identification of cataclysmic variables in large …
TRANSCRIPT
ABSTRACT
IDENTIFICATION OF CATACLYSMIC VARIABLES IN LARGE-SCALE SYNOPTIC SURVEYS BY ANALYSIS OF FREQUENCY
DISTRIBUTIONS AND POWER-LAW RELATIONS
I investigate the nature of flickering in cataclysmic variable stars (CVs) and use
the mathematical model of self-organized criticality (SOC) to show that the slope of a
power-law plot can determine whether or not an observed object is a CV. Histograms
may also be used to analyze the properties of CVs and to distinguish them from related,
detached close binary star systems. These methods were tested on a statistically complete
sample of cataclysmic variables and related objects from the Palomar-Green survey. I
have also discovered an empirical relationship between absolute magnitude and power-
law index. The observations used for this were long-term light curves of these objects, in
approximately the visible (V) band, made by the automated telescopes of the Catalina
Real-Time Transient Survey. PG 0935+087 has been discovered to be a visual binary
with characteristics of irradiation variation. The hot subdwarf (sdB) star PG 1710+567 is
also serendipitously shown to be pulsating, with a period of 11.0 hours.
Kurt Lance Shults Jr May 2021
IDENTIFICATION OF CATACLYSMIC VARIABLES IN LARGE-
SCALE SYNOPTIC SURVEYS BY ANALYSIS OF FREQUENCY
DISTRIBUTIONS AND POWER-LAW RELATIONS
by
Kurt Lance Shults Jr
A thesis
submitted in partial
fulfillment of the requirements for the degree of
Master of Science in Physics
in the College of Science and Mathematics
California State University, Fresno
May 2021
APPROVED
For the Department of Physics:
We, the undersigned, certify that the thesis of the following student meets the required standards of scholarship, format, and style of the university and the student's graduate degree program for the awarding of the master's degree. Kurt L Shults Jr
Thesis Author
Frederick Ringwald (Chair) Physics
Gerardo Munoz Physics
Ettore Vitali Physics
For the University Graduate Committee:
Dean, Division of Graduate Studies
AUTHORIZATION FOR REPRODUCTION
OF MASTER’S THESIS
_____X____ I grant permission for the reproduction of this thesis in part or in its
entirety without further authorization from me, on the condition that
the person or agency requesting reproduction absorbs the cost and
provides proper acknowledgment of authorship.
Permission to reproduce this thesis in part or in its entirety must be
obtained from me.
Signature of thesis author:
ACKNOWLEDGMENTS
I would, first and foremost, like to thank my thesis advisor and invaluable mentor
Dr. Frederick Ringwald for always guiding me in the right direction. You have always
encouraged me to pursue scientific discovery with practicality and enthusiasm. I would
also like to thank the other members of my thesis committee, Dr. Gerardo Muñoz and Dr.
Ettore Vitali, for reviewing my thesis and being an additional source of knowledge. To all
three of my thesis committee members – your passion for teaching has inspired me to
pursue the same career.
While in graduate school, I was given the opportunity to be a teaching assistant in
the Department of Physics. For this financial support, and the continued support through
the graduate program, I would like to thank the Physics Department at Fresno State and
all its associates.
I was also fortunate to find employment with the State Center Community
College District as an interning adjunct faculty instructor of physics and astronomy. I
would like to thank Clovis Community College and Madera Community College for the
financial support and experience in teaching at the college level.
I would like to thank my parents, Kurt (Sr.) and Mary Shults, for always believing
in me and supporting me through this journey. Your love and encouragement have
always been a tremendous motivation, thank you.
To my partner Xiomara Villa, our daughter Rowan, and our future children – I
could not have done this without you. You have given me the strength and determination
to pursue this dream and, ultimately, we will share in this accomplishment together as a
family.
v v
This thesis includes data collected by NASA’s TESS mission, which are publicly
available from the Mikulski Archive for Space Telescopes (MAST). Funding for the
TESS mission is provided by NASA’s Science Mission directorate.
This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium).
Funding for the DPAC has been provided by national institutions, in particular the
institutions participating in the Gaia Multilateral Agreement.
This research has made use of the SIMBAD database, operated at CDS,
Strasbourg, France.
TABLE OF CONTENTS
Page
LIST OF TABLES ...................................................................................................... viii
LIST OF FIGURES ....................................................................................................... ix
INTRODUCTION ...........................................................................................................1
Cataclysmic Variables (CVs) ...................................................................................1
The Palomar-Green Catalog .....................................................................................3
Non-CVs and “Related Objects” ..............................................................................5
Self-Organized Criticality ........................................................................................6
Catalina Real-Time Transient Survey .......................................................................9
METHODS OF DATA ANALYSIS .............................................................................. 11
Histograms............................................................................................................. 11
Power-law Index .................................................................................................... 12
DISCUSSION OF DATA .............................................................................................. 14
Comments on Non-CVs ......................................................................................... 14
CALCULATIONS OF DISTANCES, ABSOLUTE MAGNITUDES, LUMINOSITIES, AND MASS-TRANSFER RATES ........................................ 22
Distances ............................................................................................................... 22
Absolute Magnitudes ............................................................................................. 22
Luminosities .......................................................................................................... 23
Mass Transfer Rates ............................................................................................... 23
CONCLUSION ............................................................................................................. 27
APPENDICES ............................................................................................................... 31
APPENDIX A: LIGHT CURVES OF CVS AND NON-CVS ........................................ 32
APPENDIX B: HISTOGRAMS OF CVS AND NON-CVS ......................................... 115
Page
vii vii
APPENDIX C: POWER LAW PLOTS OF CVS AND NON-CVS .............................. 199
APPENDIX D: DATA TABLE FOR MASS TRANSFER RATE CALCULATION ... 283
LIST OF TABLES
Page
Table 1. Known cataclysmic variable stars (CVs) from the statistically complete sample of the Palomar-Green survey (GSL 86; Ringwald 1993). .................... 15
Table 2. Known non-CVs from the statistically complete sample of the Palomar-Green survey (GSL 86), with classifications from the SIMBAD database (Wenger et al. 2020). ...................................................................................... 16
Table 3: Suspected CVs from the Palomar-Green survey (GSL86), but not in the statistically complete sample........................................................................... 17
LIST OF FIGURES
Page
Figure 1: Cataclysmic Variable: DQ Her type (NASA’s HEASARC 2017)......................2
Figure 2: Comparison of histograms - SW Sex (CV), PG 2300+166 (non-CV) .............. 11
Figure 3: Power law analysis of BH Lyn with a slope of 0.2466, corresponding to a power-law index α = 1.255. ........................................................................... 13
Figure 4: Comparison of power-law index for non-CVs (left) and CVs (right). .............. 18
Figure 5: Comparison of standard deviations in the histograms of non-CVs and CVs. ... 18
Figure 6: Light curve of BE UMa showing irradiation variation and an eclipse .............. 19
Figure 7: Power-law plot of NY Ser where the different slopes show multiple areas of containing a high density of data, that is, multiple sources of variability .... 20
Figure 8: Analysis of orbital period and power-law index .............................................. 21
Figure 9: The relationship between the slope of the power law distribution and the mass transfer rate in CVs ............................................................................... 25
Figure 10: The relationship between absolute magnitude and period in CVs .................. 25
Figure 11: The relationship between absolute magnitude and power law index in CVs ............................................................................................................... 26
INTRODUCTION
Astronomy is now in the era of big data. With automated telescopes and
technology continually progressing, astronomers are analyzing enormous amounts of data
at once. The Rubin Observatory (formerly the Large Synoptic Survey Telescope) will
undergo testing in 2021 and is scheduled to be fully operational by 2023 at which time it
will be collecting 15 Terabytes of data every night (Kahn et al. 2020). With data
collection of this size, astronomers are in need of new techniques to more easily and
effectively analyze the information from automated telescopes.
This work is focused on distinguishing cataclysmic variables (hereafter CVs)
from related, detached binary star systems (hereafter non-CVs) by measuring a type of
noise in CV light-curves called flickering. Flickering noise is thought to be due to non-
uniform mass transfer from the secondary star to the primary white dwarf star (Mineshige
et al., 1994; Aschwanden, 2011, p. 31). When the light curves of CVs and non-CVs are
plotted as a power law relation, there is an obvious difference in the flickering noise
between the two groups. Noise is often thought of as an unwanted, unavoidable aspect of
collecting astronomical data, but in this case the flickering noise is the key to
distinguishing CVs from non-CVs.
Cataclysmic Variables (CVs)
Cataclysmic variables are close binary star systems typically consisting of a
primary white dwarf and secondary late-type star approximately on the main sequence.
The two stars are close in proximity, with orbital periods ranging from 78 minutes to
about 12 hours. In any CV, the secondary star fills its gravitational equipotential, also
called its Roche lobe, and therefore spills gas over to the primary white dwarf. (Robinson
1976; Hellier 2001).
2
Due to conservation of angular momentum, this creates an accretion disk around
the white dwarf as mass is being transferred. In about 1/3 of CVs, the white dwarf has a
magnetic field sufficiently strong to disrupt the accretion disk. Intermediate polars, also
called DQ Her stars, are a sub-class of CVs in which the inner radius of the disk is
truncated by the white dwarf’s magnetic field, see Figure 1. Polars, also called AM Her
stars, are a sub-class of CVs in which the white dwarf’s magnetic field is strong enough
to prevent any accretion disk from forming: in polars, the accretion stream from the
secondary star accretes directly onto one of both of the white dwarf’s magnetic poles
(Robinson 1976; Patterson 1984; Warner 1995; Hellier 2001).
Figure 1: Cataclysmic Variable: DQ Her type (NASA’s HEASARC 2017)
The temperature of the accretion disk or magnetic accretion stream in a CV varies
between approximately 3,000 K to 30,000 K. This makes the disk or magnetic stream
more luminous than either of the component stars in the system. The high temperature,
high energy, and turbulent accretion disks or magnetic streams may result in cataclysmic
3
changes in how bright the CV is. Classical nova eruptions are caused by thermonuclear
detonations of accreted gas on the essentially solid surface of the white dwarf. Nova
eruptions typically have amplitudes of 9-15 magnitudes (which correspond to increases in
intensity of 4,000-106 above quiescence), last hundreds of days or longer, and show only
one eruption (Robinson 1976).
Somewhat confusingly, cataclysmic variables that do not show eruptions or
outbursts are called “novalikes.” This is because spectra suggest that these are classical
novae between outbursts (Robinson 1976). Recurrent novae have eruptions that recur
over decades. This is thought to be because they have white dwarf stars that are near the
Chandrasekhar limit, which is the maximum mass that a white dwarf can have of 1.44
solar masses, where 1 solar mass = 1.989 × 1033 g. (Warner 1995, Hellier 2001).
(Throughout this work, we will use the cgs system of units, since it is still the standard in
astrophysics, in contrast to most other fields of physics and engineering, which use the SI
[MKS] system.)
Dwarf novae have completely different physics. Their outbursts are caused by
thermal instabilities in the mass flow through the accretion disk. Dwarf nova outbursts
typically have amplitudes of 2-6 magnitudes (which correspond to increases in intensity
of 6-200 above quiescence), last a few days, and recur over 10-500 days (Robinson 1976,
Patterson 1984, Warner 1995, Hellier 2001).
The Palomar-Green Catalog
The Palomar-Green catalog is a list of unresolved, apparently stellar objects that
give off an excess of ultraviolet light relative to blue light. Objects found in the survey
were included in the catalog if they had U – B < – 0.4, where U = apparent magnitude (or
intensity) in ultraviolet light, and B = apparent magnitude in blue light. This means that to
get into the Palomar-Green catalog, an object needed to be about 40% brighter in
4
ultraviolet light than in blue light. This excludes normal stars, so the Palomar-Green
catalog is composed of hot, exotic stars and galaxies so far away, they look like
unresolved points of light.
