 MHz and found records dating back to 1950-51 that

showed Jupiter radio emission that had previously been attributed to terrestrial sources.

Shain was the first to use these measurements to address the rotation period of Jupiter,

and he found that the period was very close to, but slightly shorter than the adopted

System II period. His calculation gave a result of 9h 55m 13s for the rotation of the radio

sourcess. Since the discovery of radio emission from Jupiter, several groups published

results of observations at many different frequencies [Gallet, 1957; Gardener and Shain,

1958; Carr et al., 1958].

Gallet [1957] was the first to correlate the radio emissions and their movement in

longitude with the solid body of the planet beneath the clouds. In their 1958 paper,

Carr et al. used 18 MHz observations and measured the drift of these observations with

respect to the accepted system II period. They found that the radio measurements gave a

period about 12 seconds shorter than the system II value. Since the radio rotation period

probably corresponds to the magnetic field generation zone near the core of Jupiter, Carr

et al. [1958] defined a new system based on the radio rotational period and designated it

"System 1I1". The new system coincided with the system II period on January 1, 1957,

at Oh U.T. and had a value of 9h 55m 28s.8. After several more years of observations

at frequencies from 18 MHz to 27 MHz, many revisions and improvements were made

in the accuracy and precision of the radio rotation period measurement [Douglas, 1960;

Gallet, 1961; Carr et al., 1961]. Each of these rotation period measurements was the

average period using as many years of data possible. Thermal and other nonthermal

measurements of Jupiter were also made at this time and these observations were linked






10
to the radio period. In 1959, Drake and Hvatum [1959] measured the microwave radiation

from Jupiter but found no statistical correlation between variations in the radiation

and the apparent rotational period. At the same time, Sloanaker [1959] measured the

temperature of Jupiter at 10 cm and showed that these radio measurements had only

a slight correlation with the rotation period. Because of the increasing number of

calculations of rotation period measurements, the International Astronomical Union (IAU)

proposed that a new longitude system for Jupiter be established and designated System

III (1957.0) [International Astronomical Union, 1962]. The new system coincided with

the system II period on January 1.0, 1957 with a rotational period of 9h 55m 29s.37.

This measurement was based on a statistical analysis of all the Jovian decameter data

available from 1950-1960 as gathered by C. Shain, B. Burke, K Franklin, R. Gallet, J.

Kraus, G. Reber, A. Smith, T. Carr, and J. Douglas [Douglas, 1960].

After the IAU designated a new longitude system, it was found, through more

observations, that an abrupt change had taken place in the apparent radio rotation period

[Douglas and Smith, 1963; Smith et al., 1965; Carr et al., 1965; Runcorn and Dickel,

1965]. It was believed that either the system III (1957) period was incorrect and that a

refinement was needed, or that a true change in the rotation period had occurred. Another

explanation of the abrupt change was that the change was virtual and was caused by

refraction and focusing properties in the Jovian magnetosphere and the interplanetary

medium [Lebo, 1964]. Decimeter observations at this time further confused the issue.

Bash et al. [1964], observing at 10 cm, concluded that the decimeter sources rotated

about 0.3s longer than the System mI (1957) value while Roberts and Komesaroff [1965],

observing from 6 cm to 100 cm, found that the decimeter period was within the error

of the System II value. Other observers also concurred with Roberts and Komesaroff's

decimetric measurements [Barber, 1966; Dickel, 1967]. In 1966, however, Gulkis and






11

Carr [1966] provided an explanation that while the true rotation period remained constant,

the measured rotation period had a cyclic drift with a period equal to the 12-year orbital

period of Jupiter. They explained that the decametric radiation was latitudinally beamed

and that measuring it depended on the Jovicentric declination of the Earth (DE, or

equivalently, the Jovian sub-Earth latitude). We note here that this discovery by Gulkis

and Carr [1966] led to the use of pairs of apparitions separated by 12-years so that the

DE was the same for both.

As the amount of data increased during the 1960s, so did the number of measurements

and the differing techniques to make the calculations. In 1964, Bigg found that the

decametric radiation depended strongly on the orbital position of the satellite lo. This

striking correlation had not been noticed until Bigg discovered it nine years after Jovian

radio emissions was first detected. Certain dynamic spectral features in the emission were

identified and shown to appear repeatedly at certain Jovian longitudes [Warwick, 1961,

1963].. Dulk [1967] used two techniques, the shift of histogram features and the shift

of dynamic spectral features, to measure the rotation period. His analysis of the spectral

features cast doubt on the earlier findings that there had been a true change in Jupiter's

rotation rate. He also found that the long-term gradual drifts in the histograms showed

a lengthening of the rotation period of approximately 0.s27 with respect to System III

(1957). Olsson and Smith [1968] also examined the possibility that individual sources

may have separate rotation rates. Duncan [1967], on the other hand, compiled a list

of decametric data using a periodogram technique of storm commencement times and

concluded that the Jovian rotation period was constant (i.e. no secular variations) at

9h 55m 29s.70. Olsson et al. [1969], however, used a similar technique of storm

commencement times and found the period 0.s3 shorter than Duncan's [1967] result.

Further decimetric observations at 11 cm gave a period that exceeded the System HI






12

(1957) period by 0.s46 [Komesaroff and McCulloch, 1967]. Donivan and Carr [1969]

confirmed that the rotation period was correlated with DE and not with the sunspot number

as was previously thought. This confirmation of the correlation of the rotation period

with DE was very important because accounting for changes in the DE in rotation period

measurements provided the greatest increase in accuracy for rotation period measurements

at the time. It also eliminated some previously obtained relatively sudden changes in the

apparent period. Later, cyclic variations in three parameters of the decametric emission

(mean occurrence probability, CML of source A, and effective width of source A) were

found and an average rotation period was determined, again about 0.s4 longer than the

System III (1957) value [Carr et al., 1970]. They also suggested that the System III

(1957) rotation period be revised.

Controversy remained, however, and Duncan [1971] repeated calculations using more

data and found that his measurement remained unchanged. Further observations and

calculations were made using the latest data from the University of Florida and Smith et

al. [1971] reported that the rotation period was changing and that an apparent reversal

had taken place. A short time later Carr [1971, 1972] and Mitchell [1974] compiled more

decametric data and confirmed the existence of the cyclical drift of the average rotation

period measurements due to the DE effect. Carr [1971] also compiled both decametric and

decimetric data and calculated a most probable value of the rotation period. His value

was 9h 55m 29s.75 +0.'04, and he proposed a new Jovian central-meridian longitude

system which he designated System III (1967.0).

Kaiser and Alexander [1972] used over 16 years worth of decametric data and a

new power spectrum technique and calculated a very precise rotation period. Their

calculation agrees very well with the calculations of Duncan [1971] and Carr [1972] even

though they made no corrections for changes in DE. Lecacheux [1974] studied periodic






13
variations of the decameter sources and confirmed the DE dependence and calculated

a rotation period within the errors of the other measurements at that time. Alexander

[1975] further analyzed the beaming of the radiation using a dynamic spectra technique

and found constraints on the precision of rotation period measurements. Individual pairs

of spectral landmarks could only be measured within 100 in longitude, thus constraining

the precision. He improved the measurement, however, by using a statistical basis of a

large numbers of pairs and found a value again in agreement with that of Kaiser and

Alexander [1972]. Later Duncan [1975], using all available data, confirmed his previous

[1971] rotation period value, and reaffirmed that the period was constant.

Duncan's [1967, 1971, 1975] results were obtained without correcting for the effects

of DE. It is still not clear how he was able to achieve such a relatively high accuracy

in his average rotation period measurement without correcting for the 12-year periodic

changes in DE. Two possible explanations are 1) the DE effect just happened to cancel

itself out over the time span of the data used, or more likely, 2) his storm commencement

time method is less sensitive to changes in DE than the occurrence probability versus

CML technique.

After 14 years of collecting and analyzing Jupiter radio data, it became exceedingly

clear that the System III (1957) longitude defined by the IAU in 1962 was inadequate.

Therefore in 1976 a redefinition of the System III longitude was agreed upon by the entire

scientific community [Riddle and Warwick, 1976]. In that paper twenty-five scientists

endorsed a new longitude system and defined it as System 111 (1965) with a rotation

period value of 9h 55m 29s.71. The sidereal rotation rate corresponding to this value is

870.0536 per Ephemeris Day. These values were chosen as the weighted average of four

recent decimetric and decametric rotation period measurements [Duncan, 1971; Carr,

1972; Kaiser and Alexander, 1972; Berge, 1974]. The epoch (1965) was chosen because






14
it is the mean epoch of the data used in the four calculations. Excellent reviews can be

found on both the decimetric and decametric observations of Jupiter and how they relate to

the magnetospheric rotation period [see Berge and Gulkis, 1976; Carr and Desch, 1976].

The latest measurements of Jupiter's rotation period using ground-based data were

made around 1980. Biraud et al. [1977] used polarization data at 1.4 GHz and calculated

a period within O.s02 of the System IIn (1965) value. Twenty years worth of decametric

data were compiled and a weighted mean rotation period was calculated and found to be

0.s02 shorter than the System III (1965) value [May et al., 1979]. Sixteen years worth

of decimetric data were used to calculate a rotation period value that was equal to the

System E1I (1965) value 0.'02 [Komesaroff et al., 1980]. All these latest measurements

are briefly summarized in an excellent review article [Carr et al., 1983]. Recently,

the catalogue of Jupiter decameter observations from the Nancay station in France was

extended through 1990 [Leblanc et al., 1993]. These observations began in 1978, and

using the entire set of observations, Leblanc et al. [1993] concluded that the System III

(1965) rotation period of Jupiter was "valid," but their quantitative results were not stated

nor were they compared to the IAU System III (1965) value.






15
Table 1.1: Jupiter's radio emission components

Emission Component Frequency Band Wavelength Band

Continuum* 0.1 kHz 10 kHz 3000 km 30 km
Fast Driftt 1 kHz 500 kHz 300 km 600 m
Kilometric(KOM)
broadband(bKOM)t 10 kHz 1000 kHz 30 km 300 m
smooth(sKOM)t 10 kHz 1000 kHz 30 km 300 m
narrowband (nKOM)t 40 kHz 200 kHz 7.5 km 1.5 km
Hectometric (HOM) 300 kHz 3 MHz 1 km 100 m
Decametric (DAM) 3 MHz 39.5 MHz 100 m 7.6 m
Decimetric (DIM) 100 MHz 300 GHz 3 m 1 mm

* from Kurth [1992], t from Kaiser [1993], from Reiner et al. [1994], all others from Carr et al. [1983]







16

BAND DESIGNATIONS


KILOMETRIC DECAMETRIC

HECTOMETRIC


DECIMETRIC


-18
10

N -19

E -20-
10O
CE


S10-21
Z
a -22

X 10

S10

UW -24
> 10

10-25

10-26


30 km 3 km


300 m 30 m
-4- WAVELENGTH


3 m 30 cm 3 cm


Figure 1.1: The average power flux density spectrum of Jupiter's nonthermal magnetospheric
radio emissions. Also shown are the sensitivities of the telescopes given as minimum detectable
flux densities (ASMIN) at the two extremes of the galactic background emission, the plane and
the pole.


SI I iai i.IV ri I
10 kHz 100 kHz 1 MHz 10 MHz 100 MHz 1 GHz 10 GHz
FREQUENCY -+


TRAPPED
CONTINUUM


BURST EMISSION


DAM


HOM


bKOM


nKOM


- AS near galactic plane
- ASMN near galactic pole


DIM

~%kllTIMI I"


HECTOMETRIC


sKOM






17
1957-1994 Occurrence Probability


0 30 60 90 120 150 180 210 240 270 300 330 360

System III (1965) (degrees)
Figure 1.2: Probability of detecting Jupiter radio emission for a given longitude (A) for the
observations from 1957 to 1994 at (a) 18 MHz, (b) 20 MHz, and (c) 22 MHz. The three most
probable regions are designated as source A (A=2400), source B (A=1300), and source C (A=3300).








1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2


1957-1994 Occurrence Probability


0 0 1 I, ..I 'I I I I I I I I I I
0 30 60 90 120 150 180 210 240 270 300 330 360
Central Meridian Longitude (degrees)
Figure 1.3: Normalized occurrence probability of Jovian emissions versus longitude for combined
18, 20, and 22 MHz observations from 1957 to 1994.















0.30 0


0.25 -


0.20 to- i


--


C 0.10 -


o 0.05 -


0.0 -























Figure 1.4: Shaded surface occurrence probability versus longitude (A) and the phase of Io (4)
for 18, 20, 22 MHz observations from 1957 to 1994. Overlaid is a contour plot to the same
scale. The (A,O4) coordinates of the lo-A source are (210-250, 240), lo-B (90-180, 900),
lo-C (300o-360, 2400), and non-Io-A (220o-280, 0-360).













CHAPTER 2
THE UNIVERSITY OF FLORIDA DECAMETER DATA


2.1 The Radio Telescope System


The components of a radio telescope system are rather simple and consist of an

antenna, a receiver, and a recorder. Since 1957, when the University of Florida began

its synoptic monitoring of Jovian radio emissions, three frequencies have been monitored

with the greatest reliability, longevity, and success: 18 MHz, 20 MHz, and 22.2 MHz.