The catalog was the result of the Palomar-Green survey, which was carried out at
Mount Palomar by Richard Green, and was published in 1986 (Green, Schmidt, and
Liebert 1986, hereafter GSL86). The catalog contains 1874 objects, of which 1715
comprise a statistically complete sample, with an average limiting magnitude of B = 16.2.
Classifications of these objects made by GSL86 include subdwarf stars, white dwarf
stars, UV-excess galaxies, planetary nebula nuclei, and presumed galactic cataclysmic
variables.
The purpose of the survey was to find quasars and thus observed about one-
quarter of the sky at high galactic latitude (b > |30°|). At over 30° from the plane of the
Milky Way Galaxy in which we live, the obscuration and ultraviolet absorption caused by
dust in and near the Galactic plane is negligible (Schlegel, Finkbeiner, and Davis 1998;
Schlafly and Finkbeiner 2011).
The Palomar Green survey did find 114 quasars (Schmidt and Green 1983). The
survey also found over a thousand hot, high-gravity stars such as hot subdwarf stars and
white dwarf stars, which are the end states of stellar evolution for low-mass stars like the
Sun.
The survey also found 73 objects that the catalog classified as CVs (GSL86) that
were also in the statistically complete sample. Ringwald (1993) obtained spectra of
higher resolution and signal-to-noise ratio than the classification spectra of GSL86, and
did detailed studies over time of the spectra and apparent magnitudes of all 73 objects.
Ringwald (1993) concluded that only 36 of these are actually CVs. The remaining 37
objects are referred to in this work as “non-CVs.”
5
Non-CVs and “Related Objects”
The focus of this research is to develop a method to distinguish stellar objects as
CVs or non-CVs, using large databases already taken by automated telescopes that are
easily available. The new generation of automated surveys are expected to discover
thousands of CVs. Ringwald (1993) spent three years obtaining detailed follow-up
studies of 73 objects. Such detailed follow-up simply will not be feasible for thousands of
objects: even if unlimited time on a large (multi-million dollar), observatory-class
telescope were available, doing detailed follow-up studies of 1,000 CVs would take over
50 years.
Some of these non-CVs are related to CVs, in they are binary star systems with a
white dwarf primary star and late-type, approximately main-sequence, secondary star, the
same as those in CVs. They are unlike CVs in that the secondary star is smaller than its
Roche lobe, and so does not spill gas onto the white dwarf. The Ritter-Kolb catalogue
(2003, update RKcat7.24, 2016) refers to these as “Related objects.”
These types of binary star systems have also been called “precataclysmic
binaries” (Ritter 1986). However, it has been found that the distance between the stars in
these systems are sometimes too far away to ever become cataclysmic variables in
Hubble time, and therefore the name “precataclysmic binaries” is not appropriate. Other
names for these objects include “post-common envelope binaries” or “duds” (for
degenerate underfilling dwarfs) (Eggleton 1995).
In the low-resolution classification of GSL86, these related objects can be easily
confused for CVs. One reason is that the component stars are so similar, with a hot white
dwarf giving a blue spectrum and ultraviolet excess, but the cooler secondary star
radiating light on longer, redder wavelengths. The overall, “white” energy distribution
across the spectrum is unlike that of any single, normal star, but can be confused with the
6
white colors of an accretion disk or magnetic stream, especially in low-resolution,
classification spectra.
Another reason that CVs can be confused for related objects is that a hot white
dwarf can irradiate the facing hemisphere of the cooler secondary star. The irradiated
hemisphere can make the outer layers of the secondary star radiate emission lines, much
like the emission lines of an accretion disk or stream. An example is BE Ursae Majoris
(abbreviated as BE UMa: the “M” is supposed to be a capital letter). As BE UMa goes
through its 2.29-day orbit, when the irradiated hemisphere of the cooler, secondary star
faces Earth, the entire binary star system can be a factor of 6 times brighter than when the
irradiated hemisphere is facing away from Earth.
We should emphasize that some non-CVs show no evidence of being close binary
star systems. They were probably just misclassified, in the 1874 low-resolution
classification spectra it took over 9 years for GSL86 to obtain in the 1970s and 1980s,
before modern telescope automation made it possible to obtain spectra of hundreds of
objects per night.
Self-Organized Criticality
Self-Organized Criticality (SOC) is a mathematical model used to describe
turbulent systems in nature (Bak, Tang, and Wiesenfeld 1987, 1988, Bak 1996). SOC
modeling locates an identifiable pattern in what seems like random noise. The system
must meet certain criteria to be considered an SOC phenomenon:
1. It must be a nonlinear, dissipative system.
2. It includes interacting or independent components that are combined into an
integrated whole.
3. The relationship between the magnitudes of power and frequencies of
phenomena are described by a power-law function.
7
4. It is unstable, and often turbulent.
The classic example of SOC is the sandpile model. Imagine there is a single place
on an xy-plane where sand is being dropped from the +z-direction, with gravity acting in
the -z-direction. The sand will eventually pile and as more sand is added to the system,
small avalanches will occur. The size of these avalanches, along with their frequencies of
occurrence, follow a SOC model. That is, the relationship between the log of the
magnitude of the avalanche versus the log of the frequency of occurrence for that size of
avalanche is linear. Other examples of SOC phenomena prevalent in our daily lives
include: earthquakes, snow avalanches, traffic jams, populations of cities, stock market
fluctuations, and more (Aschwanden 2011, Chapter 1).
The cosmos is full of chaotic, turbulent systems as well. Examples of SOC
phenomena in astrophysics include stellar flares (including solar flares), accretion disks,
black holes, cataclysmic variable stars, meteoroid impacts, impact cratering, and
more. Again, signals from these sources follow the SOC model, where stronger signals
are exponentially rarer than weaker signals and dictated by a power-law relationship.
This work is focused on the variability in accretion disks or magnetic streams of
CVs. The infall of mass from the secondary star onto the primary white dwarf is not
uniform and causes variations in the luminosity (which is power output) of the accretion
disk or magnetic stream. Bursts of brightness are attributed to a sudden infall of mass.
This is what creates flickering noise in the light curves of CVs. Depending on the size
and rate of the mass transfer, these bursts can create dwarf nova outbursts, or even
classical nova eruptions, when the temperature and densities are high enough to ignite
nuclear fusion (Hellier 2001).
Accretion disks and magnetic streams/reconnections of CVs meet the
requirements to be considered SOC phenomena because they (1) have nonlinear growth
in a system far from thermal equilibrium, (2) show statistically independent occurrences
8
of instability (i.e avalanches) at random times between outbursts, (3) yield power-law
distributions in the data, and (4) are highly chaotic, turbulent systems.
The power-law function in SOC models follow a specific proportionality between
power spectral density and frequency. Power spectral density is proportional to a negative
power law function of frequency: 𝑃(𝜈) ∝ 𝜈−𝛼 , with α ≥ 0. White noise has a power-law
index α = 0, and is completely random and has a mean of 0. Pink noise has α = 1: this is
called flickering noise, or 1/f noise, and is common in electrical signals since electrons do
not flow uniformly. Red noise, also called brown noise, has α = 2. Black noise has α = 3,
and is dominated by the power at low frequencies, such as the deep rumbling of the roar
of a large rocket, or thunder.
The power spectral density inferred in this work comes from the magnitudes and
frequencies of energy release (luminosity) within the accretion disks of CVs. Energy
release from a CV varies due to mass transfer rates. Multiple physical phenomena affect
the mass transfer rate. One such is a coagulation effect or “mass clumping” where mass
builds up before avalanching onto the white dwarf. Another source of variability in mass
transfer is the magnetic loop structure within an accretion disk. The Sun also has a
magnetic loop structure and is subject to magnetic reconnection which can result in
coronal mass ejections. The same physics applies to the accretion disks of CVs, but
instead of the mass being ejected outward, it is ejected (or avalanched) onto the white
dwarf (Aschwanden 2011).
In order to determine what type of noise a signal may contain, a log(power)
versus log(frequency) plot is created. The slope of this line should give information about
what degree of noise a signal contains. As we shall see, the erratic flickering in
cataclysmic variables shows a degree of pink noise.
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Catalina Real-Time Transient Survey
The Catalina Real-Time Transient Survey (CRTS) is a collection of publicly
accessible real-time data from three automated telescopes as part of the Catalina Sky
Survey. The purpose of the Catalina Sky Survey (CSS) is to detect potentially hazardous
near-Earth objects (NEOs), including asteroids and comets. The CRTS is a project that
uses the telescopes in the CSS to observe optical transients that vary on relatively short
time scales. These optical transients include supernovae, cataclysmic variables, blazars,
and active galactic nuclei (Drake et al. 2009).
The three telescopes used in the CSS and CRTS are the 0.7m Schmidt telescope
located near Mt. Bigelow in the Catalina Mountains near Tucson, Arizona, the 1.5m
Cassegrain reflector located at Mt. Lemmon near Tucson, and the 0.5m Schmidt
telescope at Siding Spring Observatory in New South Wales, Australia. Since 1995, the
CSS has discovered nearly 10,000 NEOs and currently locates about 1,000 more per year.
The CRTS has discovered close to 17,000 total optical transient objects (Catalina Sky
Survey 2019).
Apparent magnitude is the magnitude of light intensity as measured from Earth.
V-band (in which “V” stands for visual) refers to the wavelength of light the CRTS
measures. V-band measurements correlate to wavelengths of around 551nm, in the range
of wavelengths to which the unaided human eye is most sensitive.
Julian Date is a time-recording method used by astronomers. It is defined as the
number of days since the beginning of the Julian Period – January 1, 4713 BC. Modified
Julian Date refers to the number of days that have passed since November 17, 1858.
These dates were chosen arbitrarily, so that nearly all Julian Dates and Modified Julian
Dates would be positive.
The data from CRTS are accessible online and easily downloaded into Excel for
further analysis. It is given as approximate apparent magnitude in the V-band (V) versus
10
Modified Julian Date (MJD). The most recent data release (CSDR2) was collected over a
period of about seven years, observing objects for a few days at a time, therefore the data
is very unequally spaced creating problems with data analysis.
METHODS OF DATA ANALYSIS
In my research, I used two different methods to analyze the data from the CRTS.
Both of these methods provided useful results.
Histograms
One method of data analysis used is creating histograms of the data. This shows if
there may be multiple sources of variability as well as whether or not the flickering
follows a Gaussian curve. It was found that for pure flickering the data does follow a
Gaussian distribution which is expected. This method also helped determine CVs from
detached binary star systems that may become a CV. In comparing histograms of CVs
versus those of non-CVs, there is a distinct difference between the shapes of the
frequency distribution of data. Data from CRTS are unresolved in time, there are large
gaps between measurements. The highly random phenomenon of flickering is being
measured, and so randomness is being measured. For CVs there is more variability so the
Gaussian distributions are wider, with greater standard deviations, for non-CVs the
Gaussian curves looks taller and skinnier because there is less variability: see Figure 2.
Figure 2: Comparison of histograms - SW Sex (CV), PG 2300+166 (non-CV)
0
5
10
15
20
14.2
9
14.4
8
14.6
7
14.8
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15.0
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ts
approx. V data points (magnitudes)
SW Sex Histogram
0
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PG 2300+166 (variable star) Histogram
12
SW Sextantis is a CV with an active accretion disk. In addition to flickering, SW
Sex is also known to have eclipses, with the secondary star passing between the accretion
disk, and possibly also a gas stream that flows across the accretion disk (Ritter-Kolb
catalogue 2003, update RKcat7.24, 2016).
PG 2300+166 is a non-CV, with very little variability. It was incorrectly classified
as a CV in the PG catalog, possibly because it has the spectrum of a hot subdwarf, which
has an ultraviolet excess and has broad, shallow absorption lines, like those of some
nova-like CVs (Hellier 2001, Chapter 3), and easily confused in low-resolution,
classification spectra.