Other frequencies up to 32 MHz have also been monitored regularly, but Jovian activity

at these higher frequencies is too low for making precise rotation period measurements.

The antennas used for data collection are 5-element Yagis for 18 and 22.2 MHz and a

4-element Yagi for the 20 MHz channel. In 1989, however, log-spiral antennas were

added and used as a supplement or a substitute for the some of the Yagi antennas.

The Yagi-type antenna consists of a dipole radiator, a reflector element, and one or

more director elements. The reflector and director elements help focus the radiation

and increase the gain of the antenna. The log-spiral antenna design is used to collect

polarization information about the emission; thus, two antennas are needed, one left-hand

spiral and one right-hand spiral. Specifics of the physical and electrical parameters of

the Yagi antennas can be found in Appendix A.

The receiver in the radio telescope system is the heart of the system, amplifying,

filtering, and detecting the oscillating voltages from the observed electromagnetic radia-

tion. A simple receiver system is described here, but more information can be obtained

from Kraus [1986] and references therein. The receivers used most often at UF were






21

Collins 75S-1 dual conversion tunable receivers set to center frequencies of about 18.0,

20.0, and 22.2 MHz, and bandwidths of 4 kHz. In recent years the Collins receivers have

been replaced by fixed-frequency dual conversion receivers designed and built within

the UF astronomy department. This type of receiver is a superheterodyne consisting of

five stages as shown in Figure 2.1. The first stage is a low-gain radio frequency (RF)

amplifier. The second stage is a multiplier which takes the weak RF signal and a strong

local oscillator signal and multiplies them together to form an intermediate frequency

(IF) signal. Stage three is a high-amplification stage which amplifies the IF signal and

then passes it through a bandpass filter which excludes any extraneous signals. At stage

four the signal is passed through a detector (i.e. a rectifier) which multiplies the pairs

of frequencies producing both beat frequency sinusoidal components and a direct cur-

rent (DC) component. Stage five is a low-pass (LP) filter which only allows the lower

frequency components to pass to the recorder. All the frequencies that are passed are

added together in random phases and then summed with the DC component. This final

recorded signal, either analog or digital, is a function of the input radio frequency power

and is used to calculate the antenna temperature or flux density of the radio source. The

recorders used at the UF Radio Observatory are Texas Instruments Recti-riter pen de-

flection recorders. The time constant of this telescope system, which is limited by the

response of the pen recorders, is 0.5 seconds.



2.2 Data Collection


The observations for each Jovian apparition are centered around opposition (i.e. the

time Jupiter is opposite the Sun in the sky), which is generally the best time to make

observations. Listed in Tables 2.1, 2.2, and 2.3 are all the seasonal dates of observation

and listening and activity times for each of the three frequencies used in this study. Table






22

2.4 lists the summed totals for all three frequencies for all seasons of UF data. The mid-

dates are simply the decimal average year for each season. The occurrence probability

in the last column is the quotient of the total activity divided by the total listening time.

This seasonal occurrence probability is an overall measure of the likelihood of detecting

Jovian decameter emissions during the apparition. Some seasons are shortened due to

equipment problems or environmental problems, most notably during the summers when

thunderstorm activity is very high. Because the Jovian radio emission is beamed, there is

a geometrical effect which affects the probability of Earth receiving the emission. This is

the Jovicentric declination of the Earth (DE), or more simply, the latitudinal position of

Earth as seen from Jupiter. This varies sinusoidally from about +30 to -30 latitude with

a period of about 12 years, the orbital period of Jupiter. The probability of receiving

emission is much higher when the DE value is positive [Gulkis and Carr, 1966]. This

effect is very important for the determination of the rotation period and will be discussed

further in Chapter 3.

There are many diurnal factors which affect the collection of data. First, and most

obvious, Jupiter must be above the horizon. Jovian radio waves are refracted and reflected

by the Earth's ionosphere, but they have never been detected while Jupiter is below

the horizon. Strong solar bursts, however, have been detected at night [Smith et al.,

1959]. Second, the observations must take place when the Sun is below the horizon.

The reason is that the ionosphere heats up from the solar irradiance and becomes dense

enough to reflect terrestrial radio station rays back down into our antennas. Therefore

the observations begin after local sunset and continue all night until sunrise provided

Jupiter is above the horizon at these times. Other diurnal factors are more random and

essentially consist of many types of interference which may inhibit the observations.






23

Radio interference between 15 MHz and 40 MHz (the radio "window" for ground-

based Jovian decametric observations) comes in many forms. Most of the interference

occurring between local midnight and dawn is either short-lived or can be tuned out of

the receivers; therefore, it will generally not affect the overall observations appreciably.

On rare occasions, however, it is strong and persistent enough to cause the observation

to be canceled. The first and most important of these is man-made interference. Distant

radio stations and local citizen's band (CB) radios can provide strong interference which

can cause full scale deflections on the recorders. This would render any Jupiter emission

undetectable at that time. A second devastating interference is static interference from

natural sources, mostly lightning. If a lightning storm is very close, the observation is

canceled or delayed for the safety of the observer as well as the equipment. The other

natural source is termed "St. Elmo's Fire," which is caused by electrical static discharges

from the antenna itself. These discharges are not very frequent, but can be persistent and

severe when they occur causing full scale deflections on the recorder. Another type of

interference is power line buzz from local sources. If this interference is strong, there is

not much to be done, except try to inhibit it at the source.

During the observations, the data are recorded as pen deflections on strip chart paper.

The signal is also sent to audio output for the observer to hear. This helps the observer to

determine the cause of the deflections, whether it be Jupiter or some kind of interference.

The observers mark the sources of any deflections on each record to the best of their

ability. The deflections can be caused by Jupiter or any of the interference sources

mentioned above. Jovian radio emissions not only have a distinct appearance on the

pen recordings, but also have a distinct audio sound, which doubly insures the proper

identification of Jupiter radio noise. An example of a UF strip chart recording of Jovian

radio emissions is given in Figure 2.2. The baseline of the recordings is the emission






24

due to the Milky Way galaxy. This galactic background does vary seasonally and can

vary daily if there is a strong radio source present, but generally it is fairly constant

over one observation. Jupiter radio emission typically lasts for about one hour, and these

noise "storms" are very bursty in appearance [Carr et al., 1958]. When the emission has

ended, the observer makes a calibration of the data. This is done by switching the input

from the antenna to a local noise generator and attenuator, and then recording the noise

calibrator output at several intensity values on the strip chart record. Another crucial

piece of information is the time of occurrence of any emission. The time information

is recorded each minute on the recorder strip chart and can be read easily at the top

of the record in Figure 2.2. For the purposes of analyzing the data, the three essential

pieces of information that are needed are the Jupiter deflections, the calibration, and the

time of occurrence.



2.3 Data Reduction and Format


The data reduction is a very long and tedious process but nevertheless must be done.

The basic information reduced off the strip chart records is the start and end time of the

observations, start and end times of any interference, and the start and end times of any

Jupiter activity. If any Jupiter activity occurred, then the galactic background information

is recorded before and after the activity. The entire interval of Jovian activity is broken

into five minute intervals, and the time and the peak deflection are recorded for each

five minute interval. If there is more than fifteen minutes of recordings without Jovian

activity, then a new storm is designated at the next Jupiter pulse. The deflections are

recorded as the pen deflection number from 0 to 100. After all data have been recorded,

the calibration information is recorded. The noise generator used at UF is a Hewlett

Packard 461 radio frequency (RF) amplifier which has been calibrated against the standard






25

Westinghouse 5722 current-saturated noise diode (the HP 461 is a "noisy" RF amplifier

not designed to be a noise source). Each calibration step and its associated deflection are

included in the data record for that observation. A sample data reduction record and an

associated explanation of all variables are shown in Table 2.5. This constitutes one date

of observation at one frequency channel for the season. If the season is eight months

long, and there are three antennas operating, then there are approximately 720 records to

reduce for one season! This is a tremendous amount of work.

There are a few notes to be mentioned about the data reduction. The years of data

reduced according to the method described here are 1981 through 1994. All data prior to

1981 were reduced by other scientists using a different data storage format (see Thieman

[1977]. All those data have been successfully converted into the present format, so the

entire UF Jovian radio database at 18, 20 and 22 MHz is uniform. During the data

reduction, only pulses labeled as "Jupiter" or "probable Jupiter" are recorded as positive

activity. All other pulses, even those labeled as "possible Jupiter" are not counted in

the activity. The times of interference are also recorded in the data file. In theory

these times would be subtracted off the listening times thereby providing a more realistic

estimate of the amount of good listening time. In practice, however, the level of degree

of interference is very difficult to quantify. Furthermore, it is also subjective as to

whether the interference would have been severe enough to inhibit the identification of

Jupiter radio pulses. Therefore, for the new data reduced for this study, all interference

times listed are disregarded, and the more conservative estimate of total listening is used.

Another element listed in the data reduction file is the calibration number. This was

originally intended to identify each calibration to a particular Jupiter radio storm, but

very rarely was more than one calibration made on the same observing run. Thus, the

calibration number should also be disregarded for these data.









Table 2.1: 18 MHz Florida radio observation data


Listening Activity Occurrence
Season Begin End Mid-date
(hours) (hours) Probability
1957 01-01-57 03-06-57 1957.090 189.433 35.467 0.1872
1957-58 12-02-57 04-01-58 1958.085 223.417 7.017 0.0314
1959 01-01-59 04-23-59 1959.156 365.717 11.033 0.0302
1959-60 12-27-59 05-21-60 1960.187 302.850 15.983 0.0528

1961-62 02-01-61 01-30-62 1961.585 1006.133 105.467 0.1048
1962-63 03-20-62 02-26-63 1962.686 1087.233 146.517 0.1348
1963-64 03-21-63 04-13-64 1963.750 1543.067 280.300 0.1816
1964-65 04-25-64 05-10-65 1964.835 1870.617 142.250 0.0760

1965-66 07-15-65 05-07-66 1965.942 1590.083 139.967 0.0880
1966 09-02-66 11-30-66 1966.792 322.333 25.567 0.0793
1967-68 10-10-67 06-16-68 1968.114 908.233 42.950 0.0473
1968-69 10-23-68 06-03-69 1969.114 810.767 34.767 0.0429
1969-70 11-17-69 06-18-70 1970.170 584.917 20.767 0.0355
1970-71 12-07-70 08-05-71 1971.264 1179.917 16.817 0.0143
1972 01-19-72 08-29-72 1972.355 517.000 13.900 0.0269
1973 03-06-73 12-10-73 1973.560 759.017 50.267 0.0662

1974-75 04-08-74 02-14-75 1974.696 788.333 114.833 0.1457
1975-76 05-29-75 02-23-76 1975.779 1196.233 223.933 0.1872
1976-77 06-28-76 04-05-77 1976.875 1331.783 201.967 0.1516
1977-78 08-08-77 04-25-78 1977.959 1146.300 200.350 0.1748
1978-79 09-07-78 02-27-79 1978.922 541.883 39.400 0.0727
1979-80 10-17-79 03-31-80 1980.020 667.983 42.250 0.0633
1980-81 11-07-80 04-23-81 1981.078 440.183 19.033 0.0432
1981-82 12-08-81 05-13-82 1982.151 862.583 10.833 0.0126
1983 01-12-83 06-17-83 1983.246 742.600 9.017 0.0121

1984 06-22-84 09-10-84 1984.582 233.467 1.867 0.0080
1985 02-26-85 11-15-85 1985.514 875.700 59.300 0.0677
1986 04-21-86 12-19-86 1986.636 1174.567 97.033 0.0826
1987-88 05-26-87 02-25-88 1987.776 1569.517 102.150 0.0651
1988-89 08-16-88 01-28-89 1988.850 1075.550 52.000 0.0483
1989-90 09-06-89 05-04-90 1990.011 1047.117 28.150 0.0269
1990-91 10-10-90 04-12-91 1991.026 945.217 38.000 0.0402
1991-92 11-22-91 04-30-92 1992.109 897.550 25.100 0.0280
1992-93 11-09-92 05-25-93 1993.125 1117.833 29.600 0.0265
1994 01-05-94 07-29-94 1994.294 1096.550 18.367 0.0167









Table 2.2: 20 MHz Florida radio observation data

Listening Activity Occurrence
Season Begin End Mid-date
(hours) (hours) Probability
1964-65 04-25-64 05-11-65 1964.836 1686.083 52.367 0.0310
1965-66 07-15-65 05-07-66 1965.942 1602.717 111.950 0.0698
1966-67 09-01-66 05-08-67 1967.010 1244.750 116.600 0.0937
1967-68 10-10-67 06-17-68 1968.116 1059.067 37.133 0.0351
1968-69 10-21-68 07-10-69 1969.162 937.567 26.133 0.0279
1969-70 11-17-69 07-23-70 1970.218 664.150 12.833 0.0194
1970-71 12-08-70 08-05-71 1971.266 929.133 16.050 0.0173
1972 01-19-72 08-29-72 1972.355 668.583 16.133 0.0241
1973 03-05-73 12-26-73 1973.581 947.683 53.200 0.0561
1974-75 04-08-74 02-14-75 1974.696 1091.767 119.367 0.1093
1975-76 06-17-75 03-07-76 1975.822 1250.767 188.883 0.1510
1976-77 06-28-76 04-05-77 1976.875 1379.683 224.250 0.1625
1977-78 08-08-77 04-26-78 1977.960 1187.583 123.050 0.1036
1978-79 09-07-78 04-16-79 1978.988 829.417 49.583 0.0598
1979-80 10-17-79 04-11-80 1980.034 876.600 36.400 0.0415
1980-81 11-07-80 05-03-81 1981.092 630.433 20.317 0.0322
1981-82 12-08-81 05-18-82 1982.157 850.517 12.967 0.0152
1983 01-12-83 06-17-83 1983.246 823.017 9.683 0.0118
1984 06-22-84 09-10-84 1984.582 231.233 0.233 0.0010
1985 02-26-85 11-15-85 1985.514 980.083 43.133 0.0440
1986 04-24-86 12-19-86 1986.640 1247.417 59.950 0.0480
1987-88 05-26-87 02-26-88 1987.778 1464.217 76.600 0.0523
1988-89 08-16-88 02-21-89 1988.883 1027.350 23.567 0.0229
1989-90 09-22-89 05-04-90 1990.033 1088.967 23.667 0.0217
1990-91 10-10-90 04-12-91 1991.026 933.433 20.383 0.0218
1991-92 11-22-91 04-30-92 1992.109 928.900 20.000 0.0215
1992-93 11-09-92 05-25-93 1993.125 1116.833 23.650 0.0212
1994 01-05-94 07-29-94 1994.294 1110.217 15.317 0.0138









Table 2.3: 22 MHz Florida radio observation data

Listening Activity Occurrence
Season Begin End Mid-date
(hours) (hours) Probability
1957-58 12-02-57 03-31-58 1958.084 357.350 6.750 0.0189
1959 01-24-59 04-23-59 1959.188 313.233 3.983 0.0127
1960 02-11-60 05-21-60 1960.250 285.600 8.583 0.0300
1961 02-27-61 11-29-61 1961.534 644.133 25.950 0.0403

1962-63 06-06-62 03-01-63 1962.797 1006.783 56.667 0.0563
1963-64 03-26-63 04-16-64 1963.761 1561.217 115.433 0.0739
1964-65 04-25-64 05-11-65 1964.836 1736.583 80.417 0.0463
1965-66 07-10-65 05-07-66 1965.936 1653.683 59.950 0.0362
1966-67 09-02-66 05-05-67 1967.007 1298.917 45.717 0.0352
1967-68 10-10-67 06-20-68 1968.120 1133.767 32.850 0.0290
1968-69 10-21-68 07-23-69 1969.180 1137.333 21.817 0.0192

1969-70 11-17-69 07-23-70 1970.218 778.433 12.450 0.0160
1970-71 12-07-70 08-05-71 1971.264 1057.850 17.533 0.0166
1972 01-19-72 08-29-72 1972.355 789.750 14.150 0.0179
1973 03-05-73 12-26-73 1973.581 983.733 68.967 0.0701
1974-75 04-08-74 02-14-75 1974.696 1182.300 86.900 0.0735

1975-76 06-02-75 03-08-76 1975.802 1267.083 118.467 0.0935
1976-77 06-28-76 04-05-77 1976.875 1420.167 208.567 0.1469
1977-78 08-08-77 04-25-78 1977.959 1263.417 94.850 0.0751
1978-79 09-07-78 04-16-79 1978.988 876.867 48.150 0.0549
1979-80 10-17-79 04-17-80 1980.042 959.450 54.033 0.0563
1980-81 11-07-80 05-12-81 1981.104 685.367 21.033 0.0307

1981-82 12-08-81 05-18-82 1982.157 842.500 12.167 0.0144
1983 01-12-83 06-17-83 1983.246 820.517 11.483 0.0140
1984 06-22-84 09-10-84 1984.582 231.733 2.583 0.0111

1985 02-26-85 11-15-85 1985.514 929.533 33.167 0.0357
1986 05-01-86 12-19-86 1986.649 1063.800 45.433 0.0427
1987-88 05-26-87 02-26-88 1987.778 1592.800 61.133 0.0384
1988-89 08-16-88 02-21-89 1988.883 1140.750 28.067 0.0246
1989-90 09-22-89 05-04-90 1990.033 1088.717 17.883 0.0164
1990-91 10-10-90 04-12-91 1991.026 875.717 21.450 0.0245
1991-92 11-22-91 04-30-92 1992.109 953.617 17.983 0.0188
1992-93 11-09-92 05-25-93 1993.125 1089.167 20.200 0.0185
1994 01-05-94 07-29-94 1994.294 1084.833 12.600 0.0116






29
Table 2.4: Totals for UF radio observatory decameter data

Frequency Listening Activity Occurrence

Begin End

(MHz) (hours) (hours) Probability
18 01-01-57 04-29-94 31,017.8 2384.2 0.0769
20 04-25-64 04-29-94 28,788.2 1533.4 0.0533
22 12-02-57 04-29-94 34,106.7 1487.4 0.0436









Table 2.5: Example


30

of a Jupiter data


reduction file


Line Entry Line Entry Explanation Line Entry Line Entry Explanation

F052486.22y filename with date and antenna 32.5 galactic level, begin activity #2

052486 date of observation, mmddyy 958 UT 1st 5 minute interval

22y frequency and antenna 77.27 peak deflection in 5 minute interval

710 UT start observation 1003 UT last 5 minute interval

1030 UT end observation 55.68 deflection of last 5 minute interval

2 number of activity intervals 23.54 galactic level, end activity #2

800 UT begin activity interval #1 $ file delimiter marker

817 UT end activity interval #1 C1052486.22y calibration filename

958 UT begin activity interval #2 052486 date of calibration, mmddyy

1006 UT end activity interval #2 22y frequency and antenna type

2 number of interference intervals 1 calibration number

710 UT begin interference interval #1 3 number of calibration steps

720 UT end interference interval #1 35 Ist decibel value

X type of interference, X=static 28.36 deflection for decibel value

1018 UT begin interference interval #2 31 2nd decibel value

1030 UT end interference interval #2 55.64 2nd deflection

S type of interference, S=stations 27 last decibel value

19.50 galactic level, begin activity #1 88.73 last deflection value

1 calibration number

4 number of 5 minute intervals

800 UT 1st 5 minute interval

25.0 peak deflection in 5 minute interval

805 UT #2

37.0 deflection #2

810 UT #3

38.0 deflection #3

815 UT#4

39.77 deflection #4

20.35 galactic level, end activity #1

























u.. o
00






Ol)
o

0

ca a




0 0
"-- -- O.
o



-=
_ mu.




0


o "
a) C13





._ C












C4-












986 't ellN
Akz u!iBG


9861 'tVZ AW
AZ PU3


o
c 4












E 0
oP



00









-0
o
Nz























E1
a .
















0 0







&0
o
oD -0


(be u







ou
1.e 1.













CHAPTER 3
ROTATIONAL PERIOD CALCULATION



The method used for the calculation of the Jovian rotation period is straightforward.

We use the seasonal probability of occurrence histograms as a function of Jovian central

meridian longitude (CML) as the basis for the rotation period calculation. Occurrence

probability histograms are used instead of a more direct quantity, such as emission

flux density or absolute intensity, because the Jovian emission is inherently bursty and

compiling statistical information would not be possible. These histograms, introduced

in Chapter 1, are based on an assumed rotation period and are used to track the CML

position of the individual sources over time. If these sources are found to be consistently

changing position in longitude (i.e. "drifting"), then the rotation period is inaccurate and

a modification is needed. From the measured rate of this longitude drift, a correction is

calculated and applied to the initially assumed rotation period in order to obtain a new,

more accurate period value. The occurrence probability histograms are created by inning

the 'times of observation' and the 'times of Jovian detection' into 50 longitude bins.

We can measure the shift between any two seasonal occurrence probability histograms

by cross correlating the two curves. The occurrence probability sources change position

cyclically with time due to the 12-year orbital DE effect [Gulkis and Carr, 1966]. Because

this effect can bias the results, we negate it by cross correlating seasons that are separated

by multiples of 12 years. Another possible bias is the use of seasonal data more than

once for cross correlations (see Section 3.1.5); therefore, to preserve the independence

of the data, no seasonal data are used more than once. Finally all the data are weighted






34

based on both the quantity and quality of the data and then are properly combined to

produce a new and more precise Jovian rotation period.

The last time the Florida and Chile data were used for a rotation period determination

was 1979 [May et al., 1979]. At that time all the data were read by hand and then entered

on computer cards. In 1985, the data were converted to a computer cartridge tape readable

by the Northeast Regional Data Center computers. In 1992, the data were copied onto an

8mm data cartridge tape (ExatapeTM) for use with the astronomy department workstations.

It is this set of data from which I make my calculations of the rotation period of Jupiter.

In the process of manipulating the data for my computer programs, many errors were

found within the data files. Most of these errors were either typographical errors or errors

in the conversion of the data from one format to another. Enormous amounts of time were

spent checking and re-checking the data, and to the best of my ability, the data are accurate

and consistent. An important consequence from all this data analysis and reduction is

that all the data are converted to the format described in Chapter 2. One caveat is that

the data before 1964 were calibrated with a different calibrator system; therefore, the

calibrator readings and deflections are different, but the file format is the same. For the

purposes of this analysis, however, these inconsistencies are not a hindrance, because I

use only the bulk listening and activity information for my calculations.

All the years of data used in the May et al. (1979) paper, except the one year of

Australian data, are incorporated into this thesis, but in a different manner. Due to the

addition of the seasons from 1977 to 1994, for the first time we are able to cross correlate

seasons separated by 24 years. These additional data allow us to use each season only

once for cross correlations thereby keeping the data independent and unbiased. Another

difference is that the UF occurrence probability data for these calculations are based on

the System HI (1965) longitude system rather than on System 1n (1957). Because the






35

Chile strip chart data were not readily available, the occurrence probability histograms

used in the May et al. (1979) paper are used here with no changes. In addition, we

used one more pair of Chile seasons not used by May et al. (1979), the 22 MHz seasons

of 1964 and 1977. Finally, the method of weighting and combining the data have been

improved in such a way that the quantity as well as the quality of the data are taken into

account. All these factors are believed to be important in the improved rotation period

results that are presented here. Complete details about the data analysis and the data

manipulation are discussed in the next section.


3.1 Cross Correlation Technique


3.1.1 Calculation of Occurrence Probabilities

The first step in determining the rotation period from these radio data is to calculate

the probability of occurrence of emission for each frequency as a function of Jovian

CML. The longitude system used for these relations is System 111n (1965) which is based

on the rotation period that is under investigation. These occurrence probability plots are

created using the Jovian activity and listening data and a program to calculate the Jovian

ephemeris data. The ephemeris program uses the Universal Time (UT) of an event (an

activity or listening interval) as input and calculates the CML of Jupiter and the orbital

phase of the satellite lo, both with an accuracy of less than 1. More details about

the ephemeris program used for these analyses are found in Appendix B. The longitude

system for the ephemeris output is System In (1965). The reference for this system is

the longitude of the central meridian of Jupiter at Oh UT on February 26, 1977, the day

that System 111 (1965) was adopted by the International Astronomical Union (IAU).

Once the correct longitude for each event is found, the data are sorted into 50 bins

of longitude. Because the data are read every five minutes in time, and because Jupiter






36

rotates approximately once in 10 hours, the minimum bin size for data is 30.1. For ease in

calculation we have chosen 50 longitude bins. Thus there are 72 bins for the activity data

and 72 bins for the listening data. The program increments the appropriate CML bin by

one count for each activity or listening datum point. As a result of this ephemeris program,

all the data for each season of observation are compiled and occurrence probability

histograms are created. This process is repeated for every season of data, 1957 to 1994,

and for each of the three frequencies used in this study, 18 MHz, 20 MHz, and 22 MHz.

Tables of the seasonal data were given in Chapter 2, and the occurrence probability plots

for all the seasons and for each frequency are given in Figures 3.1 to 3.9. All plots are

nearly the same scale, therefore they can be analyzed for seasonal variations. For each

of the histograms, the seasonal mid-date is given in years. Most of the histograms have

3 peaks which are the main sources of emission and correspond to the sources labeled

in Figure 1.2. The A source is the largest peak and is located near 2400 CML; the B

source is located near 1200 CML and the C source is located near 3200 CML (see Carr

et al. [1983]).

There are several important features of interest in the occurrence probability graphs.

The first is the noticeable lack of activity and reduced occurrence probability for the years

near 1959, 1971 and 1983. This is almost certainly a result of the change in the latitude

of Earth as seen from Jupiter which is referred to as DE, the Jovicentric declination of

Earth [Gulkis and Carr, 1966]. The value of DE varies from -3.3 to +3.30 with a period

of 11.9 years, the orbital period of Jupiter. Because the emission is apparently beamed

into the plane just above the Jovian equator, Earth moves in and out of the beam over

the course of 12 years causing a change in the occurrence probability. As a result of this

geometrical effect, it has been found that the width and the midpoint of source A varies

with DE [Carr et al., 1970]. This effect can be seen quite easily in Figures 3.1 3.9 for






37

the main source (source A), and less obviously for the other peaks. This movement in

longitude is attributed to the changing orbital geometry of Earth and Jupiter over time

and will cause an error in an average rotation period measurement if the DE effect is not

taken into account. The longitudinal positions of source A are measured for each season

at all three frequencies and are plotted as a function of time in Figure 3.10. Measuring

the boundaries of source A is somewhat arbitrary, and even more difficult for sources

B and C, so they are not included in the figure. The location of the peaks of source A

are plotted as well as the mid-longitude of the half probability values. If the source is

missing for a particular season, then it is not included in the plot. The errors in these

measurements are approximately 20. The 12-year cyclical effect is very evident, and

must be taken into account in this investigation of the calculation of the rotational period.