Power-law Index
The second method used is transforming the data into a modified power law plot.
Since the apparent magnitudes of stars do not carry a linear relationship, they were not
subject to a logarithmic application. The plots that I created are apparent magnitude (V)
versus log(rank), where the data points are ranked from brightest (smaller values of V) to
faintest (larger V). The smallest value of V is assigned a rank of 1, the second smallest
value is given a rank of 2, and so on. The x-axis labeled “log(rank)” refers to the log base
10 of these assigned “rank” values. Plotting this relationship provides a linear
relationship with a steep drop off: see Figure 3. The slope of the line is determined and
the drop-off ignored. Since apparent magnitudes are already logarithms, the power-law
index 𝛼 = 1000.2 𝑚, where m is measured slope. This is because a difference of +5
magnitudes corresponds to a ratio of intensity of 100, so that a first-magnitude star (with
V = 1) is 100(1/5) ≈ 2.512 times brighter than a second-magnitude star (with V = 2).
13
Figure 3: Power law analysis of BH Lyn with a slope of 0.2466, corresponding to a
power-law index α = 1.255.
y = 0.2466x + 14.652R² = 0.9423
14
15
16
17
18
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
ud
e)
log(rank)
BH Lyn Power Law
DISCUSSION OF DATA
The slopes of the lines for CVs and the slopes of the lines for non-CVs are
converted to the power-law index. The power-law indices are compared and there is a
distinction. From a sample of 36 known CVs (Table 1), the power-law indices have an
average of 1.46 with a standard deviation of 0.398. For a sample of 37 known non-CVs
(Table 2), power-law indices have an average of 1.05 with a standard deviation of 0.0207.
I was also provided a list of suspected CVs not in the statistically complete
sample of GSL86 (Table 3). Applying this method to these confirms that one of them (PG
2254+075) very probably is a CV and two more are likely to be CVs (PG 0008+186 and
PG 2357+027).
In Table 1 and Table 2, “Address” means equatorial coordinates (right ascension
and declination), in the 1950 coordinates given by GSL86. The histogram standard
deviations from Method 1 are recorded as σ. From Method 2, the coefficient of
correlation for power-law fit is recorded as R2, and the power-law index is recorded as α.
Comments on Non-CVs
Nearly all the non-CVs have power-law indices that are close to 1.0. This is
consistent with noise from atmospheric scintillation and from shot noise, both being
forms of completely random white noise.
Signals with high standard deviations seem to indicate binary star systems with
irradiation variations or other variability. The white dwarf radiates onto the surface of the
secondary star, when that side of the secondary star faces the observer, the apparent
magnitude measurements increase.
PG 0935+087 was classified by Ringwald (1993) as a DO-type white dwarf star.
It has, however, a suspiciously high power-law index, 1.114. PG 0935+087 is a visual
15
Table 1. Known cataclysmic variable stars (CVs) from the statistically complete sample
of the Palomar-Green survey (GSL 86; Ringwald 1993).
Address Name Period (hr) σ (mag) R2
Measured power-
law slopes
α
0027+260 PX And 3.512472 0.178 0.9615 0.285 1.30
0134+070 AY Psc 5.215704 0.719 0.8331 0.556 1.67
0149+137 BG Ari 1.97808 1.16 0.9745 1.164 2.92
0244+104 WX Ari 3.344424 0.721 0.949 0.338 1.37
0808+627 SU UMa 1.8324 0.853 0.901 0.445 1.51
0818+513 BH Lyn 3.741 0.405 0.9423 0.247 1.26
0834+488 EI UMa 6.4344 0.228 0.9717 0.2 1.20
0849+580 BZ UMa 1.63176 0.774 0.9586 0.778 2.05
0858+181 SY Cnc 9.177 0.716 0.945 0.278 1.29
0859+415 BP Lyn 3.667488 0.065 0.9617 0.095 1.09
0911-066 MM Hya 1.38216 0.84 0.9722 0.66 1.84
0917+342 BK Lyn 1.79952 0.585 0.8942 0.383 1.42
0935+075 HM Leo 4.4832 0.368 0.9861 0.407 1.45
0943+521 ER UMa 1.52784 0.82 0.9458 0.751 2.00
0948+344 RZ LMi 1.4016 0.967 0.8088 0.243 1.25
1000+667 LN UMa 3.4656 0.231 0.9756 0.134 1.13
1003+678 CH UMa 8.236416 0.439 0.965 0.424 1.48
1012-029 SW Sex 3.238512 0.413 0.9148 0.199 1.20
1030+590 DW UMa 3.278568 0.291 0.9472 0.443 1.50
1038+155 DO Leo 5.62836 0.657 0.8945 0.21 1.21
1101+453 AN UMa 1.914072 0.457 0.9535 0.455 1.52
1135+036 QZ Vir/T Leo 1.41168 0.995 0.9963 1.046 2.62
1142-041 TW Vir 4.38408 1.104 0.8778 0.393 1.44
1230+226 0.217 0.9307 0.215 1.22
1341-079 HS Vir 1.8456 0.574 0.9267 0.278 1.29
1510+234 NY Ser 2.3472 1.186 0.954 0.113 1.11
1524+622 ES Dra 4.2384 0.388 0.8729 0.409 1.46
1543+145 CT Ser 4.68 0.161 0.957 0.278 1.29
1550+191 MR Ser 1.891152 0.745 0.9141 0.332 1.36
1633+115 V849 Her 3.384 0.219 0.8082 0.11 1.11
1642+253 AH Her 6.194784 0.705 0.956 0.37 1.41
1711+336 V795 Her 2.597928 0.146 0.993 0.251 1.26
1717+413 V825 Her 4.944 0.211 0.9387 0.242 1.25
2133+115 LQ Peg 2.993928 0.274 0.9576 0.134 1.13
2337+300 V378 Peg 3.32592 0.128 0.9856 0.186 1.19
2337+123 HX Peg 4.8192 0.669 0.8544 0.214 1.22
16
Table 2. Known non-CVs from the statistically complete sample of the Palomar-Green
survey (GSL 86), with classifications from the SIMBAD database (Wenger et al. 2020).
Address Name σ (mag) R2
Measured power-law
slopes α Class Comment
0023+298 0.041 0.8734 0.04 1.038 sdOA Hot subdwarf
0048+091 0.0364 0.9701 0.054 1.051 sdB Pulsating
variable star
0051+169 Psc 1 0.0301 0.9126 0.04 1.038 sdB Variable star
0914+120 0.0465 0.9517 0.0534 1.050 sdB Hot subdwarf/
NO HA
0935+087 0.117 0.9593 0.117 1.114 Bin Visual binary
0947+462 Mrk 125 0.0231 0.9307 0.0313 1.029 Gal Galaxy
1002+506 UMa 2 0.0237 0.0241 1.023 Be High-latitude
Be star
1038+270 0.0254 0.9357 0.0301 1.028 HBB High proper-motion star
1104+022 Leo 1 0.0305 0.9654 0.05 1.047 sdB Variable star
1114+187 HK Leo 0.0334 0.9219 0.028 1.026 DA/dM P(orb) = 1.76 d
1119+147 SA79-B1 0.09 0.9648 0.075 1.072 Bin: Hot subdwarf
1128+098 Leo 3 0.0259 0.9476 0.0339 1.032 sdOA Hot subdwarf
1136+581 Mrk 1450 0.08571 0.9632 0.0475 1.045 Gal HII galaxy
1146+228 Leo 4 0.0327 0.9115 0.0303 1.028 sdB-O Hot subdwarf 1155+492 BE UMa 0.662 0.8008 0.0531 1.050 Bin CV progenitor
1156-037 0.0361 0.8927 0.021 1.020 sdB Hot subdwarf
1157+004 Vir 1 0.0423 0.9489 0.0702 1.067 DA White dwarf
1217-067 0.037 0.9317 0.0454 1.043 sdB Star
1257+010 0.0734 0.9395 0.0574 1.054 sdO Hot subdwarf
1314+041 Vir 2 0.0257 0.9328 0.0339 1.032 sdB Binary star
system
1315-123 0.0335 0.9754 0.0596 1.056 sdB Hot subdwarf
1316+678 Dra 1 0.034 0.9262 0.0544 1.051 Bin: DA+dM
1443+337 CBS 200 0.0873 0.921 0.0371 1.035 DA2 Double or
multiple star
1459-026 Lib 1 0.0369 0.9315 0.0583 1.055 sdB Hot subdwarf
1517+265 Ton 228 0.0293 0.9332 0.0417 1.039 Bin Hot subdwarf 1520-050 Lib 2 0.064 0.9574 0.0734 1.070 sdB Hot subdwarf
1522+122 Ser 2 0.0314 0.965 0.0438 1.041 sdB Hot subdwarf
1550+131 NN Ser 0.2817 0.8914 0.098 1.095 Bin CV progenitor
1617+150 Her 1 0.0457 0.8383 0.0254 1.024 sdB Hot subdwarf
candidate
1639+338 Her 3 0.151 0.8973 0.0644 1.061 sdB Hot subdwarf 1657+656 0.0466 0.9633 0.0574 1.054 sdB-O Hot subdwarf
1710+567 0.0745 0.9611 0.0921 1.089 sdB Pulsating hot
subdwarf
1712+493 Her 4 0.0398 0.9321 0.0329 1.031 PNN Planetary
nebula nucleus
2200+085 0.0828 0.906 0.0354 1.033 K Star
2240+193 KQ Peg 0.108 0.971 0.0607 1.057 sdB-O Nova, variable
star
2300+166 Peg 3 0.0759 0.9462 0.0471 1.044 sdOA/Bin: Variable star
2315+071 Psc 2 0.3354 0.8065 0.0429 1.040 Bin Hot subdwarf
17
binary: the high power-law index suggests that the system is a triple, with the hot
component having an unseen cooler companion that shows an irradiation variation.
PG 1710+567 also has a power-law index on the higher end for non-CVs, α=1.09.
Upon further investigation this has been found to be a pulsating hot dwarf, previously
classified as a subdwarf B star and possible CV candidate (GSL 86). Pulsating hot
subdwarf stars are rare, with only about a hundred known (Geier et al. 2017): this
serendipitous discovery that PG 1710+567 is a pulsating subdwarf-B star is therefore
among the more notable results of this thesis.
The highlighted objects in Table 3 (PG 0008+186, PG 2254+075, and PG
2357+027) are found by this research to be likely CVs.
Table 3: Suspected CVs from the Palomar-Green survey (GSL86), but not in the
statistically complete sample.
In Figure 4, notice that the power-law index values for non-CVs fit within roughly
the first five percent of the range of values for CVs. Notice the binning is different in
each histogram. The power-law index for non-CVs range from 1.02 to 1.11, while the
power-law index for CVs range from 1.09 to 2.92. Also, the five greatest power law
indices for CVs correspond to dwarf novae experiencing outbursts during data collection
(BG Ari, MM Hya, BZ UMa, ER UMa, QZ Vir). If these data points are removed, the
histogram to the right in Figure 4 becomes even more uniform and centered around the
average.
Object Location Slope, α R-Squared Std. Dev. Power Law Index
PG 0008+186 0.187 0.9254 0.174 1.187955028 PG 0240+066 0.0739 0.9397 0.427 1.070434259
PG 0248+054 0.0912 0.9495 0.0941 1.087627049
PG 0322+078 0.0452 0.9253 0.046 1.042509449
PG 0947+036 0.0914 0.9683 0.0678 1.087827416
PG 1116+349 0.0279 0.879 0.0255 1.02602986
PG 1200-095 0.0951 0.9764 0.0703 1.091540866
PG 1403-111 0.0752 0.9652 0.0909 1.071716705
PG 2254+075 0.3559 0.9877 0.1907 1.38790583 PG 2357+027 0.1197 0.9803 0.0956 1.11655469
18
Figure 4: Comparison of power-law index for non-CVs (left) and CVs (right).