As stated previously, a simple way to negate this 12-year effect is to compare seasonal

occurrence probability plots that are separated by 12 years (i.e. seasons with very nearly

the same DE value). This is exactly what is done, and further details are discussed below.

A final feature to note in the occurrence probability graphs (Figures 3.1 3.9) is

the very subtle effect that the emission sources are changing longitude slowly with time.

This change in longitude, or drift, can be seen in Figures 3.1 3.9 if one looks at the

position of the sources separated by 12, or preferably, 24 years. Figures 3.1 3.9 are

shown such that the location of the graph for each frequency on each successive page

is at a 12 year interval (except for the 1992-93 and 1994 seasons). For example season

1957.1 is at top of Figure 3.1 and season 1969.1 is at the top of Figure 3.2. This makes

it easy to examine the subtle shifts of the sources with time. The cause of this shift is

due to a slightly incorrect rotation period system. The availability of the long-term data

base at the University of Florida allows us to find more subtle changes in the occurrence

probability graphs, and, therefore, make a more precise rotation period calculation.








3.1.2 Cross Correlation

Once the occurrence probability graphs are complete, the data are smoothed with a

two-step routine which is a 3-point then a 4-point smoothing program. It doubles the

number of points by reducing the CML bin size from 50 to 2.5. The smoothing formulae,

showing the weighting for each datum point (x) for the corresponding bin (i) is given by

2xi-1 + 4xi + 2xi+1
8
(3.1)
xi1 a + 3xi + 3xa+1 + i+42
xi+ = 8
After the graphs are smoothed, each one is cross correlated with another occurrence

probability graph that is separated by 12 or 24 years. This technique negates any

geometrical effects from the changing value of DE. The cross correlation program

calculates the cross correlation coefficient r given by

r -N E xjyj Ex yj (3.2)


where N is the number of 2.5 bins, and x and y are the bin values for the two graphs

that are cross correlated. The coefficient r is a quantitative measure of how well two

curves are correlated and ranges from -1 to +1 (i.e. perfect correlation corresponds to

+1 and perfect anti-correlation corresponds to -1). One cross correlation coefficient is

calculated and then one curve is shifted by 2.5 with respect to the other curve. A

cross correlation coefficient is again calculated and this process is repeated for all 20.5

bins in CML (i.e. 144 times). Once these coefficients are computed, a cross correlation

coefficient curve is plotted as a function of longitude to show where the peak correlation

coefficient is located. An example of this method is shown in Figure 3.11. The top

panel is the occurrence probability histogram for the 1963 season at 22 MHz, and the

middle panel is the 1987 season, 24 years later. The bottom panel is a plot of all the






39

correlation coefficients as a function of the shift in CML. The peak of the curve is found

easily around -5, with a correlation of 0.975. In an effort to determine the peak of the

correlation curve more accurately, a 4th-order polynomial is fit for the peak of the curve

from -30 to +300. The thick dashed curve overlaying the cross correlation curve in the

bottom panel of Figure 3.11 is a typical polynomial fit where the accuracy in finding the

peak is 0.10. This method is used for all years at all three frequencies, and a listing of

the cross correlation statistics is found in Tables 3.1, 3.2, and 3.3.

The first two columns of Tables 3.1, 3.2, and 3.3 are a list of the mean epochs of

the two seasons that are cross correlated and the 12-year average. Column three is the

separation of the two epochs in years. Column four is the peak correlation coefficient for

the two occurrence probability curves. This quantity is one of the two parameters used in

determining the weighting factor for the rotation period measurements. Column five is the

geometric mean of the number of activity hours for the two apparitions listed in column

1. This is the other parameter that is used in the weighting (see below). Column six is

the CML shift that is needed to give the maximum correlation for the two occurrence

probability graphs. Finally, the last two columns are the rotation periods calculated using

these data along with the weight of each measurement. These quantities are discussed

in the next sections. Another important note on these data is that some of the data are

separated by 24 years. These data can be used for rotation period calculations as well,

because the DE value will also be approximately the same. Cross correlation with data

that are separated by 24 years has never been done before and is available now due to

the extension of the Florida database by 17 years. It is also an advantage to use these 24-

year data because, theoretically, if the sources are undergoing a constant drift due to an

incorrect rotation period, they will have a larger drift than the 12-year data. This allows

for improved precision and more confidence in the technique and the final calculation.








3.1.3 Rotation Period Calculation

The rotation period is calculated in a very straightforward way using the drift of

features in the occurrence probability plots. Only three parameters are needed to calculate

a new period: the old period, the time interval between apparitions, and the longitude shift

of the occurrence probability curve. A simple equation can be derived in a few steps. First

the number of rotations of Jupiter is calculated over the time interval between apparitions

(about 12 years). This number of rotations is then converted to degrees, and the longitude

shift between the two occurrence probability curves is subtracted. This corrected value

is converted back to a number of rotations of Jupiter then divided into the time between

apparitions which gives a new rotation rate. In essence, we are calculating a rotation

period that would cause a 00 shift in CML. If the CML shift is truly 00, then the old

rotation period value is correct and no change is needed. These steps are easily shown

in the form of an equation,

Timel2yr
Perzodnew = e --Er 3600) Shi ft(3.3)
{[( -3600)- Shifcr]- }

Simplifying this gives

360Pt
P/ = (3.4)
(360t PAA)

where

P' = New rotation period value (hours)

P = Old rotation period value (hours)

t = time between apparitions ( ~12 years, converted to hours)

AA = shift in longitude of the second histogram with respect to the first that maximizes

the correlation coefficient (degrees)

360 = number of degrees per rotation.








It is easily seen that

A A = 0 = P' = P

AA < 0 = P' < P (3.5)

AA > 0 = P' > P.

This means that if the sign of the CML shift between the two occurrence probability

graphs is known, then the relation between the new rotation period and the old rotation

period is known. Another useful representation of the rotation period formula is

1 1 AA
P' P 360t (

which shows that the AA term can be thought of as a correction factor for the old

rotation period value.

3.1.4 Weighting Method

The rotation period is calculated for all the years of data listed in Tables 3.1 to 3.3.

The rotation periods are listed in column seven, and are written as seconds in excess of

9h 55m. It is obvious from the entries in the tables that a negative CML shift causes a

rotation period value to be smaller than the System III (1965) value of 9h 55m 29.s71,

and a positive CML drift corresponds to a lengthening of the period. This corresponds to

the relations given in Equation 3.5. On examining the CML shift data in column six of

Tables 3.1 to 3.3, we see that nearly all of the CML shifts are negative. This interesting

result gives a strong indication that the rotation period is in error and a correction is

needed. These data are further explored later in this chapter.

The final column in Tables 3.1 to 3.3 is a normalized weight value given each rotation

period calculation. These weights are used to calculate a final weighted mean rotation

period using all the data possible. The weights are chosen to represent an objective

confidence measure of each rotation period measurement. The weight for each rotation






42

period value is the product of the maximum correlation coefficient (r) and the square

root of the geometric mean of the total activity times during the two apparitions (act)G,

and is given by


wi = ri V(ac )G, (3.7)


This weighting method is chosen because, on the one hand, the expected root-mean-

square (rms) uncertainty of the final average due to statistical fluctuation is inversely

proportional to the square root of the effective activity time; in our case, the activity time

is the geometric mean of activity times of the two apparitions. On the other hand, the

value of the maximum correlation coefficient for the two histograms is a direct measure

of the quality of the data used. For example, if two histograms represent a relatively

large quantity of data but the correlation was small, then it is concluded that the data are

of poor quality and the weight is adjusted accordingly. Note that this weighting method

is different from May et al. [1979], where they used weights that were only proportional

to the square root of the geometric mean of the activity for the two apparitions. We

believe our method of using weights that are a function of both the correlation and the

geometric mean activity is more objective and can be better justified.

3.1.5 Final Data Set

The data listed in tables 3.1 to 3.3 includes all Florida data, both 12-year and 24-year

calculations, and the Chile data from May et al. [1979]. There are a total of 105 rotation

periods that can be calculated with these data, but some of these are not independent. The

measurements taken at 3 frequencies are not necessarily independent because Jupiter may

(or may not) emit over a wide range of frequencies. Thus if Jupiter emits at one frequency,

then it is more likely that it will be emitting at the other frequencies as well (although

not necessarily at the same time). Therefore to eliminate any frequency dependence,






43

the multifrequency data for the same apparition are combined into one weighted value.

Another problem to be avoided is the use of data for more than one cross correlation.

For example, the apparition 1971 can either be correlated with the 1959 season or with

the 1983 season, but not with both. We found that in 19 of the 31 apparitions that

could be used twice, the longitude shift from the cross correlation changed signs from

the first measurement to the second. Using the same example, the CML shift for the

18 MHz 1959 to 1971 apparitions is -7.0', but for the 1971 to 1983 apparitions, the

CML shift is +6.750. We find that the first measurement is biasing the second, and the

two measurements cannot be regarded as independent. Thus to avoid these dependence

problems, we use all seasons that are separated by 24 years, and then the remaining data

separated by 12 years. No apparitions are used more than once in the calculations.

In addition to the Florida 24-year independent data, we have Florida 12-year inde-

pendent data, as well as Chile 12-year independent data. All these independent data are

listed in Tables 3.4 and 3.5. The periods listed in column 3 are a weighted mean value

of the individual frequency measurements listed in column 5. The weights that are listed

in column 4 are the sums of the individual weights, where the method for assigning

individual weights was described earlier. We treat the two groups separately because the

24-year data have a longer averaging time than the 12-year data, and therefore are more

accurate. For each group of data, we calculate a weighted mean rotation period (P,) and

a weighted standard deviation (ow). These are calculated in a straightforward way from

pW_ Pi Wi
wi

(3.8)
Ewi.-(Pi P)2
aw (n -1) Ewi '
where Pi and wi are the individual rotation period measurements and weights, respectively

[Scarborough, 1966]. The value of n is the number of measurements used in the






44

calculation. Using the 24-year and the 12-year data, the weighted mean rotation periods

and standard deviations are

P24yr = 9h55m29s.6854 08.0035
(3.9)
P12yr = 9h55m298.6767 0s.0125.
The proper technique to weigh these two values is to let the weight be inversely

proportional to the squares of the standard deviations. Therefore if we let the standard

deviation of P12yr have unit weight, then the weight of P24yr is or 12.76. Then

the weighted mean is given by

EA Pi- wi 0r12yr
P = (3.10)


where o12yr in this equation is the standard deviation that was assigned unit weight

(i.e. 0s.0125). Therefore, the final weighted mean rotation period value and standard

deviation are

P = 9h55m29s.6848 -0s.0034. (3.11)


We are confident that this is the most precise rotation period value ever calculated for

Jupiter's inner magnetosphere.

Figure 3.12 is a breakdown of the entire method of combining and weighting the

data. Column 1 is a list of all the seasons and frequencies used in the calculation of

the period based on a separation of 24 years. There are 31 pairs of apparitions listed

that are then subjected to the cross correlation technique and weighting as described

above. The result is column 2. Because the measurements listed in column 2 are not

independent of frequency, they are combined using a weighted mean and the result is

column 3. Column 3 represents 13 independent rotation period values based on 24-year

averages. The weights for each of these measurements are the sum of the weights of each

frequency used in the mean. This gives more importance to those measurements based






45

on more frequencies. Thus measurements 2-7 have twice the importance of number 1,

and measurements 8-13 have three times the importance of measurement number 1. A

weighted mean of these thirteen values is given in column 4 and labeled 24-year data.

A similar scheme is employed to reduce the 12-year data and the weighted mean of 11

independent rotation period values is listed in the lower box of column 4 as 12-year

data. These two measurements are then combined into a final rotation period using their

individual standard deviations as weights.

Before we can discuss the statistical significance of this result, we must analyze the

distribution of the data. In general, errors associated with an experimental technique are

normally distributed [Box et al., 1978]. We mentioned earlier that 105 rotation period

values can be calculated with our data set, however, only 47 of those rotation period values

were calculated from data that were used only once. Therefore our parent distribution

of data contains 47 items and is shown in Figure 3.13. The data points are plotted

by frequency, cross correlation separation, and by observing station as indicated by the

legend. System III (1965) is plotted as the horizontal dotted line for reference. Error bars

are inversely proportional to the individual weights and give a relative confidence for each

rotation period value. The distribution of these data are plotted as a histogram in Figure

3.14. The data are binned into 0s.02 intervals, and the distribution is roughly normal

with an unweighted mean and standard deviation indicated by the text. A normal curve

with the same mean and standard deviation is plotted on the same graph for reference.

A more quantitative calculation to check the normality of the data follows.

A rigorous method for checking the randomness and normality of a population is

the X2 (chi-square) test statistic [Freund, 1984]. In this test we compare the "observed"

frequencies (fobs) of the data to the "expected" frequencies (fxp) which are based on

the assumption of a normal distribution. This test is also called "goodness of fit" and








is given by


x = (fobs. fe,xp)2 (3.12)
fexp

The data are divided into equal intervals of 0s.02 in the distribution and the observed

and expected frequencies are given in Table 3.6. Because the sampling distribution

only approximates a chi-square distribution, we must combine intervals if the expected

frequency is less than 5. Thus the first three intervals are combined and the last three

intervals are combined. The result of the test is x2 = 5.73 which must be compared with

a chi-square distribution with the proper number of degrees of freedom. For our data,

the number of degrees of freedom (v) is

v = k- m (3.13)

where k is the number of terms in the X2 equation, and m is the number of quantities we

must determine from the observed data to calculate the expected frequencies. For these

data, k = 5, and m = 3, because we must determine the mean, the standard deviation,

and the total frequency from the observed data. Thus, for two degrees of freedom, the

value of the chi-square distribution with 95% confidence is 5.991. Since our result (X2

= 5.73) does not exceed the x2 table value (x2 = 5.991), we conclude that the data are

a random sample from a normal distribution.

After all the data have been combined in the process described above, there are 24

independent determinations of the rotation period (see Tables 3.4 and 3.5). Figure 3.15

shows the final set of data plotted versus the mid-date of the 12- or 24-year correlations.

Error bars are again inversely proportional to the individual weights. These data are also

subjected to the same "test for normality" as the data before they were combined. The

X2 test statistic shows that these data are also normally distributed with a confidence

level of 95%. A histogram of these final independent data is given in Figure 3.16, where






47

a normally distributed curve with the same unweighted mean and standard deviation is

plotted for reference. The significance of these distribution figures is twofold: 1) the data

are normally distributed and can be used in statistical applications, and 2) the method

of data combination has not skewed or changed the initial distribution in any way. This

second point indicates that the method of data combination is reasonable and suitable.

3.1.6 Statistical Significance

The new rotation period measurement presented here can be compared statistically

with the accepted System II (1965) period. Since the number of independent data points

used to calculate our new period is less than 30 (n = 24) and the data are approximately

normal, we use a one-sample t test statistic [Freund, 1984]. This test is given by the

equation

t P= (3.14)

where P is the sample mean period, Ito is the accepted value of the mean period, System

III (1965), and o-p is the standard deviation of the sampling distribution. For our system

we have 23 degrees of freedom, and using our calculated results we find a t value of 7.4

which is significant well beyond the 99.9% confidence level. Another way of stating this

is that the new rotation period value is highly significantly different from the System II

(1965) value as portrayed in Figure 3.17. A normal distribution curve having the same

weighted mean and weighted standard deviation as our new period is plotted to represent

our calculation. A reference for the System In (1965) period is also given to show

the significance between our result and the currently accepted period. This calculation

demonstrates that the currently accepted System III period needs revision.






48

3.2 Statistical Power Spectral Analysis



There is another method of analysis of the data which can lead to a determination of

the rotation period of Jupiter. This method is power spectral analysis using the properties

of Fourier analysis methods. It is incorporated here as a general exercise in examining

some of the Fourier periodicities that are present in the data. The precision obtainable

for rotation period calculations is much less than that obtained by the cross correlation

method discussed in Sections 3.1.2 and 3.1.3. One reason is that no correction is made

for the error resulting from the DE effect; we simply look for periodicities in the data

without making any adjustments. We treat the seasonal occurrence probability versus

longitude graphs as a discretely sampled function over time. Figure 3.18 is a graph of all

the seasonal occurrence probabilities as a function of time. Each season of occurrence

probability was originally plotted as a function of Jovian longitude (see Figures 3.1 to 3.9)

which can be thought of as a time unit. Here we simply combine all three frequencies and

plot each occurrence probability end-to-end in longitude (00-359, 00-359, etc.), thus

enabling one to analyze the curve over time. On examining Figure 3.18, we immediately

see there are two periodicities in the data. The low-order, or fundamental periodicity,

is a 12-year orbital geometrical effect caused by Jupiter's 30 inclination of its equator

with respect to the ecliptic plane (i.e. the DE effect). This effect was also discussed in

Section 3.1.1 and results in a cyclical change of the Earth's position in Jovian latitude

over Jupiter's 11.86 orbital period [Carr et al., 1983]. Thus, our probability for detecting

Jupiter's radio emission varies cyclically with this same period. This can be seen clearly

in Figure 3.18 from the maxima near the seasons 1963, 1975 and 1986, and the minima

near the seasons 1971 and 1983. The other noticeable periodicity in Figure 3.18 is

the regular pattern of emission sources for each apparition. These emission sources are






49

regulated by Jupiter's rotation and thus show a periodicity that is equal to the rotation

period of Jupiter. Using Fourier analysis techniques we examine these data for this

periodicity and estimate the rotation period of Jupiter.

The data in Figure 3.18 are discretely sampled and the interval is 2.50 in longitude,

which is 144 data points per rotation. Since we have data for 33 seasons, or in essence,

33 rotations, the total number of data points on the curve is 4752. The sampling interval

time is the time it takes Jupiter to rotate 2.50 or 4m.14. Because our sampling rate is finite,

our precision is limited to twice the sampling period, or about 8 minutes. To calculate

the periodicities, we take a Fourier transform of the data and compute the spectral power

at each frequency. A spectral power versus frequency curve is shown in Figure 3.19.

The peaks in the curve represent periodicities in the data. The largest peak corresponds

to the rotation period of Jupiter, and the other peaks are simple harmonics of this period.

The peak frequency corresponds to a rotation period of 9h 55m 29S.72. The fact that this

result is close to our previous result, and to System 111(1965), is coincidental because the

error in this result is 8 minutes! The error is due to the sampling rate and also due to

the DE effect. Further investigation into this method may be warranted.











Table 3.1: 18 MHz rotation period information



Separ- MeanG CML Period
Season Correl-
mid-date ation activity shift (sec + 91 Weight
1 2 ation
(yrs) (hrs) (0) 55m)


1957 1969

1958 1970

1959 1971

1960 1972

1961 1973

1962 1974

1963 1975

1964 1976

1965 1977

1966 1978

1968 1980

1969 1981

1970 1982

1971 1983

1972 1984

1973 1985

1974 1986

1975 1987

1976 1988

1977 1990

1978 1991

1980 1992

1981 1993

1982 1994


1963.102

1964.128

1965.210

1966.271

1967.572

1968.691

1969.764

1970.855

1971.956

1972.857

1974.067

1975.096

1976.160

1977.255

1978.468

1979.537

1980.666

1981.778

1982.862

1983.985

1984.974

1986.064

1987.102

1988.222


1957 1981 1969.084

1958 1982 1970.118

1959 1983 1971.201

1960 1984 1972.384

1961 1985 1973.550

1962 1986 1974.661

1963 1987 1975.764

1964 1988 1976.842

1965 1990 1977.977

1966 1991 1978.909

1968 1992 1980.111

1969 1993 1981.120

1970 1994 1982.232


I I A I. I .1


12.024

12.085

12.108

12.168

11.975

12.010

12.029

12.040

12.027

12.130

11.906

11.964

11.981

11.982

12.227

11.954

11.940

11.999

11.975

12.052

12.104

12.089

12.047

12.143


37.200

12.072

11.091

14.905

75.757

129.711

243.206

169.499

164.593

31.739

43.230

26.951

14.999

10.027

5.094

56.806

105.558

152.890

102.481

75.099

38.694

32.565

23.475

14.106


29.7338

29.6403

29.6450

29.8453

29.6687

29.6983

29.6927

29.6946

29.7179

29.6336

29.7426

29.6795

29.8643

29.7733

29.6452

29.7617

29.7138

29.6857

29.6209

29.6401

29.7258

29.6510

29.6918

29.6239


0.3274

0.0518

0.0685

0.2141

0.5084

0.7093

1.0000

0.8288

0.7991

0.2976

0.3944

0.2415

0.1361

0.1496

0.0156

0.4506

0.6521

0.7847

0.6006

0.5358

0.3715

0.3258

0 2709

0.1254


0.2666

0.0481

0,0685

0.0020

0.5182

0.6873

0.7822

0.5709

0.4882

0.3199

0.3406

0.2428

0.0613


23.988

24.066

24.090

24.395

23.929

23.950

24.028

24.015

24.068

24.234

23.995

24.011

24.124


25.982

8.719

9.974

5.463

79.083

119.235

162.493

86.006

61.696

31.170

33.320

33.984

19.530


-0.90

-15.15

9.65

-17.15

-0.50

-1.05

-4.60

-9.00

-5.45

-5.85

-4.65

-5.35

2.65


29.7058

29.6393

29.7550

29.6310

29.7077

29.7051

29.6885

29.6679

29.6846

29.6829

29.6882

29.6850

29.7223










Table 3.2: 20 MHz rotation period information


Separ- MeanG CML Period
Season Correl-
mid-date ation activity shift (sec + 9h Weight
1 2 ation
(yrs) (hrs) (0) 55m)

1964 1976 1970.856 12.039 0.938 109.256 1.45 29.7235 0.6442

1965 1977 1971.951 12.018 0.901 117.369 0.65 29.7161 0.6413

1966 1978 1972.999 11.978 0.903 79.025 -8.40 29.6312 0.5274

1968 1980 1974.075 11.918 0.924 35.684 2.15 29.7303 0.3626

1969 1981 1975.127 11.930 0.753 23.042 -6.15 29.6521 0.2375

1970 1982 1976.188 11.939 0.738 12.765 -1.55 29.6954 0.1732

1971 1983 1977.256 11.980 0.551 12.466 2.40 29.7325 0.1278

1972 1984 1978.468 12.227 0.007 1.939 -0.30 29.7072 0.0006

1973 1985 1979.547 11.933 0.907 47.465 -2.70 29.6846 0.4105

1974 1986 1980.668 11.944 0.954 84.953 -3.75 29.6747 0.5765

1975 1987 1981.800 11.956 0.965 120.285 -4.50 29.6677 0.6953

1976 1988 1982.879 12.008 0.854 72.684 -11.75 29.6000 0.4783

1977 1990 1983.996 12.073 0.922 53.965 -3.85 29.6742 0.4450

1978 1991 1985.007 12.038 0.714 31.791 -11.95 29.5985 0.2645

1980 1992 1986.072 12.075 0.908 26.981 -7.15 29.6435 0.3099

1981 1993 1987.108 12.033 0.709 21.921 -4.95 29.6638 0.2181

1982 1994 1988.226 12.137 0.810 14.093 -6.10 29.6535 0.1998

1964 1988 1976.860 24.047 0.871 35.425 -8.95 29.6682 0.3406

1965 1990 1977.987 24.091 0.955 51.473 -3.90 29.6918 0.4501

1966 1991 1979.018 24.016 0.860 50.668 -17.40 29.6286 0.4022

1968 1992 1980.112 23.993 0.909 26.451 -4.55 29.6887 0.3071

1969 1993 1981.144 23.963 0.746 24.860 -5.50 29.6842 0.2444

1970 1994 1982.256 24.076 0.694 14.020 -1.25 29.7042 0.1707











Table 3.3: 22 MHz rotation period information



Separ- MeanG CML Period
Season Correl-
mid-date action activity shift (sec + 9h Weight
1 2 ation
(yrs) (hrs) (0) 55m)