Figure 5: Comparison of standard deviations in the histograms of non-CVs and CVs.
19
It is possible to determine levels of variation in data sets using standard deviation,
however standard deviation can stem from many different types of variability in the data.
For example, there may be a detached binary star system that is eclipsing such as NN Ser
or HK Leo. Notice that BE UMa has a relatively large standard deviation of 0.662
magnitudes, see Figure 5. This is due to irradiation variation and not flickering as
observed in this research. Irradiation variation occurs when the hot white dwarf of a
binary star system shines upon the Earth-facing side of the secondary star which
energizes that side of the star and emits at a greater magnitude (Russell 1945). In Figure
6, V in BE UMa ranges roughly between 14-16 magnitudes. Measurements of around 14
correlate to when the heated side of the secondary star is facing the observer, while
measurements around 16 correlate to when the non-heated side of the secondary star is
facing the observer. There is also an eclipse shown in the light curve at around V = 19.
Figure 6: Light curve of BE UMa showing irradiation variation and an eclipse
14
15
16
17
18
19
20
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1155+492 (BE UMa)
irradiation variation
eclipse
20
Gathering data from these types of systems would give variable data with a
significant standard deviation like one may find in the data from a CV. The difference is
that the variability given from the power-law index is directly linked to the flickering
nature of CVs and is characteristic of CVs. If one were to analyze a power law
relationship of an eclipsing binary star system, the power-law index would be
significantly lower than that of a CV.
There is useful information other than the slopes of the power law plots. The
overall shape of the graph gives information about the distribution of data, the presence
of an eclipse, possible outbursts, etc. The shapes of some curves inherently have multiple
slopes, this indicates multiple points containing a high density of data, see Figure 7.
Figure 7: Power-law plot of NY Ser where the different slopes show multiple areas of
containing a high density of data, that is, multiple sources of variability
A relationship between the orbital period of a CV and the power-law index was
also investigated. The two values were plotted against each other, as seen in Figure 8.
There does not appear to be any obvious correlation between the orbital period and
power-law index.
y = 0.1129x + 14.667R² = 0.954
y = 1.5095x + 12.401R² = 0.9072
14
15
16
17
18
19
20
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
NY Ser Power Law
21
Figure 8: Analysis of orbital period and power-law index
It is suspected, from identifying the plotted CVs in Figure 8, that there may be a
correlation between the mass transfer rate of an accretion disk onto a white dwarf and the
power-law index found earlier in this work. The next section will investigate this idea.
1
1.5
2
2.5
3
3.5
0 1 2 3 4 5 6 7 8 9 10
Po
we
r-la
w In
de
x
Period (hrs)
Power-law Index vs. Period (CVs)
CALCULATIONS OF DISTANCES, ABSOLUTE MAGNITUDES, LUMINOSITIES, AND MASS-TRANSFER RATES
Distances
Measuring distances of many cataclysmic variables was impossible until the 2018
release of data from Gaia, the space observatory belonging to the European Space
Agency (ESA). Gaia is able to measure parallax angles with unprecedented precision (on
the order of milliarcseconds), thus giving us a way to measure the distances to deep space
objects. The distance in parsecs to an object is calculated by taking the inverse of the
parallax in arcseconds.
Absolute Magnitudes
Once the distance is known, the absolute magnitude can be calculated using the
equation:
𝑴𝒗 = 𝑽 − 𝟓 𝐥𝐨𝐠(𝒅) + 𝟓 − 𝑨𝒗
where:
𝑴𝒗 = absolute magnitdue in the 𝑉 − band (magnitudes)
𝑽 = apparent magnitude in the 𝑉 − band (magnitudes)
𝒅 = distance to the object (in parsecs)
𝑨𝒗 = extinction from interstellar dust (magnitudes)
Apparent magnitude is known from the CRTS, the original survey used in this
research. The distance to the object is calculated using the parallax angle from Gaia. The
extinction from interstellar dust is given in the NASA Extragalactic Database (NED)
(Schlegel, Finkbeiner, and Davis 1998; Schlafly and Finkbeiner 2011). With all of these
known quantities, the absolute magnitude may be calculated using the equation above.
23
Luminosities
Absolute magnitude is related to luminosity by the following equation:
𝑳
𝑳𝑺𝒖𝒏= 𝟐. 𝟓𝟏𝟐(𝟒.𝟖𝟑−𝑴)
where:
𝑳 = luminosity of the observed object (erg/s)
𝑳𝑺𝒖𝒏 = luminosity of the Sun (erg/s)
𝑴𝒗 = absolute magnitude of the observed object in the 𝑉 − band (magnitudes)
The luminosity of the Sun is known (3.846 × 1033erg/s) and its absolute
magnitude MV = 4.83, therefore the luminosity of the observed object can be determined.
Mass Transfer Rates
Hellier (2001) describes a strategy to determine mass transfer rates in CVs by
using the total luminosity of the CV and setting it equal to the rate of change of the
gravitational potential energy of the white dwarf. This gives the following equation:
|�̇�| =𝑮𝑴𝟏�̇�
𝑹𝟏= 𝑳
where:
|�̇�| = gravitational potential energy rate of change of the white dwarf (erg)
𝑮 = the gravitational constant = 6.6743 × 10-8 cm3 g-1 s-2
𝑴𝟏 = mass of the white dwarf (g)
�̇� = mass transfer rate onto the white dwarf (g/s)
𝑹𝟏 = radius of the white dwarf (cm)
𝑳 = total luminosity of the CV (erg/s)
24
Determining the mass and radius of a white dwarf is not trivial. There are,
however, limiting conditions which can guide us to a close approximation. It is known
from the Chandrasekhar limit that the mass of a white dwarf may not exceed 1.44 solar
masses. The lower limit for the mass of a white dwarf is about 0.3 set by stellar evolution
theory. The mass of single, field white dwarfs is strongly peaked at 0.6 solar masses, with
most white dwarfs having masses between 0.5 and 0.7 solar masses (Kepler et al. 2007).
The radius of a white dwarf is dependent of the mass of the white dwarf. Therefore, once
an estimation is made for the mass of the white dwarf, the radius follows.
For now, an estimation will be used for the mass and radius of a white dwarf. The
mass will be approximated as 1 solar mass, which correlates to roughly the radius of the
Earth. With this, all values are known and the mass transfer rate can be approximated.
See Appendix D for the complete data table.
Figure 8 seems to show some inverse relationship between power-law index and
the mass transfer rate of the accretion disk onto the white dwarf. It appears that higher
mass transfer rates occur for those CVs with power law indices around 1.2.
Figure 10 shows that there may be a direct correlation between the period of the
system and the absolute magnitude. As the system gets closer and the orbital period
shortens, it appears that the power output decreases.
Note there are a few points from Figures 9 and 10 that may need to be removed
due to presumed error in measurements. Gaia includes a standard deviation with the data,
and some of them are significant.
25
Figure 9: The relationship between the slope of the power law distribution and the mass
transfer rate in CVs
Figure 10: The relationship between absolute magnitude and period in CVs
EI Uma
BZ UMa
SY Cnc
ER UMaQZ Vir
V795 Her
V825 HerV378 Peg
BG AriMM Hya
CT Ser
0
2E+16
4E+16
6E+16
8E+16
1E+17
1.2E+17
1 1.5 2 2.5 3 3.5
Mas
s Tr
an
sfe
r R
ate
s (g
/sμ
)
Power-law Index
Power Law Index vs. Mass Transfer Rates
y = -0.5648x + 8.4524R² = 0.28413.000
4.000
5.000
6.000
7.000
8.000
9.000
10.000
11.000
12.000
0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000
Ab
solu
te M
agn
itu
de
(Mv)
Period (hrs)
Absolute Magnitude vs. period (CVs)
26
In Figure 11, it appears that the lesser power-law index correlates to a greater
power output from the CV. This could be explained from the theory that the inner part of
the accretion disk is much hotter, therefore is more luminous at higher frequency
wavelengths. High frequency wavelengths correspond to lower values in the power-law
index. The accretion disks that are further away from the white dwarf would be less
luminous and radiate at a lower frequency, this having a higher power-law index. (Pringle
1981)
Figure 11: The relationship between absolute magnitude and power law index in CVs
y = 3.4237x + 1.3765
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
1 1.5 2 2.5 3 3.5
Ab
solu
te M
agn
itu
de
(Mv)
Power-law Index
Absolute Magnitude vs. Power Law Index (CVs)
CONCLUSION
Two methods of data analysis are described in this thesis. Seemingly, the most
useful method of identifying CVs from non-CVs is the determination of the power-law
index from plotting the light signals of stellar objects using a power-law relation. The use
of histograms is also helpful is determining the sources of variability in light curves as
well as visually interpreting the standard deviation from a signal.
Using the methods described above, three stellar objects from the PG Survey (PG
0008+186, PG 2254+075, and PG 2357+027), which have never been confirmed as CVs,
are determined to likely be CVs. A previously misclassified object (PG 0935+087) has
been determined to be a visual binary due to the suspiciously high power-law index.
Another misclassified object (PG 1710+567) has been identified as a pulsating hot
subdwarf due to having a power-law index on the high end for a non-CV. Also, an
empirical relationship between the absolute magnitude and power-law index of CVs has
been discovered through this research.
In the new age of automated telescopes, scientists are tasked with identifying new
objects from terabytes of data, daily. This thesis introduces techniques to quickly and
effectively classify objects based on the analysis of raw synoptic data.
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APPENDICES
APPENDIX A: LIGHT CURVES OF CVS AND NON-CVS
33
14.2
14.4
14.6
14.8
15
15.2
15.4
15.6
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PX And
34
14
14.5
15
15.5
16
16.5
17
17.5
18
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
AY Psc
CSS
MLS
35
12
13
14
15
16
17
18
19
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
WX Ari
CSS
MLS
36
11
11.5
12
12.5
13
13.5
14
14.5
15
15.5
16
53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
SU UMa
37
14.5
15
15.5
16
16.5
17
17.5
18
53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
BH Lyn
38
14
14.2
14.4
14.6
14.8
15
15.2
15.4
53500 54000 54500 55000 55500 56000 56500 57000
app
rox
V. (
mag
nit
ud
es)
MJD
EI UMa
39
10
11
12
13
14
15
16
17
18
53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
BZ UMa
40
10
10.5
11
11.5
12
12.5
13
13.5
14
14.5
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox
V. (
mag
nit
ud
es)
MJD
SY Cnc
CSS
MLS
41
14
14.05
14.1
14.15
14.2
14.25
14.3
14.35
14.4
14.45
53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
BP Lyn
42
13.5
14
14.5
15
15.5
16
16.5
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
BK Lyn
43
12
12.5
13
13.5
14
14.5
15
15.5
16
16.5
53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
ER UMa
44
13
14
15
16
17
18
19
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
RZ LMi
45
15
15.2
15.4
15.6
15.8
16
16.2
53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
LN UMa
46
12
12.5
13
13.5
14
14.5
15
15.5
53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
CH UMa
47
14
14.5
15
15.5
16
16.5
17
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
SW Sex
CSS
SSS
48
13.5
14
14.5
15
15.5
16
53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
DW UMa
49
14
14.5
15
15.5
16
16.5
17
17.5
18
18.5
19
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
DO Leo
50
15
15.5
16
16.5
17
17.5
18
18.5
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
AN UMa
51
10
11
12
13
14
15
16
17
18
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
QZ Vir
52
11
12
13
14
15
16
17
18
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
TW Vir
CSS
MLS
SSS
53
17
17.5
18
18.5
19
19.5
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1230+226
54
13
13.5
14
14.5
15
15.5
16
16.5
17
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
HS Vir
CSS
MLS
SSS
55
14.8
15
15.2
15.4
15.6
15.8
16
16.2
16.4
16.6
16.8
53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
ES Dra
56
14
14.5
15
15.5
16
16.5
17
17.5
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
MR Ser
57
14.5
15
15.5
16
16.5
17
17.5
18
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
V849 Her
CSS
MLS
58
11
11.5
12
12.5
13
13.5
14
14.5
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
AH Her
59
12.4
12.6
12.8
13
13.2
13.4
13.6
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
V795 Her
60
13.4
13.6
13.8
14
14.2
14.4
14.6
14.8
15
15.2
15.4
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
V825 Her
61
14
14.2
14.4
14.6
14.8
15
15.2
15.4
15.6
15.8
16
16.2
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
LQ Peg
62
13.4
13.5
13.6
13.7
13.8
13.9
14
14.1
14.2
14.3
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
V378 Peg
63
12
12.5
13
13.5
14
14.5
15
15.5
16
53000 53500 54000 54500 55000 55500 56000 56500 57000
ap
pro
x. V
(m
agn
itu
de
s)
MJD
HX Peg
64
14
15
16
17
18
19
20
21
22
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
BG Ari
CSS
MLS
65
15
15.5
16
16.5
17
17.5
18
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
HM Leo
66
14
15
16
17
18
19
20
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
NY Ser
67
15.8
16
16.2
16.4
16.6
16.8
17
17.2
17.4
17.6
17.8
18
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
CT Ser
68
14
14.5
15
15.5
16
16.5
17
17.5
53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 0008+186
69
15.6
15.8
16
16.2
16.4
16.6
16.8
17
17.2
17.4
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 0240+066
CSS
MLS
70
14.8
15
15.2
15.4
15.6
15.8
16
16.2
16.4
16.6
16.8
17
53000 53500 54000 54500 55000 55500 56000 56500 57000
ap
pro
x. V
(m
agn
itu
de
s)
MJD
PG 0248+054
71
14.6
14.8
15
15.2
15.4
15.6
15.8
16
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 0322+078
72
16.8
16.9
17
17.1
17.2
17.3
17.4
17.5
17.6
17.7
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 0947+036
73
13.3
13.35
13.4
13.45
13.5
13.55
13.6
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1116+349
74
16
16.2
16.4
16.6
16.8
17
17.2
17.4
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1200-095
CSS
SSS
75
14.4
14.6
14.8
15
15.2
15.4
15.6
15.8
16
16.2
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1403-111
CSS
MLS
SSS
76
15.5
16
16.5
17
17.5
18
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 2254+075
77
15.9
16
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 2357+027
CSS
MLS
78
15
15.05
15.1
15.15
15.2
15.25
15.3
15.35
15.4
15.45
15.5
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 0023+298
79
13.7
13.8
13.9
14
14.1
14.2
14.3
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 0048+091
CSS
MLS
80
15.5
15.6
15.7
15.8
15.9
16
16.1
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 0051+169
81
15.9
16
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 0914+120
CSS
MLS
82
15
15.5
16
16.5
17
17.5
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 0935+087
CSS
MLS
83
14.55
14.6
14.65
14.7
14.75
14.8
14.85
14.9
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 0947+462
84
14.98
15
15.02
15.04
15.06
15.08
15.1
15.12
15.14
15.16
15.18
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1002+506
85
15.2
15.25
15.3
15.35
15.4
15.45
15.5
15.55
15.6
15.65
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1038+270
86
14.6
14.65
14.7
14.75
14.8
14.85
14.9
14.95
15
15.05
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1104+022
CSS
MLS
87
14.6
14.62
14.64
14.66
14.68
14.7
14.72
14.74
14.76
14.78
14.8
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1114+187
88
15.6
15.7
15.8
15.9
16
16.1
16.2
16.3
16.4
16.5
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1119+147
CSS
MLS
89
13.95
14
14.05
14.1
14.15
14.2
14.25
14.3
14.35
14.4
14.45
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1128+098
CSS
MLS
90
15.2
15.4
15.6
15.8
16
16.2
16.4
53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1136+581
91
14.8
14.85
14.9
14.95
15
15.05
15.1
15.15
15.2
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1146+228
92
14
15
16
17
18
19
20
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1155+492
93
13.36
13.38
13.4
13.42
13.44
13.46
13.48
13.5
13.52
13.54
13.56
53000 53500 54000 54500 55000 55500 56000 56500 57000
ap
pro
x. V
(m
agn
itu
de
s)
MJD
PG 1156-037
CSS
MLS
94
15.4
15.5
15.6
15.7
15.8
15.9
16
16.1
16.2
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1157+004
95
15.05
15.1
15.15
15.2
15.25
15.3
15.35
15.4
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1217-067
CSS
MLS
SSS
96
14.8
15
15.2
15.4
15.6
15.8
16
16.2
16.4
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1257+010
CSS
MLS
97
15.7
15.72
15.74
15.76
15.78
15.8
15.82
15.84
15.86
15.88
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1314+041
CSS
MLS
98
14.9
14.95
15
15.05
15.1
15.15
15.2
15.25
15.3
15.35
15.4
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1315-123
CSS
MLS
SSS
99
15.8
15.85
15.9
15.95
16
16.05
53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1316+678
100
15.65
15.7
15.75
15.8
15.85
15.9
15.95
16
16.05
16.1
16.15
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1443+337
101
14.55
14.6
14.65
14.7
14.75
14.8
14.85
14.9
14.95
15
53000 53500 54000 54500 55000 55500 56000 56500 57000
ap
pro
x. V
(m
agn
itu
de
s)
MJD
PG 1459-026
CSS
MLS
102
15.7
15.75
15.8
15.85
15.9
15.95
16
16.05
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1517+265
103
14.9
15
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1520-050
CSS
MLS
SSS
104
16
16.05
16.1
16.15
16.2
16.25
16.3
16.35
16.4
16.45
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1522+122
105
15.5
16
16.5
17
17.5
18
18.5
19
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1550+131
106
14.5
14.6
14.7
14.8
14.9
15
15.1
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1617+150
CSS
MLS
107
12
12.5
13
13.5
14
14.5
15
15.5
16
16.5
53000 53500 54000 54500 55000 55500 56000 56500 57000
ap
pro
x. V
(m
agn
itu
de
s)
MJD
PG 1639+338
108
16
16.05
16.1
16.15
16.2
16.25
16.3
16.35
16.4
16.45