1958 1970

1959 1971

1960 1972

1961 1973

1962 1974

1963 1975

1964 1976

1965 1977

1966 1978

1968 1980

1969 1981

1970 1982

1971 1983

1972 1984

1973 1985

1974 1986

1975 1987

1976 1988

1977 1990

1978 1991

1980 1992

1981 1993

1982 1994


24.073

24.058

24.332

23.980

23.852

24.017

24.047

24.097

24.019

23.989

23.945

24.076


0.778

0.601

0.100

0.894

0.930

0.975

0.948

0.942

0.919

0.952

0.760

0.562


a a a a a


1964.151

1965.226

1966.303

1967.557

1968.746

1969.782

1970.856

1971.947

1972.997

1974.081

1975.142

1976.188

1977.255

1978.468

1979.547

1980.672

1981.790

1982.879

1983.996

1985.007

1986.076

1987.114

1988.226


12.134 0.262

12.076 0.610

12.105 0.882

12.047 0.944

11.889 0.941

12.041 0.989

12.039 0.975

12.023 0.946

11.981 0.863

11.922 0.978

11.924 0.876

11.939 0.630

11.982 0.771

12.227 -0.05

11.933 0.925

11.953 0.959

11.976 0.985

12.008 0.904

12.074 0.954

12.038 0.882

12.067 0.939

12.021 0.846

12.137 0.843


9.167

8.357

11.020

41.775

77.173

135.336

129709

74.541

46.918

41.636

21.421

12.308

14.189

6.046

47.228

62.834

89.876

76.510

40.712

32.137

31.172

20.612

12.382


29.6683

29.6718

29.7225

29.6862

29.6869

29.6657

29.7077

29.7245

29.6608

29.7411

29.6652

29.7641

29.6917

29.6461

29.6973

29.6804

29.6926

29.7198

29.6193

29.6554

29.6327

29.6782

29.6568


1970.120

1971.217

1972.416

1973.524

1974.723

1975.769

1976.860

1977.985

1979.017

1980.114

1981.153

1982.256


0.0521

0.1159

0.1924

0.4009

0.5431

0.7559

0.7295

0.5366

0.3884

0.4146

0.2664

0.1452

0.1908

0.0000

0.4176

0.4994

0.6135

0.5195

0.3999

0.3285

0.3444

0.2523

0.1949


0.1539

0.1027

0.0143

0.3181

0.4352

0.6146

0.4296

0.3541

0.3379

0.3065

0.2288

0.1307


9.062

6.763

4.708

29.337

50.740

92.055

47.582

32.743

31.315

24.020

20.993

12.525


29.6843

29.6605

29.6107

29.69.73

29.6791

29.6782

29.7142

29.6781

29.6726

29.6870

29.6804

29.6605








Table 3.4: Independent rotation period determinations based on 24-year data

Florida 24-year data

24-year Period Frequencies
# Weight
mid-date (sec) used (MHz)
1 1969.084 29.7058 0.2666 18
2 1970.120 29.6736 0.2020 18, 22
3 1971.210 29.6983 0.1712 18, 22
4 1972.400 29.6132 0.0162 18, 22
5 1973.535 29.7037 0.8364 18, 22
6 1974.690 29.6950 1.1225 18, 22
7 1975.765 29.6840 1.3968 18, 22
8 1976.853 29.6828 1.3411 18, 20, 22
9 1977.987 29.6853 1.2925 18, 20, 22
10 1978.983 29.6590 1.0599 18, 20, 22
11 1980.110 29.6880 0.9542 18, 20, 22
12 1981.136 29.6832 0.7160 18, 20, 22
13 1982.250 29.6915 0.3627 18, 20, 22





Table 3.5: Independent rotation period determinations based on 12-year data

Florida and Chile 12-year data

12-year Period Frequencies
# Weight
mid-date (sec) used (MHz)
1 1966.380 29.7576 0.6686 18 & 22 Chile
2 1967.530 29.6345 0.9892 18 & 22 Chile
3 1968.600 29.6789 1.3139 18 & 22 Chile
4 1969.700 29.7100 1.3610 18 & 22 Chile
5 1970.800 29.6463 0.8862 18 & 22 Chile
6 1977.260 29.7325 0.1278 20
7 1978.470 29.7072 0.0006 20
8 1979.550 29.6846 0.4105 20
9 1980.670 29.6747 0.5765 20
10 1981.800 29.6677 0.6953 20
11 1982.880 29.6000 0.4783 20






54
Table 3.6: Data for


X2 test


Expected Observed

Number Interval Probability

Frequency Frequency
1 x < 61 0.0233 1.10 1

2 61 < x < 63 0.0531 2.50 3

3 63 x < 65 0.1130 5.31 4

4 65 x < 67 0.1813 8.52 6

5 67 < x < 69 0.2164 10.20 17

6 69 < x < 71 0.1952 9.17 8

7 71 < x < 73 0.1259 5.92 4

8 73 < x < 75 0.0617 2.90 2

9 x > 75 0.0301 1.41 2











18 MHz Occurrence Probability

0.40 -
0.o30- 1957.1
0.20 -
0.50
0.40
0.30 1958.1
0.20-
0.10 ---
0.50
0.40
0.30o 1959.2
0.20
0.10

0_5Q ; ------ ------ ~~-------------- ------ ---
0.40-
0.30 1960.2
0.20
0.10





0.40-




0.30- 1963.8
0.20 -
0.10
0.40




0.30 196.8
0.20








0.10 L__": ----- 7~~ ------------------ -- -- --
0.10








0.30 1965.9 :
0.30 1966.8
















0 30 60 90 120 150 180 210 240 270 300 330 360
System III (1965) (degrees)


Figure 3.1: Probability of occurrence of Jupiter as a function of Jovian longitude at 18 MHz for
the seasons from 1957 to 1968. The probabilities are given as histograms and are calculated for 50
bins in longitude. Note that the sources, especially source A (240-270), move back-and-forth
in position over time showing the cyclical observational effects of changing latitude.
in position over time showing the cyclical observational effects of changing latitude.








56


18 MHz Occurrence Probability
0.50
0.40
0.30 1969.1
0.20
0.10-
0.50 ------'--
0.40
0.30 1970.2
0.20
0.10
0.50 ,
0.40-
0.30 1971.3
0.20-
0.10-
0.50 -
0.40
0.30 1972.4
0.20
0.50 ,.-- ,-----.--' '-----, ,-'---- ----

0.40
0.30 1973.6
0.20
0.101
0.50
0.40
0.30 1974.7
0.20b
0.10
0.50
0.40
0.30 1975.8
0.20
0.10
0.50 .
0.40
0.30 1976.9
0.20


0.40


0.30 1978.9



0.30 1980.09
0.20
0.10





0 30 60 90 120 150 180 210 240 270 300 330 36

System III (1965) (degrees)


Figure 3.2: Occurrence probability for seasons 1969-1980 at 18 MHz


0







57


18 MHz Occurrence Probability
0.3-
0.2 1981.1
0.1-
0.3
0.2 1982.2
0.1-
0.3
0.2 1983.2
0.1-
0.3 -
0.2 1984.6

0.3 :-
o.2 -1985.5


0 0.1 -





0) 0.2 1988.9
0 03 ~ .J=--"l--- --l----------------

0.1 -




0.1 -
S 0.3 -
0.2 1988.9









0 .2- 1990.1
0 0.1



0.3
0.2 1991.0
0.1

0.2- 1994.31
0.1 -




0 30 60 90 120 150 180 210 240 270 300 330 360
System III (1965) (degrees)


Figure 3.3: Occurrence probability for seasons 1981-1994 at 18 MHz










20 MHz Occurrence Probability


0.3
0.2 1964.8
0.1

0 .2 1 9 6 5 .9 r- r-L

0.3 .. .
0.2 1967.0 ""
0.1


1968.1


0 30 60 90 120 150 180 210 240 270 300 330 360

System III (1965) (degrees)


Figure 3.4: Occurrence probability for seasons 1964-1968 at 20 MHz


I ....







59


20 MHz Occurrence Probability
0.50
0.40
0.30 1969.1
0.20
0.10
0.50
0.40
0o.30 1970.2
0.20-
0.10-
0.50 -
0.40-
0.30 1971.3
0.20-
0.10
0.50 --
0.40
0.30 1973.6
0.20
0.50 ----"
0.40




Z) 0.30- 1973.6
Co 0.20

















0.10
0. '1 -- O.l -- r-- -- ---_ _Z--'- ------ ^ ^

0 0.50





0.40
0.:30o 1974.9
0.20 _L_
0.10
0.50








0.40




0.30 1970.8
0.20
Q o.o 0.. .

0.20
0.10













0 30 60 90 120 150 180 210 240 270 300 330 360
System III (1965) (degrees)


Figure 3.5: Occurrence probability for seasons 1969-1980 at 20 MHz
Figure 3.5: Occurrence probability for seasons 1969-1980 at 20 MHz







60


20 MHz Occurrence Probability
0.3
0.1 -

0.2 1982.2
0.1 -

0.2 1983.2
0.1 -

0.2 1984.6
0.1 -
0.3:----1 -----
0. 0.2 1985.5
IQ 0.3 ----- ---" "- '---------"r----------- ---r ^--

0y (.21- 1986.6



0 o.1
0 o.2 1988.9



0 0.2 1990.0


t o 1991.0
0.1 -

0.2- 1992.1



0.1 -

System III (1965) (degrees).3


0.Figure 1993.6: Occurrence probability for seasons 1981-1994 at 20 MHz




Figure 3.6: Occurrence probability for seasons 1981-1994 at 20 MHz







61


22 MHz Occurrence Probability



0.40
0.30- 1958.1
0.20-
0.10
0.40
0.30 1959.2
0.20-
0.10
0.40 Q3' I---- --- -
0o.30 1960.2


0.40n ,, ,, n
S0.30- 1961.5
0.20 -
0.10-
S0 0.40 ..
0.30 1962.8


0.20 -1


0 0.30 1964.8








0.30 1967.0



0.3o 1968.1
0.20-



0.10-

0 30 60 90 120 150 180 210 240 270 300 330 360

System III (1965) (degrees)

Figure 3.7: Occurrence probability for seasons 1958-1968 at 22 MHz
Figure 3.7: Occurrence probability for seasons 1958-1968 at 22 MHz







62


22 MHz Occurrence Probability
0.30 1969.2
0.20-
0.10
0.40
0.30 1970.2
0.20-
0.10-
0.40
0.30- 1971.3
0.20-
0.10-
0.40
0o.30 1972.4
0.20-
, 0.10
,= 0.40 .------

0 0.40

0.30- 1974.7


0 0.40
S0.30- 1975.8
0.20-
S0.40


0.30- 1976.9 _r -
0.20






0.10 -



0 30 60 90 120 150 180 210 240 270 300 330 30
System III (1965) (d 197.9grees)
0.208: Occurrence probability for seasons 1969-1980 at 22 MHz
0.40 -------





0.20-



0 30 60 90 120 150 180 210 240 270 300 330 360

System III (1965) (degrees)

Figure 3.8: Occurrence probability for seasons 1969-1980 at 22 MHz







63


0.3 1922 MHz Occurrence Probability
0.3
0.2 1981.1
0.1 -
0.3
0.2 1982.2
0.1-

0.2 1983.2
0.1 -
0.3 :- -
0.2 1984.6
0.11986.6





0.3
0.2 1985.5












0.2 1990.0
0.1-
0.3
0.2 1986.6
0.12 1992.1
0.3:
0.2 199387.1
0.1
0.3






0.3 ------- "f ^ '*--'---r -'- ---- =::--- m -
0.2 1988.9
0.1

0.2 1990.0
0.1
0.3
0.2 1991.0
0.1

0.2 1992.1
0.1

0.2 1993.1
0.1
0.3
0.2 1994.3
0.1
30 6,010 10 18 1 4 7 0


30 60 90 120 150 180 210 240 270 300
System III (1965) (degrees)


Figure 3.9: Occurrence probability for seasons 1981-1994 at 22 MHz


330 360






64

Source A Position


Time (years)


Figure 3.10: The longitudinal position of the source A over time for (a) 18 MHz, (b) 20 MHz,
and (c) 22 MHz. The filled points represent the peak probability point of the source, and the
open points represent the average of the two half-probability points. The 12-year DE effect can
be seen at all frequencies as the sinusoidal component in the curves.









Cross Correlation Techni


0 30 60 90 120 150 180 210 240 270 300 330 360
Central Meridian Longitude (deg)


Cross Correlation


-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

Longitude Shift (deg)

Figure 3.11: Example of the cross correlation technique to calculate the shift of the curves
over 12 or 24 year intervals. Panel (a) is the smoothed 22 MHz occurrence probability for
the 1963 season, and panel (b) is the 22 MHz 1987 season. Panel (c) is a plot of the cross
correlation coefficients that were calculated for every 20.5 longitude shift of the 1987 occurrence
probability with respect to the 1963 occurrence probability. The maximum correlation is 0.975
and corresponds to a longitude shift of-6.8. The thick dashed curve from -30 to +300 represents
a polynomial fit to the peak of the correlation.











1 A 2
18MHz 1957 ,
18MHz 1981 18 1957,81
18MHz 1958
18 MHZ 1982 18 1958.82
22MHz 1958 22 1958,82
22 MHz 1982 1

18MHz 1959

218MHz 1983 .1 159.83
22 MHz 1983
18 MHz 1960
18MHz 1984 18 1960.84
22 MHz 1960 22 1960,84
22 MHz 1984
18 MHz 1961
18 MHz 1985 18 19685
22MHz 1961_-- 22 1961.85

18MHz 1962
18 MHz 1986 18 1962,86
22MHz 1962 22 1962.86
22MHz 1986



18 MHz 1963
18 MHz 1987 18 1963,87

22 MHz 1987
18 MHz 1964
18MHz 1988

20 MHz 1988
22 1964,88
22 MHz 1964
22MHz 1988
18MHz 1965
18 MHz 1990
'18 1965.90
20MH 1990 20 19665,9
20MHz1922 1965,96
22MHz 1965
22MHz 1990

18 MHz 19669
--- 1 8 1 9 6 6 9 1
20 Mz 991 22 1966.91
22 MHz 1966
22 MHz 1991
18 MHz 1968
18 MHz 1992

20MHz 199683 2
20 MHZ 1992 | [is |] /

22 MHz 1992
18 MHz 1969
18 MHz 1993
18 1969,93 /




18 MHz 1970
18MHz 1994
18 1970.94 /
20MHz 1994
22MHz 1970
22 MHz 1994


Steps For Combining Data


(A) Cross correlate the
occurrence probability graphs.