16.5
16.55
53500 54000 54500 55000 55500 56000 56500 57000
ap
pro
x. V
(m
agn
itu
de
s)
MJD
PG 1657+656
109
14.6
14.7
14.8
14.9
15
15.1
15.2
15.3
15.4
53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1710+567
110
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 1712+493
111
13.4
13.6
13.8
14
14.2
14.4
14.6
14.8
15
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 2200+085
112
15.5
16
16.5
17
17.5
18
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 2240+193
113
12
12.2
12.4
12.6
12.8
13
13.2
13.4
13.6
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
ud
es)
MJD
PG 2300+166
114
12
13
14
15
16
17
18
19
53000 53500 54000 54500 55000 55500 56000 56500 57000
app
rox.
V (
mag
nit
du
es)
MJD
PG 2315+071
APPENDIX B: HISTOGRAMS OF CVS AND NON-CVS
116
0
2
4
6
8
10
12
14
16
18
14.3
2
14.3
5
14.3
8
14.4
1
14.4
4
14.4
7
14.
5
14.5
3
14.5
6
14.5
9
14.6
2
14.6
5
14.6
8
14.7
1
14.7
4
14.7
7
14.
8
14.8
3
14.8
6
14.8
9
14.9
2
14.9
5
14.9
8
15.0
1
15.0
4
15.0
7
15.
1
15.1
3
15.1
6
15.1
9
15.2
2
15.2
5
15.2
8
15.3
1
15.3
4
15.3
7
15.
4
15.4
3
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PX And Histogram
117
0
1
2
3
4
5
6
7
8
914
.35
14.4
2
14.4
9
14.5
6
14.6
3
14.7
14.7
7
14.8
4
14.9
1
14.9
8
15.0
5
15.1
2
15.1
9
15.2
6
15.3
3
15.4
15.4
7
15.5
4
15.6
1
15.6
8
15.7
5
15.8
2
15.8
9
15.9
6
16.0
3
16.1
16.1
7
16.2
4
16.3
1
16.3
8
16.4
5
16.5
2
16.5
9
16.6
6
16.7
3
16.8
16.8
7
16.9
4
17.0
1
17.0
8
17.1
5
17.2
2
17.2
9
17.3
6
17.4
3
17.5
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
AY Psc Histogram
118
0
2
4
6
8
10
12
1414
.33
14.4
1
14.4
9
14.5
7
14.6
5
14.7
3
14.8
1
14.8
9
14.9
7
15.0
5
15.1
3
15.2
1
15.2
9
15.3
7
15.4
5
15.5
3
15.6
1
15.6
9
15.7
7
15.8
5
15.9
3
16.0
1
16.0
9
16.1
7
16.2
5
16.3
3
16.4
1
16.4
9
16.5
7
16.6
5
16.7
3
16.8
1
16.8
9
16.9
7
17.0
5
17.1
3
17.2
1
17.2
9
17.3
7
17.4
5
17.5
3
17.6
1
17.6
9
17.7
7
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
WX Ari Histogram
119
0
0.5
1
1.5
2
2.5
3
3.5
4
4.512
.14
12.2
2
12.3
12.3
8
12.4
6
12.5
4
12.6
2
12.7
12.7
8
12.8
6
12.9
4
13.0
2
13.1
13.1
8
13.2
6
13.3
4
13.4
2
13.5
13.5
8
13.6
6
13.7
4
13.8
2
13.9
13.9
8
14.0
6
14.1
4
14.2
2
14.3
14.3
8
14.4
6
14.5
4
14.6
2
14.7
14.7
8
14.8
6
14.9
4
15.0
2
15.1
15.1
8
15.2
6
15.3
4
15.4
2
15.5
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data pointa (magnitudes)
SU UMa Histogram
120
0
1
2
3
4
5
6
7
81
4.7
4
14
.81
14
.88
14
.95
15
.02
15
.09
15
.16
15
.23
15.3
15
.37
15
.44
15
.51
15
.58
15
.65
15
.72
15
.79
15
.86
15
.93
16
16
.07
16
.14
16
.21
16
.28
16
.35
16
.42
16
.49
16
.56
16
.63
16.7
16
.77
16
.84
16
.91
16
.98
17
.05
17
.12
17
.19
17
.26
17
.33
17.4
17
.47
17
.54
17
.61
17
.68
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
BH Lyn Histogram
121
0
2
4
6
8
10
12
14
14.0
8
14.1
1
14.1
4
14.1
7
14.2
14.2
3
14.2
6
14.2
9
14.3
2
14.3
5
14.3
8
14.4
1
14.4
4
14.4
7
14.5
14.5
3
14.5
6
14.5
9
14.6
2
14.6
5
14.6
8
14.7
1
14.7
4
14.7
7
14.8
14.8
3
14.8
6
14.8
9
14.9
2
14.9
5
14.9
8
15.0
1
15.0
4
15.0
7
15.1
15.1
3
15.1
6
15.1
9
Mo
re
Fre
qu
en
cy o
f d
ata
po
ints
approx. V data points (magnitudes)
EI UMa Histogram
122
0
1
2
3
4
5
6
7
811
.36
11.4
8
11.6
11.7
2
11.8
4
11.9
6
12.0
812
.2
12.3
2
12.4
4
12.5
6
12.6
8
12.8
12.9
2
13.0
4
13.1
6
13.2
8
13.4
13.5
2
13.6
4
13.7
6
13.8
8
14
14.1
2
14.2
4
14.3
6
14.4
8
14.6
14.7
2
14.8
4
14.9
6
15.0
8
15.2
15.3
2
15.4
4
15.5
6
15.6
8
15.8
15.9
2
16.0
4
16.1
6
16.2
8
16.4
16.5
2
16.6
4
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
BZ UMa Hstogram
123
0
2
4
6
8
10
12
14
10.6
1
10.6
9
10.7
7
10.8
5
10.9
3
11.0
1
11.0
9
11.1
7
11.2
5
11.3
3
11.4
1
11.4
9
11.5
7
11.6
5
11.7
3
11.8
1
11.8
9
11.9
7
12.0
5
12.1
3
12.2
1
12.2
9
12.3
7
12.4
5
12.5
3
12.6
1
12.6
9
12.7
7
12.8
5
12.9
3
13.0
1
13.0
9
13.1
7
13.2
5
13.3
3
13.4
1
13.4
9
13.5
7
13.6
5
13.7
3
13.8
1
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
SY Cnc Histogram
124
0
5
10
15
20
25
30
14
.05
14
.06
14
.07
14
.08
14
.09
14.1
14
.11
14
.12
14
.13
14
.14
14
.15
14
.16
14
.17
14
.18
14
.19
14.2
14
.21
14
.22
14
.23
14
.24
14
.25
14
.26
14
.27
14
.28
14
.29
14.3
14
.31
14
.32
14
.33
14
.34
14
.35
14
.36
14
.37
14
.38
14
.39
14.4
14
.41
14
.42
14
.43
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
BP Lyn Histogram
125
0
1
2
3
4
5
6
7
813
.79
13.8
5
13.9
1
13.9
7
14.0
3
14.0
9
14.1
5
14.2
1
14.2
7
14.3
3
14.3
9
14.4
5
14.5
1
14.5
7
14.6
3
14.6
9
14.7
5
14.8
1
14.8
7
14.9
3
14.9
9
15.0
5
15.1
1
15.1
7
15.2
3
15.2
9
15.3
5
15.4
1
15.4
7
15.5
3
15.5
9
15.6
5
15.7
1
15.7
7
15.8
3
15.8
9
15.9
5
16.0
1
16.0
7
16.1
3
16.1
9
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
BK Lyn Histogram
126
0
1
2
3
4
5
6
7
8
912
.63
12.7
1
12.7
9
12.8
7
12.9
5
13.0
3
13.1
1
13.1
9
13.2
7
13.3
5
13.4
3
13.5
1
13.5
9
13.6
7
13.7
5
13.8
3
13.9
1
13.9
9
14.0
7
14.1
5
14.2
3
14.3
1
14.3
9
14.4
7
14.5
5
14.6
3
14.7
1
14.7
9
14.8
7
14.9
5
15.0
3
15.1
1
15.1
9
15.2
7
15.3
5
15.4
3
15.5
1
15.5
9
15.6
7
15.7
5
15.8
3
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
ER UMa Histogram
127
0
1
2
3
4
5
6
7
8
914
.21
14.2
914
.37
14.4
514
.53
14.6
114
.69
14.7
714
.85
14.9
315
.01
15.0
915
.17
15.2
515
.33
15.4
115
.49
15.5
715
.65
15.7
315
.81
15.8
915
.97
16.0
516
.13
16.2
116
.29
16.3
716
.45
16.5
316
.61
16.6
916
.77
16.8
516
.93
17.0
117
.09
17.1
717
.25
17.3
317
.41
17.4
917
.57
17.6
517
.73
17.8
1
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
RZ LMi Histogram
128
0
1
2
3
4
5
6
7
8
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
LN UMa Histogram
129
0
1
2
3
4
5
6
7
812
.61
12.6
7
12.7
3
12.7
9
12.8
5
12.9
1
12.9
7
13.0
3
13.0
9
13.1
5
13.2
1
13.2
7
13.3
3
13.3
9
13.4
5
13.5
1
13.5
7
13.6
3
13.6
9
13.7
5
13.8
1
13.8
7
13.9
3
13.9
9
14.0
5
14.1
1
14.1
7
14.2
3
14.2
9
14.3
5
14.4
1
14.4
7
14.5
3
14.5
9
14.6
5
14.7
1
14.7
7
14.8
3
14.8
9
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
CH UMa Histogram
130
0
2
4
6
8
10
12
14
16
14.2
914
.34
14.3
914
.44
14.4
914
.54
14.5
914
.64
14.6
914
.74
14.7
914
.84
14.8
914
.94
14.9
915
.04
15.0
915
.14
15.1
915
.24
15.2
915
.34
15.3
915
.44
15.4
915
.54
15.5
915
.64
15.6
915
.74
15.7
915
.84
15.8
915
.94
15.9
916
.04
16.0
916
.14
16.1
916
.24
16.2
916
.34
16.3
916
.44
16.4
9M
ore
Fre
qu
en
cy o
f d
ata
po
ints
approx. V data points (magnitudes)
SW Sex Histogram
131
0
1
2
3
4
5
6
713
.66
13.7
1
13.7
6
13.8
1
13.8
6
13.9
1
13.9
6
14.0
1
14.0
6
14.1
1
14.1
6
14.2
1
14.2
6
14.3
1
14.3
6
14.4
1
14.4
6
14.5
1
14.5
6
14.6
1
14.6
6
14.7
1
14.7
6
14.8
1
14.8
6
14.9
1
14.9
6
15.0
1
15.0
6
15.1
1
15.1
6
15.2
1
15.2
6
15.3
1
15.3
6
15.4
1
15.4
6
15.5
1
15.5
6
Fre
qu
en
cy o
f d
ata
po
ints
approx. V data points (magnitudes)
DW UMa Histogram
132
0
1
2
3
4
5
6
7
8
9
10
15.3
7
15.4
4
15.5
1
15.5
8
15.6
5
15.7
2
15.7
9
15.8
6
15.9
3
16
16.0
7
16.1
4
16.2
1
16.2
8
16.3
5
16.4
2
16.4
9
16.5
6
16.6
3
16
.7
16.7
7
16.8
4
16.9
1
16.9
8
17.0
5
17.1
2
17.1
9
17.2
6
17.3
3
17
.4
17.4
7
17.5
4
17.6
1
17.6
8
17.7
5
17.8
2
17.8
9
17.9
6
18.0
3
18
.1
18.1
7
18.2
4
18.3
1
18.3
8
18.4
5
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
DO Leo Histogram
133
0
1
2
3
4
5
6
715
.45
15.5
1
15.5
7
15.6
3
15.6
9
15.7
5
15.8
1
15.8
7
15.9
3
15.9
9
16.0
5
16.1
1
16.1
7
16.2
3
16.2
9
16.3
5
16.4
1
16.4
7
16.5
3
16.5
9
16.6
5
16.7
1
16.7
7
16.8
3
16.8
9
16.9
5
17.0
1
17.0
7
17.1
3
17.1
9
17.2
5
17.3
1
17.3
7
17.4
3
17.4
9
17.5
5
17.6
1
17.6
7
17.7
3
17.7
9
17.8
5
17.9
1
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
AN UMa Histogram
134
0
1
2
3
4
5
6
7
8
9
10
10
.67
10
.81
10
.95
11
.09
11
.23
11
.37
11
.51
11
.65
11
.79
11
.93
12
.07
12
.21
12
.35
12
.49
12
.63
12
.77
12
.91
13
.05
13
.19
13
.33
13
.47
13
.61
13
.75
13
.89
14
.03
14
.17
14
.31
14
.45
14
.59
14
.73
14
.87
15
.01
15
.15
15
.29
15
.43
15
.57
15
.71
15
.85
15
.99
16
.13
16
.27
16
.41
16
.55
16
.69
16
.83
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (mangitudes)
QZ Vir Histogram
135
0
1
2
3
4
5
6
7
812
.27
12.3
8
12.4
9
12.6
12.7
1
12.8
2
12.9
3
13.0
4
13.1
5
13.2
6
13.3
7
13.4
8
13.5
9
13.7
13.8
1
13.9
2
14.0
3
14.1
4
14.2
5
14.3
6
14.4
7
14.5
8
14.6
9
14.8
14.9
1
15.0
2
15.1
3
15.2
4
15.3
5
15.4
6
15.5
7
15.6
8
15.7
9
15.9
16.0
1
16.1
2
16.2
3
16.3
4
16.4
5
16.5
6
16.6
7
16.7
8
16.8
9
17
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
TW Vir Histogram
136
0
2
4
6
8
10
12
1417
.37
17.4
2
17.4
7
17.5
2
17.5
7
17.6
2
17.6
7
17.7
2
17.7
7
17.8
2
17.8
7
17.9
2
17.9
7
18.0
2
18.0
7
18.1
2
18.1
7
18.2
2
18.2
7
18.3
2
18.3
7
18.4
2
18.4
7
18.5
2
18.5
7
18.6
2
18.6
7
18.7
2
18.7
7
18.8
2
18.8
7
18.9
2
18.9
7
19.0
2
19.0
7
19.1
2
19.1
7
19.2
2
19.2
7
19.3
2
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1230+226 Histogram
137
0
2
4
6
8
10
12
13.3
4
13.4
2
13.5
13.5
8
13.6
6
13.7
4
13.8
2
13.9
13.9
8
14.0
6
14.1
4
14.2
2
14.3
14.3
8
14.4
6
14.5
4
14.6
2
14.7
14.7
8
14.8
6
14.9
4
15.0
2
15.1
15.1
8
15.2
6
15.3
4
15.4
2
15.5
15.5
8
15.6
6
15.7
4
15.8
2
15.9
15.9
8
16.0
6
16.1
4
16.2
2
16.3
16.3
8
16.4
6
16.5
4
16.6
2
16.7
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
HS Vir Histogram
138
0
1
2
3
4
5
614
.91
14.9
5
14.9
9
15.0
3
15.0
7
15.1
1
15.1
5
15.1
9
15.2
3
15.2
7
15.3
1
15.3
5
15.3
9
15.4
3
15.4
7
15.5
1
15.5
5
15.5
9
15.6
3
15.6
7
15.7
1
15.7
5
15.7
9
15.8
3
15.8
7
15.9
1
15.9
5
15.9
9
16.0
3
16.0
7
16.1
1
16.1
5
16.1
9
16.2
3
16.2
7
16.3
1
16.3
5
16.3
9
16.4
3
16.4
7
16.5
1
16.5
5
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
ES Dra Histogram
139
0
1
2
3
4
5
6
7
8
914
.62
14.6
8
14.7
4
14.8
14.8
6
14.9
2
14.9
8
15.0
4
15.1
15.1
6
15.2
2
15.2
8
15.3
4
15.4
15.4
6
15.5
2
15.5
8
15.6
4
15.7
15.7
6
15.8
2
15.8
8
15.9
4
16
16.0
6
16.1
2
16.1
8
16.2
4
16.3
16.3
6
16.4
2
16.4
8
16.5
4
16.6
16.6
6
16.7
2
16.7
8
16.8
4
16.9
16.9
6
17.0
2
17.0
8
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
MR Ser Histogram
140
0
2
4
6
8
10
12
14
16
18
15.0
415
.115
.16
15.2
215
.28
15.3
415
.415
.46
15.5
215
.58
15.6
415
.715
.76
15.8
215
.88
15.9
416
16.0
616
.12
16.1
816
.24
16.3
16.3
616
.42
16.4
816
.54
16.6
16.6
616
.72
16.7
816
.84
16.9
16.9
617
.02
17.0
817
.14
17.2
17.2
617
.32
17.3
817
.44
17.5
17.5
617
.62
17.6
817
.74
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
V849 Her Histogram
141
0
1
2
3
4
5
6
7
811
.37
11.4
3
11.4
9
11.5
5
11.6
1
11.6
7
11.7
3
11.7
9
11.8
5
11.9
1
11.9
7
12.0
3
12.0
9
12.1
5
12.2
1
12.2
7
12.3
3
12.3
9
12.4
5
12.5
1
12.5
7
12.6
3
12.6
9
12.7
5
12.8
1
12.8
7
12.9
3
12.9
9
13.0
5
13.1
1
13.1
7
13.2
3
13.2
9
13.3
5
13.4
1
13.4
7
13.5
3
13.5
9
13.6
5
13.7
1
13.7
7
13.8
3
13.8
9
13.9
5
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
AH Her Histogram
142
0
2
4
6
8
10
12
14
16
18
12.5
2
12.5
5
12.5
8
12.6
1
12.6
4
12.6
7
12.7
12.7
3
12.7
6
12.7
9
12.8
2
12.8
5
12.8
8
12.9
1
12.9
4
12.9
7
13
13.0
3
13.0
6
13.0
9
13.1
2
13.1
5
13.1
8
13.2
1
13.2
4
13.2
7
13.3
13.3
3
13.3
6
13.3
9
13.4
2
13.4
5
13.4
8
Fre
qu
en
cy o
f d
ata
po
ints
approx. V data points (magnitudes)
V795 Her Histogram
143
0
2
4
6
8
10
12
14
16
18
13.5
9
13.6
3
13.6
7
13.7
1
13.7
5
13.7
9
13.8
3
13.8
7
13.9
1
13.9
5
13.9
9
14.0
3
14.0
7
14.1
1
14.1
5
14.1
9
14.2
3
14.2
7
14.3
1
14.3
5
14.3
9
14.4
3
14.4
7
14.5
1
14.5
5
14.5
9
14.6
3
14.6
7
14.7
1
14.7
5
14.7
9
14.8
3
14.8
7
14.9
1
14.9
5
14.9
9
15.0
3
15.0
7
15.1
1
15.1
5
15.1
9
15.2
3
15.2
7
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
V825 Her Histogram
144
0
2
4
6
8
10
12
14
16
18
20
14.2
8
14.3
2
14.3
6
14.4
14.4
4
14.4
8
14.5
2
14.5
6
14.6
14.6
4
14.6
8
14.7
2
14.7
6
14.8
14.8
4
14.8
8
14.9
2
14.9
6
15
15.0
4
15.0
8
15.1
2
15.1
6
15.2
15.2
4
15.2
8
15.3
2
15.3
6
15.4
15.4
4
15.4
8
15.5
2
15.5
6
15.6
15.6
4
15.6
8
15.7
2
15.7
6
15.8
15.8
4
15.8
8
15.9
2
15.9
6
16
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
LQ Peg Histogram
145
0
2
4
6
8
10
12
14
16
13.5
2
13.5
4
13.5
6
13.5
8
13.6
13.6
2
13.6
4
13.6
6
13.6
8
13.7
13.7
2
13.7
4
13.7
6
13.7
8
13.8
13.8
2
13.8
4
13.8
6
13.8
8
13.9
13.9
2
13.9
4
13.9
6
13.9
8
14
14.0
2
14.0
4
14.0
6
14.0
8
14.1
14.1
2
14.1
4
14.1
6
14.1
8
14.2
14.2
2
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
V378 Peg Histogram
146
0
1
2
3
4
5
6
7
81
2.6
91
2.7
51
2.8
11
2.8
71
2.9
31
2.9
91
3.0
51
3.1
11
3.1
71
3.2
31
3.2
91
3.3
51
3.4
11
3.4
71
3.5
31
3.5
91
3.6
51
3.7
11
3.7
71
3.8
31
3.8
91
3.9
51
4.0
11
4.0
71
4.1
31
4.1
91
4.2
51
4.3
11
4.3
71
4.4
31
4.4
91
4.5
51
4.6
11
4.6
71
4.7
31
4.7
91
4.8
51
4.9
11
4.9
71
5.0
31
5.0
91
5.1
51
5.2
11
5.2
71
5.3
31
5.3
9
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
HX Peg Histogram
147
0
1
2
3
4
5
6
7
814
.64
14.7
9
14.9
4
15.0
9
15.2
4
15.3
9
15.5
4
15.6
9
15.8
4
15.9
9
16.1
4
16.2
9
16.4
4
16.5
9
16.7
4
16.8
9
17.0
4
17.1
9
17.3
4
17.4
9
17.6
4
17.7
9
17.9
4
18.0
9
18.2
4
18.3
9
18.5
4
18.6
9
18.8
4
18.9
9
19.1
4
19.2
9
19.4
4
19.5
9
19.7
4
19.8
9
20.0
4
20.1
9
20.3
4
20.4
9
20.6
4
20.7
9
20.9
4
21.0
9
21.2
4
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
BG Ari Histogram
148
0
1
2
3
4
5
6
7
8
913
.58
13.7
2
13.8
6
14
14.1
4
14.2
8
14.4
2
14.5
6
14.7
14.8
4
14.9
8
15.1
2
15.2
6
15.4
15.5
4
15.6
8
15.8
2
15.9
6
16.1
16.2
4
16.3
8
16.5
2
16.6
6
16.8
16.9
4
17.0
8
17.2
2
17.3
6
17.5
17.6
4
17.7
8
17.9
2
18.0
6
18.2
18.3
4
18.4
8
18.6
2
18.7
6
18.9
19.0
4
19.1
8
19.3
2
19.4
6
19.6
19.7
4
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
MM Hya Histogram
149
0
2
4
6
8
10
1215
.32
15.3
8
15.4
4
15.5
15.5
6
15.6
2
15.6
8
15.7
4
15.8
15.8
6
15.9
2
15.9
8
16.0
4
16.1
16.1
6
16.2
2
16.2
8
16.3
4
16.4
16.4
6
16.5
2
16.5
8
16.6
4
16.7
16.7
6
16.8
2
16.8
8
16.9
4
17
17.0
6
17.1
2
17.1
8
17.2
4
17.3
17.3
6
17.4
2
17.4
8
17.5
4
17.6
17.6
6
17.7
2
17.7
8
17.8
4
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
HM Leo Histogram
150
0
1
2
3
4
5
6
714
.7
14.8
14.9 15
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9 16
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9 17
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9 18
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18.8
18.9
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
NY Ser Histogram
151
0
2
4
6
8
10
12
14
16
18
16.0
7
16.1
1
16.1
5
16.1
9
16.2
3
16.2
7
16.3
1
16.3
5
16.3
9
16.4
3
16.4
7
16.5
1
16.5
5
16.5
9
16.6
3
16.6
7
16.7
1
16.7
5
16.7
9
16.8
3
16.8
7
16.9
1
16.9
5
16.9
9
17.0
3
17.0
7
17.1
1
17.1
5
17.1
9
17.2
3
17.2
7
17.3
1
17.3
5
17.3
9
17.4
3
17.4
7
17.5
1
17.5
5
17.5
9
17.6
3
17.6
7
17.7
1
17.7
5
17.7
9
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
CT Ser Histogram
152
0
10
20
30
40
50
60
14.4
314
.49
14.5
514
.61
14.6
714
.73
14.7
914
.85
14.9
114
.97
15.0
315
.09
15.1
515
.21
15.2
715
.33
15.3
915
.45
15.5
115
.57
15.6
315
.69
15.7
515
.81
15.8
715
.93
15.9
916
.05
16.1
116
.17
16.2
316
.29
16.3
516
.41
16.4
716
.53
16.5
916
.65
16.7
116
.77
16.8
316
.89
16.9
517
.01
17.0
717
.13
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 0008+186 Histogram
153
0
5
10
15
20
25
30
35
40
45
5015
.71
15.7
5
15.7
9
15.8
3
15.8
7
15.9
1
15.9
5
15.9
9
16.0
3
16.0
7
16.1
1
16.1
5
16.1
9
16.2
3
16.2
7
16.3
1
16.3
5
16.3
9
16.4
3
16.4
7
16.5
1
16.5
5
16.5
9
16.6
3
16.6
7
16.7
1
16.7
5
16.7
9
16.8
3
16.8
7
16.9
1
16.9
5
16.9
9
17.0
3
17.0
7
17.1
1
17.1
5
17.1
9
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 0240+066 Histogram
154
0
5
10
15
20
25
30
35
40
15.0
4
15.0
8
15.1
2
15.1
6
15.2
15.2
4
15.2
8
15.3
2
15.3
6
15.4
15.4
4
15.4
8
15.5
2
15.5
6
15.6
15.6
4
15.6
8
15.7
2
15.7
6
15.8
15.8
4
15.8
8
15.9
2
15.9
6
16
16.0
4
16.0
8
16.1
2
16.1
6
16.2
16.2
4
16.2
8
16.3
2
16.3
6
16.4
16.4
4
16.4
8
16.5
2
16.5
6
16.6
16.6
4
16.6
8
16.7
2
16.7
6
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 0248+054 Histogram
155
0
10
20
30
40
50
60
70
8014
.79
14.8
2
14.8
5
14.8
8
14.9
1
14.9
4
14.9
7
15
15.0
3
15.0
6
15.0
9
15.1
2
15.1
5
15.1
8
15.2
1
15.2
4
15.2
7
15.3
15.3
3
15.3
6
15.3
9
15.4
2
15.4
5
15.4
8
15.5
1
15.5
4
15.5
7
15.6
15.6
3
15.6
6
15.6
9
15.7
2
15.7
5
15.7
8
15.8
1
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 0322+078 Histogram
156
0
5
10
15
20
25
30
35
40
16
.9
16.9
2
16.9
4
16.9
6
16.9
8
17
17.0
2
17.0
4
17.0
6
17.0
8
17
.1
17.1
2
17.1
4
17.1
6
17.1
8
17
.2
17.2
2
17.2
4
17.2
6
17.2
8
17
.3
17.3
2
17.3
4
17.3
6
17.3
8
17
.4
17.4
2
17.4
4
17.4
6
17.4
8
17
.5
17.5
2
17.5
4
17.5
6
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 0947+036 Histogram
157
0
10
20
30
40
50
60
70
80
13.35 13.36 13.37 13.38 13.39 13.4 13.41 13.42 13.43 13.44 13.45 13.46 13.47 13.48 13.49 13.5 13.51 13.52 13.53 13.54 13.55 13.56 More
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1116+349 Histogram
158
0
5
10
15
20
25
30
35
40
4516
.15
16.1
8
16.2
1
16.2
4
16.2
7
16.3
16.3
3
16.3
6
16.3
9
16.4
2
16.4
5
16.4
8
16.5
1
16.5
4
16.5
7
16.6
16.6
3
16.6
6
16.6
9
16.7
2
16.7
5
16.7
8
16.8
1
16.8
4
16.8
7
16.9
16.9
3
16.9
6
16.9
9
17.0
2
17.0
5
17.0
8
17.1
1
17.1
4
17.1
7
17.2
17.2
3
17.2
6
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1200-095 Histogram
159
0
5
10
15
20
25
30
35
40
45
50
14.5
4
14.5
8
14.6
2
14.6
6