(B) Combine frequencies.
Weight = correlation /activity


S3

S1 1969


2 1970

3 1971 (C)

S4 1972


5 1973

6 1974


7 1975

8 1976


(C) Calculate weighted mean.
Weight = sum of individual
weights

(D) Calculated weighted mean.
Weight = o



4


\ 24 year data

) 29 6854 0 0035


Final Result

29.6848 0.0034


29.6767 0.0125


12 year data


Figure 3.12: Overview of the data combination and weighting method. Column 1 is all the

24-year pairs of seasons used in this study. Column 2 represents the cross correlated data.

Column 3 is the combined frequency data. Column 4 is the results for the 24-year and 12-year

calculations, and Column 5 is the final result. The calculations done between each column are

labeled A, B, C, and D, and are summarized in the legend.










Period Values


I r~T *1


-



System III
- (1965)


i>


Q)
0
()

C-



0
O0


c


0

cr


I I


14


29.80


29.75


29.70


29.65


29.60


29.55


I I


1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984

mid-date (year)

Figure 3.13: Rotation period values for each frequency plotted as a function of each 12 year or
24 year mid-date. The legend in the upper right shows the frequency and station where the data
were gathered. Error bars are inversely proportional to the individual weights. System HI (1965)
is plotted as the horizontal dotted line for reference.


29.90


Rotation


29.85 h


24yr UF
24yr UF
24yr UF
12yr UF
12yr Chile
12yr Chile
i


I I I


18 MHz
20 MHz
22 MHz
20 MHz
18 MHz
22 MHz
I


29.50


I I


I I I


I I I






68

Frequency Distribution: Rotation Periods
1 8 'II I I I '

1 6 = 29'.6819
S= 0'.0362
1 4 bin = 0'.02
N = 47
o 12
C
10

U-
C)

6-

E
3 4-
z

2 -

0
54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84
Rotation Period (x 0'.01, in excess of 9' 55' 29')


Figure 3.14: The distribution of all the data given in Figure 3.13 plotted as a histogram with a
bin size of 0s.02. The unweighted mean (pi) and standard deviation (oa) are shown, and a normal
curve with the same parameters is overplotted for reference.






69

Independent Rotation Period Values


I I I


29.85


29.80


29.75-


29.70


29.65


29.60


I I I I


I I I


* .


I I I


1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984

mid-date (year)

Figure 3.15: Rotation period values for each mid-date after the frequencies are combined. Error
bars are again inversely proportional to the weights.


29.90


I
* 24yr
] 12yr


CD
0


(D
o--




0

0
C-

O
CY


System III

40
.


29.55

29.50


' '








Frequency Distribution: Independent Periods


56 58 60 62 64 66 68 70 72 74 76 78 80 82 84
Rotation Period (x 0'.01, in excess of 9" 55"' 29')


Figure 3.16: The distribution of data after the frequencies are combined shown as a histogram
with a bin size of 0s.02. The unweighted mean (yu) and standard deviation (or) are shown, and a
normal curve with the same parameters is overplotted for reference.


OL
54






71

Statistical Significance


0.50 -
0.40 -
0.50 -
0.20 -
0.10 -
0.00 -
66


66.5 67 67.5 68 68.5 69 69.5 70 70.5 71 71.5 72
Rotation Period (x 0'.01, in excess of 9' 55"' 29')


Figure 3.17: The statistical significance of the final weighed rotation period. The vertical
line is a reference for System III (1965), and the normal curve has the weighted mean and
weighted standard deviation of our final calculation. The statistical significance between the two
measurements (7.4o~) is shown by the horizontal arrow.


1.20
1.10
1.00
0.90
0.80
0.70
0.60
































LO




0


_Q

0
C_

0






(D
U


C
L_
0




0


>) 0

i) iqqo
/{1-!lqeqojd


0 0

0d
@oU.Jjn.lo0


O


o)

0
0)


co
00
(.0
00

00


o.-






r--.-

0
0 ,,

00


Qo


(O0
0
CO
(D
00
LO
r--
mn


0

2
S.




~) cu

oo
0 m
Big





0 01
o1)


*0
0 0-
C.1





cn


N a






0

~cu


N g








00
U U &
















-4
2d CA
*s 0 I

6 0 <4.

.0 0





0 >- 0






















I I I I I I I I I I I I j I I I I I


CM


O4

E







o
Ln





0


x
C)


I I 111111111 III I


0
CN

iGMOd


Ln 0


IDJ-p ds


I I I I


I


111111 III


0
















.-
a '



















ob
W 4.
C3l
0
0
*-D













6














S0
'-0





L -o












.- 0
II


I


I I I I I I I I I I I I I I I I I I I I I I I













CHAPTER 4
STRUCTURE WITHIN HOM EMISSION


4.1 Introduction


Ground-based radio wave data dating back to the 1950s indicated that Jupiter has

an extensive magnetic field and complex radio wave emissions in the decametric and

decimetric wavelength ranges. More recent measurements by spacecraft revealed the

existence of additional complex Jovian radio emission components in the kilometric

(KOM) and hectometric (HOM) wavelength ranges. Spacecraft are needed to receive the

KOM and HOM wavelength range emissions because these emissions are blocked by the

Earth's ionosphere and cannot be monitored from the ground. In particular, the planetary

radio astronomy (PRA) instruments aboard the Voyager 1 and 2 spacecraft have provided

detailed measurements of the Jovian HOM radiation [Warwick et al., 1979a, 1979b].

The spectral characteristics of HOM show that the frequency extent of the emission

covers most of the low-frequency band of the PRA instrument (1.2 kHz 1326 kHz)

from approximately 300 kHz to at least 1.3 MHz [Warwick et al., 1977; Thieman, 1980;

Boischot et al., 1981].

The features we have discovered are spectral "lanes" of decreased emission intensity

within the HOM emission component [Green et al., 1992]. These lane features are defined

by their sloping, linear emission patterns at relatively specific longitudes in frequency-time

spectrograms. Figure 4.1 shows a typical low-band frequency versus central meridian

longitude (CML) intensity spectrogram observed by Voyager 2 for one Jovian rotation.

CML is a left-handed longitude system representing the sub-observer longitude [Dessler,






75

1983]. Emission intensity, in millibels, is proportional to the amount of shading defined

by the gray scale where the zero millibel reference level is 3.5 x 10-22 W m-2 Hz-1. The

HOM emissions are seen from 40 to 1200 CML and from 3000 to 3600 CML. Consistent

morphological features are not easily discernible in examination of spectrograms rotation

by rotation because of short-term temporal variations of the emission. The lane features

are apparent in Figure 4.1, however, as the diagonal regions of low-intensity emission at

900 and 3300 CML. As we will demonstrate, the consistency of the lane features only

becomes apparent after combining observations over many planetary rotations.

A generally recognized characteristic of HOM in frequency-time spectrograms, com-

pared to the other Jovian free-escaping radio emissions, is a lack of distinctively consistent

morphological features. It is well-known that the observed HOM is modulated by the

rotation of the planet such that very little HOM activity is observed when the CML is

within 900 of the longitude of the northern magnetic dipole (2000 CML). The probability

of occurrence of HOM, however, approaches 100% at other longitudes.

The higher-frequency resolution of the low-band receiver makes the study of detailed

HOM structure possible, but its reception ends at 1.326 MHz. HOM extends into

the high-band receiver of the PRA instrument (1.2 MHz 40.5 MHz), but due to the

lower resolution and decreased sensitivity, the lane features presented here were not

apparent at frequencies above 1.3 MHz. Other structure is apparent, however, in the

high-band receiver of the PRA; most notable are the decameter (DAM) arcs [Leblanc,

1981; Goldstein and Thieman, 1981]. In section 4.2 we analyze these DAM features,

as well as investigate the discontinuity in sensitivity between the low- and high-band

receivers and the relation to the features studied in this paper.

Green et al. [1992], using only inbound Voyager 2 observations, first recognized

the presence of these lane features within the high-probability HOM regions. We






76
extend that analysis by including more data and investigating new aspects of the Jovian

HOM radio emission. We will show that by superimposing PRA data from multiple

observations sorted according to longitude as well as magnetic latitude and by performing

an occurrence probability analysis, we uncover the semipermanent lane features in the

HOM. These features are well-defined by their sloping, linear borders at relatively

consistent longitudes in frequency-time spectrograms. In analyzing both inbound and

outbound data of Voyager 2, we notice that the lane features are clearly visible in the

composite spectrograms in frequency versus CML and in frequency versus magnetic

latitude. In an effort to explain how the HOM lanes are generated, we investigate the

HOM emission intensity and polarization on either side of the lanes. In addition, we

include an analysis of the HOM lanes with respect to the correlation of HOM with the

solar wind particles and fields. An explanation of these lane features will provide us with

a better understanding of the emission characteristics, source regions, and propagation

effects of HOM in the Jovian magnetosphere. In particular, these lane features should

provide constraints or boundary conditions for HOM radio emission sources, HOM

propagation, and Jovian magnetospheric models.


4.2 Data Analysis


4.2.1 Occurrence Probability: Frequency Versus CML

From the examination of individual events of HOM, it is difficult to distinguish

between seemingly random emissions and possibly repeatable characteristics, due in part

to the spacecraft distance from the planet and the dependence of the emission on the solar

wind [Zarka and Genova, 1983; Barrow and Desch, 1989]. In order to enhance stable

HOM features, we combine multiple PRA observations with similar viewing geometries

and analyze these data by an intensity-independent, occurrence probability technique.






77
Data taken for each observed frequency from periods before and after the Jovian encounter

of Voyager 2 are combined separately and sorted into half-degree longitude bins. In

each CML-frequency bin, the occurrence probability is determined by the number of

"activity" counts divided by the total number of observing counts for that bin. An

"activity" count occurs when the observed emission exceeds a threshold level calculated

in accordance with that rotation's level of activity. This technique provides equal weight

to stronger and weaker HOM events, greatly reducing any bias toward strong events.

For our analysis we calculate and subtract a background value from all bins for each

frequency and each rotation. To investigate whether the background subtraction level

affects the presence, intensity, or quality of the lanes, we create occurrence probability

spectrograms with different background levels. We find that for different background

subtraction levels the structure of the individual lanes remains equal (i.e., each feature

disappeared at equal background levels as the level was raised). Moreover, the quality and

structure of the lanes remain nearly the same. This agrees with our analysis of intensity

variations across the lanes (see Section 4.6). This occurrence probability technique

enhances therefore the appearance of stable HOM emission characteristics by eliminating

the intensity variation of HOM itself. This method has been used extensively for the

determination of characteristics of similar free-escaping radio emissions from the Earth

(see, for example, Green et al., [1977]).

Figure 4.2 shows the occurrence probability of HOM using pre-encounter Voyager

2 PRA data during 40 consecutive planetary rotations from June 16 to July 6, 1979,

(276 Rj 46 Rj, where Rj is the distance of one Jovian radius). This time period is

selected due to the strength and consistent appearance of HOM before the encounter

with Jupiter so that only far-field effects of the radiation and roughly constant viewing

geometry are examined. Due to the inverse-square radial distance effect, occurrence






78

probability spectrograms inside ~ 50 Rj show an increased intensity and become very

amorphous. Figure 4.2a clearly shows that there is a high probability of observing HOM

at longitudes from 2800 to 3600 and 00 to 1200. A closer examination of this high-

probability CML zone reveals regions of decreased probability appearing as diagonal

"lanes" within certain frequency and CML ranges. The frequency range for the lanes

is 500 kHz to 1200 kHz, and the CML range is 700 to 1200 and 2800 to 10. The

lanes have reasonably well-defined linear borders (highlighted in white in Figure 4.2a)

and are consistent in their location in CML and HOM emission frequency. These lane

features can often be seen in the frequency-time (or -CML) spectrograms for individual

rotations once one knows where to look. This becomes evident when one compares the

lane features as illustrated in Figure 4.2a with the HOM observations shown in Figure

4.1. Low-intensity HOM regions in Figure 4.1 tend to coincide with regions of low

occurrence probability in Figure 4.2.

Similar lanes appear in Figure 4.2b which represents post-encounter Voyager 2 PRA

data from July 13 to July 29, 1979. This occurrence probability plot is calculated in the

same way as Figure 4.2a, and has lane features that are nearly identical in frequency and in

CML. We do not draw highlighted regions on Figure 4.2b so the reader can view the plot

without obstruction or bias. The lanes are evident at these two different spacecraft times

and viewing geometries, and Figures 4.2a and 4.2b show that the general morphology

remains intact. The differences that are evident in Figures 4.2a and 4.2b are most likely

due to the change in the spacecraft latitude from the inbound and the outbound pass.

The jovigraphic latitude of the Voyager 2 spacecraft was approximately +70 inbound

and +50 outbound (see Figure. 1 of Alexander, [1981]). The occurrence probability

technique demonstrates the long-term stability of the lane features, because the lanes

do not smear out in longitude, latitude, or frequency as multiple rotations are added to






79

the spectrogram. This gives strong evidence that the features are not transient effects

but have some permanence. Figure 4.2c shows the magnetic latitude of the Voyager

2 spacecraft as a reference for Figures 4.2a and 4.2b. The lane features occur most

prominently when the Voyager spacecraft is making an excursion from the magnetic

equator to +100 magnetic latitude or vice versa (white regions shown in Figure 4.2c).

The lane in the longitude range from 3500 to 200, however, occurs when the spacecraft

is below the magnetic equator. This lane may be attributed to one or a combination of

two events: (1) the lane is similar to the other lanes except that it occurs at negative

magnetic latitudes, or (2) the lane may be due to the lower edge of the latitudinal beam of

HOM. A lane begins to appear at 3500 longitude at the higher frequencies in Figures 4.2a

and 4.2b, but as the spacecraft crosses the magnetic equator, the pattern is interrupted.

For the Voyager 2 outbound data, when the spacecraft moves to latitudes lower than

-50, most of the emission ceases. This cutoff in emission may be due to the spacecraft

moving out of the HOM beam. Notice that the high frequencies disappear first, followed

by progressively lower frequencies, indicating some structure within the HOM beam.

Based on this argument, the lower edge of the beam occurs at approximately -50 latitude.

The lowest occurrence probability for HOM occurs when the spacecraft is above +100

magnetic latitude [Ladreiter and Leblanc, 1989]. Given these two constraints, the beam

is approximately 150 wide in latitude (-50 to +100), which is consistent with the Ladreiter

and Leblanc [1989] beam width of 100 to 200. This latitude effect is shown more clearly

in Figure 4.3 (an extension of Figure 9 from Ladreiter and Leblanc, [1989]) which

provides a summary of the spacecraft trajectory and a simple model of the observed

latitudinal beaming of HOM emission. The two sets of sinusoidal curves represent the

magnetic latitude versus CML of the inbound (dayside) and outbound (nightside) position

of the spacecraft over the many planetary rotations of HOM data used in this analysis.






80

It illustrates that the lack of HOM emissions from 1200 to 2800 CML coincides with the

time when the Voyager 2 spacecraft is above +100 magnetic latitude. It also illustrates the

lack of HOM emission seen in the outbound data plot from 3550 to 700 CML coinciding

with the time when Voyager 2 is below -50 magnetic latitude.

It is important to note that the lane features in Figures 4.2a and 4.2b can also be seen

in Plate 1 of Alexander et al. [1981] in both the pre-encounter and post-encounter data

from Voyager 1 as well as Voyager 2. However, there was no discussion or interpretation

of the lane features in that paper. In the following sections we provide more evidence

and analyses that these features are indeed important and that they should be considered

for HOM source and beaming models.

4.2.2 HOM-DAM Relation

A logical starting point in the attempt to account for the lanes is to investigate a

possible connection of HOM with the well-studied arc-like structure found in the DAM

emission [Leblanc, 1981; Goldstein and Thieman, 1981]. We did investigate whether

the HOM lanes are an extension of the DAM arc features. The DAM emission that is

consistent in longitude is labeled as vertex early arcs (VEA) and vertex late arcs (VLA)

[Leblanc, 1981]. In our investigation, we plot both the low- and high-bands of the PRA

instrument together and examine the features in both bands. High-band plots were chosen

when the arc structures were very prominent and when they were nonexistent. Low-band

plots were also chosen when the lane features in HOM were prominent and when they

were nonexistent. We find that there is no correlation of the occurrence of the arc

features with the occurrence of the lane features. Furthermore, these arc structures occur

at all longitudes and range in frequencies from 1.5 to 10 MHz. The arcs open toward

decreasing time (VLA) before 2000 CML and open toward increasing time (VEA) after

2000 CML. Since there are two lanes of opposite slope on either side of 2000 CML,






81

an extension of the arc features is not likely to explain both lanes. In addition, the arc

features occur at all longitudes, whereas the lane features are consistently seen within

limited longitude ranges.

We did have some difficulty in this investigation of the HOM and DAM in the

low- and high-band receivers, respectively, of the PRA instrument. The main problem

is the difference in resolution between the two receivers. The low-band receiver has a

frequency resolution of 19.2 kHz and bandwidth of 1 kHz, while the high-band receiver

has resolution of 307.2 kHz and bandwidth 200 kHz [Warwick et al., 1977]. Reducing the

low-band receiver resolution to that of the high-band receiver gives approximately four

frequency ranges for the low band receiver. If we collapse the occurrence probability

spectrograms in Figure 4.2 down to four thin bands, the structure of the HOM lanes, as

well as other general structure, would not be apparent. In fact, the lanes would not even

be discernible at this resolution because the lanes would only appear as small gaps in one

thin band. Furthermore, spacecraft interference caused problems in the frequency range

of 4-5 MHz making it even more difficult to interpret the HOM and DAM emission near

the discontinuity between the low- and high-band receivers.


4.2.3 Polarization Studies


In investigating the lane features, the polarization of HOM provides important clues

for the origin of these structures. The polarization of HOM has been investigated by

Ortega-Molina and Lecacheux [1991]. Their findings strongly indicate that this emission

is predominantly right-hand circularly (RHC) polarized when observed from the Jovian

northern hemisphere and left-hand circularly (LHC) polarized when observed from the

southern hemisphere. The polarization measurements have led those authors and many

others to the conclusion that HOM is generated by the cyclotron maser instability (CMI)






82

in the right-hand extraordinary (R-X) mode from latitudes close to the northern and

southern magnetic poles [Wang, 1994].

The propagation characteristics of HOM have been studied by Ladreiter and Leblanc

[1990a, b] by comparing observations with computer ray tracing calculations. These

authors suggest that HOM is beamed from high-altitude northern and southern hemisphere

sources into the magnetic equator in overlapping right-hand and left-hand polarized

hollow emission cones. The HOM beam width is approximately 150 in magnetic latitude

and is slightly offset north of the magnetic equator. Figure 4.3 is a summary of the

observed beaming of HOM emission. It shows the polarization of the HOM emission

and the overlap near the magnetic equator believed to arise from northern and southern

hemisphere sources. The most recent study of HOM was conducted by Reiner et al.

[1993] using the Unified Radio and Plasma Wave (URAP) instrument data gathered

by the Ulysses spacecraft. They found that the northern hemisphere HOM emission

is predominantly RHC polarized, consistent with X-mode emission. LHC polarization

data were also detected, however, suggesting the presence of O-mode emissions from a

northern hemisphere source.

The Voyager 2 spacecraft was unable to make a complete polarization determination

because of the antenna characteristics and the lack of a complete Stokes parameters

determination. Only the net polarization sense of the waves can be unambiguously

determined when the spacecraft was in particular orientations relative to the source. For

these orientations the degree of polarization can be bounded if the angle between the

direction normal to the antenna plane and the source of the emission (angle 0) is known

[Thieman, 1980]. Using times when 0 is favorable, we determine the polarization of the

HOM emission on either side of the lanes. When a lane is discernible in the intensity

plots we find that the polarization is always right-hand (RH) on both sides of the lane.






83

We also find several intensity plots where the lane boundaries are RH polarized, but

the composition of the lane center is low-intensity, left-hand (LH) polarized HOM. It

is significant to note that there are no plots where a lane is bounded by LH polarized

emission on both sides of the lane. Since the polarization is the same on both sides

of the lane, the lanes are not a result of a gap in oppositely polarized HOM emission

emanating from northern and southern hemisphere source regions. These results suggest

that the lanes are generated in the northern hemisphere and are consistent with source

region structure or propagation characteristics from a specific hemisphere.

4.2.4 Occurrence Probability: Magnetic Latitude Versus Frequency

To further investigate the magnetic latitude dependence of the lane features, we plot

in Figure 4.4 the HOM occurrence probability as a function of the Voyager 2 magnetic

latitude and observed frequency. Figure 4.4 represents a coordinate transformation of the

spectrogram data from Figure 4.2. This transformation shows that the lane structure is

similar in its dependence on frequency and magnetic latitude, even in different longitude

ranges. Figure 4.2c shows white areas which isolate the times when clear lane events are

seen in the data. These appear when the magnetic latitude varies between 0 and +10.

To compare lane dependence on magnetic latitude in different longitude regions, both

inbound and outbound data are plotted in Figure 4.4 for the longitude ranges in which

the magnetic latitude varies from 0 to 100. The lane in the longitude range from 3450

wrapping around to 200 is not included in this comparison since it occurs in a latitude

range below 0 and there is no corresponding lane in a different longitude range with

which to compare. Consequently, only those data for which the magnetic latitude of the

spacecraft is between 0 and +100 are used in this analysis. This can be seen more clearly

in Figure 4.3 if one looks closely at the longitude ranges of the plots given in Figure 4.4.

Another consequence of this longitude/latitude range is that it will enhance the effects






84

of any northern hemisphere emission sources. This is consistent with the polarization

results in section 4.2.3. We also wish to show that the lane features depend similarly on

magnetic latitude for what is believed to be northern hemisphere emission occurring in

different longitude ranges. The similarities give evidence that the lanes are a result of

northern hemispheric emission and propagation processes.

In order to show similarities in the inbound data from different longitude regions,

Figures 4.4a and 4.4b are plotted separately for 700 to 130 CML (Figure 4.4a) and for

2650 to 3350 CML (Figure 4.4b). Figures 4.4c and 4.4d show the outbound data separately

from 820 to 1420 CML and from 2530 to 3230 CML in the same magnetic latitude range

of 00 to +100. The CML range for the outbound data is shifted by 120 because the latitude

of the spacecraft decreased by 20 (refer to Figure 4.3). Jovian kilometric radiation is also

seen in these plots at frequencies below 300 kHz and at magnetic latitudes greater than

6. For the HOM emissions the following characteristics are discernible in Figure 4.4:


1. The lanes in the spectrograms start at +100 magnetic latitude at 500 kHz and extend

down to the magnetic equator for HOM frequencies greater than 1 MHz.

2. The lane features in these four panels are morphologically similar and depend

similarly on magnetic latitude for these longitude ranges.

3. These features are persistent because they are similar for both Voyager 1 and 2

inbound and outbound data (see Plate 1 of Alexander et al., [1981]).


4.2.5 Solar Wind Interactions

Barrow and Desch [1989], as well as others, demonstrated that the HOM inten-

sity varies with solar wind density and/or solar wind pressure. Using the occurrence

probability technique and Voyager 2 solar wind density data, we study the effects that

different solar wind densities may have on the appearance of the lanes. We also search






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for a correlation of the HOM lanes with the interplanetary magnetic field (IMF) and find

that the IMF varied considerably in magnitude and in time over the periods studied; no

correlation of IMF with the lanes is likely.

Solar wind proton density data were analyzed versus time and spacecraft range from

Jupiter for the pre-encounter period of Voyager 2. Solar wind data end at day 183.5

of 1979 when the spacecraft reaches Jupiter's bow shock and enters the magnetosphere

(~ 100 Rj). For reference, Voyager 2's encounter with Jupiter occurred on day 191 of

1979. No solar wind data are available for the outbound pass of Voyager 2 because the

spacecraft was still inside the magnetosphere of Jupiter during the period of observations.

We investigate the possibility that solar wind interactions may cause or enhance the HOM

lanes by calculating the occurrence probability at times of different solar wind densities.

The time periods we investigate include days 167-171 (low solar wind density, psw <

0.15 cm-3), days 173-177 (high density, Psw = 0.50 cm-3), and days 178-182 (low density,

Psw < 0.15 cm-3). We find that lanes are evident in both low and high solar wind density

time periods and that the lane characteristics are the same. While Barrow and Desch

[1989] conclude that HOM emission intensity varies directly with solar wind density, we

find that the lane features seen within the amorphous HOM emission show no correlation

with solar wind. Therefore we are reasonably confident that changes in the density of

the solar wind are not a major influence on the lanes seen in the HOM emission.


4.2.6 Intensity Profiles


In order to determine if there are any significant variations in HOM intensity along

or across the lanes, we examine intensity spectrograms (similar to Figure 4.1) for all

the data. In particular, we examine two-dimensional slices (frequency versus intensity

at a given time) of the intensity data when a lane was discernible. We find that the






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intensities of the emission on both sides of the lane are nearly equal. Furthermore, we

analyze the data for changes in the probability of occurrence by varying the background

threshold. Emission that exceeds the background threshold is counted as activity, and

an activity count determines whether each individual measurement is counted as an

occurrence probability event. We find that the lanes remained qualitatively similar for

widely different background subtraction levels (refer to section 4.2.1). We may conclude

here that the lanes have approximately equal HOM intensities and occurrence probabilities

on each boundary of the lane. It appears that the conditions for receiving emission are

nearly similar on each side of the lane and that the lanes are caused by some break in

the source regions) or by some obstruction or refraction in the magnetosphere.




4.3 Discussion


The lane features do not seem to be an effect of refraction by the lo torus since

the modeled plasma density in the torus is not large enough to alter ray paths for those

frequencies at the upper end of the HOM frequency range [see Green et al., 1992; Wang,

1994]. Using the charge density values from Bagenal et al. [1985], the center of the

Io torus has charge densities of approximately 3000 cm-3. The plasma frequency for

this density is approximately 500 kHz, which is the lower end of the HOM frequency

range of interest (500 kHz to 1300 kHz). Since the lanes are continuous across the HOM

frequencies and the upper end of the frequency range will not be significantly refracted by

the lo torus, we do not believe that simple torus refraction is the source of the lanes. We

also examine the Io plasma torus model of Bagenal [1994] and find that the new model

is not significantly different from the previous model in the inner Jovian magnetosphere.

Therefore our results are not affected by this latest Io plasma torus model.