14.7
14.7
4
14.7
8
14.8
2
14.8
6
14.9
14.9
4
14.9
8
15.0
2
15.0
6
15.1
15.1
4
15.1
8
15.2
2
15.2
6
15.3
15.3
4
15.3
8
15.4
2
15.4
6
15.5
15.5
4
15.5
8
15.6
2
15.6
6
15.7
15.7
4
15.7
8
15.8
2
15.8
6
15.9
15.9
4
15.9
8
16.0
2
16.0
6
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1403-111 Histogram
160
0
2
4
6
8
10
12
14
16
18
15.6
8
15.7
3
15.7
8
15.8
3
15.8
8
15.9
3
15.9
8
16.0
3
16.0
8
16.1
3
16.1
8
16.2
3
16.2
8
16.3
3
16.3
8
16.4
3
16.4
8
16.5
3
16.5
8
16.6
3
16.6
8
16.7
3
16.7
8
16.8
3
16.8
8
16.9
3
16.9
8
17.0
3
17.0
8
17.1
3
17.1
8
17.2
3
17.2
8
17.3
3
17.3
8
17.4
3
17.4
8
17.5
3
17.5
8
17.6
3
17.6
8
17.7
3
17.7
8
17.8
3
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 2254+075 Histogram
161
0
5
10
15
20
25
30
16
16.0
2
16.0
4
16.0
6
16.0
8
16.1
16.1
2
16.1
4
16.1
6
16.1
8
16.2
16.2
2
16.2
4
16.2
6
16.2
8
16.3
16.3
2
16.3
4
16.3
6
16.3
8
16.4
16.4
2
16.4
4
16.4
6
16.4
8
16.5
16.5
2
16.5
4
16.5
6
16.5
8
16.6
16.6
2
16.6
4
16.6
6
16.6
8
16.7
16.7
2
16.7
4
16.7
6
16.7
8
16.8
16.8
2
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 2357+027 Histogram
162
0
10
20
30
40
50
60
15.0
3
15.0
4
15.0
5
15.0
6
15.0
7
15.0
8
15.0
9
15
.1
15.1
1
15.1
2
15.1
3
15.1
4
15.1
5
15.1
6
15.1
7
15.1
8
15.1
9
15
.2
15.2
1
15.2
2
15.2
3
15.2
4
15.2
5
15.2
6
15.2
7
15.2
8
15.2
9
15
.3
15.3
1
15.3
2
15.3
3
15.3
4
15.3
5
15.3
6
15.3
7
15.3
8
15.3
9
15
.4
15.4
1
15.4
2
15.4
3
15.4
4
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 0023+298 Histogram
163
0
10
20
30
40
50
60
70
80
90
100
Fre
qu
en
cy o
f d
ata
po
ints
approx. V data points (magnitudes)
PG 0048+091 Histogram
164
0
10
20
30
40
50
60
70
80
15.5615.58 15.6 15.6215.6415.6615.68 15.7 15.7215.7415.7615.78 15.8 15.8215.8415.8615.88 15.9 15.9215.9415.9615.98 16 16.02More
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 0051+169 Histogram
165
0
20
40
60
80
100
120
16.0
2
16.0
4
16.0
6
16.0
8
16.1
16.1
2
16.1
4
16.1
6
16.1
8
16.2
16.2
2
16.2
4
16.2
6
16.2
8
16.3
16.3
2
16.3
4
16.3
6
16.3
8
16.4
16.4
2
16.4
4
16.4
6
16.4
8
16.5
16.5
2
16.5
4
16.5
6
16.5
8
16.6
16.6
2
16.6
4
16.6
6
16.6
8
16.7
16.7
2
16.7
4
16.7
6
16.7
8
16.8
16.8
2
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 0914+120 Histogram
166
0
10
20
30
40
50
6015
.25
15.3
15.3
5
15.4
15.4
5
15.5
15.5
5
15.6
15.6
5
15.7
15.7
5
15.8
15.8
5
15.9
15.9
5
16
16.0
5
16.1
16.1
5
16.2
16.2
5
16.3
16.3
5
16.4
16.4
5
16.5
16.5
5
16.6
16.6
5
16.7
16.7
5
16.8
16.8
5
16.9
16.9
5
17
17.0
5
17.1
17.1
5
17.2
17.2
5
17.3
17.3
5
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 0935+087 Histogram
167
0
10
20
30
40
50
60
70
80
90
100
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 0947+462 Histogram
168
0
10
20
30
40
50
60
14.99 15 15.01 15.02 15.03 15.04 15.05 15.06 15.07 15.08 15.09 15.1 15.11 15.12 15.13 15.14 15.15 15.16 More
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1002+506 Histogram
169
0
20
40
60
80
100
120
140
15.2
2
15.2
3
15.2
4
15.2
5
15.2
6
15.2
7
15.2
8
15.2
9
15.3
15.3
1
15.3
2
15.3
3
15.3
4
15.3
5
15.3
6
15.3
7
15.3
8
15.3
9
15.4
15.4
1
15.4
2
15.4
3
15.4
4
15.4
5
15.4
6
15.4
7
15.4
8
15.4
9
15.5
15.5
1
15.5
2
15.5
3
15.5
4
15.5
5
15.5
6
15.5
7
15.5
8
15.5
9
15.6
15.6
1
15.6
2
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1038+270 Histogram
170
0
10
20
30
40
50
60
70
80
90
14.6
2
14.6
3
14.6
4
14.6
5
14.6
6
14.6
7
14.6
8
14.6
9
14.7
14.7
1
14.7
2
14.7
3
14.7
4
14.7
5
14.7
6
14.7
7
14.7
8
14.7
9
14.8
14.8
1
14.8
2
14.8
3
14.8
4
14.8
5
14.8
6
14.8
7
14.8
8
14.8
9
14.9
14.9
1
14.9
2
14.9
3
14.9
4
14.9
5
14.9
6
14.9
7
14.9
8
14.9
9
15
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1104+022 Histogram
171
0
10
20
30
40
50
60
14.61 14.62 14.63 14.64 14.65 14.66 14.67 14.68 14.69 14.7 14.71 14.72 14.73 14.74 14.75 14.76 14.77 14.78 More
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1114+187 (HK Leo) Histogram
172
0
10
20
30
40
50
60
70
80
15.7
1
15.7
3
15.7
5
15.7
7
15.7
9
15.8
1
15.8
3
15.8
5
15.8
7
15.8
9
15.9
1
15.9
3
15.9
5
15.9
7
15.9
9
16.0
1
16.0
3
16.0
5
16.0
7
16.0
9
16.1
1
16.1
3
16.1
5
16.1
7
16.1
9
16.2
1
16.2
3
16.2
5
16.2
7
16.2
9
16.3
1
16.3
3
16.3
5
16.3
7
16.3
9
16.4
1
16.4
3
16.4
5
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1119+147 Histogram
173
0
20
40
60
80
100
120
13.9
914
14.0
114
.02
14.0
314
.04
14.0
514
.06
14.0
714
.08
14.0
914
.114
.11
14.1
214
.13
14.1
414
.15
14.1
614
.17
14.1
814
.19
14.2
14.2
114
.22
14.2
314
.24
14.2
514
.26
14.2
714
.28
14.2
914
.314
.31
14.3
214
.33
14.3
414
.35
14.3
614
.37
14.3
814
.39
14.4
14.4
114
.42
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1128+098 Histogram
174
0
5
10
15
20
25
30
15.2
7
15.3
15.3
3
15.3
6
15.3
9
15.4
2
15.4
5
15.4
8
15.5
1
15.5
4
15.5
7
15.6
15.6
3
15.6
6
15.6
9
15.7
2
15.7
5
15.7
8
15.8
1
15.8
4
15.8
7
15.9
15.9
3
15.9
6
15.9
9
16.0
2
16.0
5
16.0
8
16.1
1
16.1
4
16.1
7
16.2
16.2
3
16.2
6
16.2
9
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1136+581 Histogram
175
0
10
20
30
40
50
60
70
80
Fre
qu
en
cy o
f d
ata
po
ints
approx. V data points (magnitudes)
PG 1146+228 Histogram
176
0
2
4
6
8
10
12
141
4.4
9
14.6
14
.71
14
.82
14
.93
15
.04
15
.15
15
.26
15
.37
15
.48
15
.59
15.7
15
.81
15
.92
16
.03
16
.14
16
.25
16
.36
16
.47
16
.58
16
.69
16.8
16
.91
17
.02
17
.13
17
.24
17
.35
17
.46
17
.57
17
.68
17
.79
17.9
18
.01
18
.12
18
.23
18
.34
18
.45
18
.56
18
.67
18
.78
18
.89
19
19
.11
19
.22
19
.33
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1155+492 (BE UMa)Histogram
177
0
10
20
30
40
50
60
70
80
90
13.37 13.38 13.39 13.4 13.41 13.42 13.43 13.44 13.45 13.46 13.47 13.48 13.49 13.5 13.51 13.52 13.53 13.54 13.55 More
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1156-037 Histogram
178
0
5
10
15
20
25
30
35
40
45
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1157+004 Histogram
179
0
10
20
30
40
50
60
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1217-067 Histogram
180
0
10
20
30
40
50
60
14.8
9
14.9
2
14.9
5
14.9
8
15.0
1
15.0
4
15.0
7
15
.1
15.1
3
15.1
6
15.1
9
15.2
2
15.2
5
15.2
8
15.3
1
15.3
4
15.3
7
15
.4
15.4
3
15.4
6
15.4
9
15.5
2
15.5
5
15.5
8
15.6
1
15.6
4
15.6
7
15
.7
15.7
3
15.7
6
15.7
9
15.8
2
15.8
5
15.8
8
15.9
1
15.9
4
15.9
7
16
16.0
3
16.0
6
16.0
9
16.1
2
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1257+010 Histogram
181
0
20
40
60
80
100
120
15.72 15.73 15.74 15.75 15.76 15.77 15.78 15.79 15.8 15.81 15.82 15.83 15.84 15.85 15.86 More
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1314+041 Histogram
182
0
10
20
30
40
50
60
70
14.9
6
14.9
7
14.9
8
14.9
9
15
15.0
1
15.0
2
15.0
3
15.0
4
15.0
5
15.0
6
15.0
7
15.0
8
15.0
9
15.1
15.1
1
15.1
2
15.1
3
15.1
4
15.1
5
15.1
6
15.1
7
15.1
8
15.1
9
15.2
15.2
1
15.2
2
15.2
3
15.2
4
15.2
5
15.2
6
15.2
7
15.2
8
15.2
9
15.3
15.3
1
15.3
2
15.3
3
15.3
4
15.3
5
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1315-123 Histogram
183
0
2
4
6
8
10
12
14
15.82 15.83 15.84 15.85 15.86 15.87 15.88 15.89 15.9 15.91 15.92 15.93 15.94 15.95 15.96 15.97 15.98 15.99 16 16.01 16.02 16.03 More
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1316+678 Histogram
184
0
5
10
15
20
25
30
35
40
15.6
915
.715
.71
15.7
215
.73
15.7
415
.75
15.7
615
.77
15.7
815
.79
15.8
15.8
1
15.8
2
15.8
315
.84
15.8
5
15.8
6
15.8
715
.88
15.8
915
.915
.91
15.9
2
15.9
3
15.9
4
15.9
515
.96
15.9
7
15.9
815
.99
1616
.01
16.0
216
.03
16.0
416
.05
16.0
616
.07
16.0
816
.09
16.1
16.1
116
.12
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1443+337 Histogram
185
0
10
20
30
40
50
60
70
14.6
1
14.6
2
14.6
3
14.6
4
14.6
5
14.6
6
14.6
7
14.6
8
14.6
9
14.7
14.7
1
14.7
2
14.7
3
14.7
4
14.7
5
14.7
6
14.7
7
14.7
8
14.7
9
14.8
14.8
1
14.8
2
14.8
3
14.8
4
14.8
5
14.8
6
14.8
7
14.8
8
14.8
9
14.9
14.9
1
14.9
2
14.9
3
14.9
4
14.9
5
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1459-026 Histogram
186
0
5
10
15
20
25
30
35
40
45
50
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1517+265 Histogram
187
0
10
20
30
40
50
601
4.9
8
15
15
.02
15
.04
15
.06
15
.08
15.1
15
.12
15
.14
15
.16
15
.18
15.2
15
.22
15
.24
15
.26
15
.28
15.3
15
.32
15
.34
15
.36
15
.38
15.4
15
.42
15
.44
15
.46
15
.48
15.5
15
.52
15
.54
15
.56
15
.58
15.6
15
.62
15
.64
15
.66
15
.68
15.7
15
.72
15
.74
15
.76
15
.78
15.8
15
.82
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1520-050 Histogram
188
0
10
20
30
40
50
60
70
16.0
5
16.0
6
16.0
7
16.0
8
16.0
9
16.1
16.1
1
16.1
2
16.1
3
16.1
4
16.1
5
16.1
6
16.1
7
16.1
8
16.1
9
16.2
16.2
1
16.2
2
16.2
3
16.2
4
16.2
5
16.2
6
16.2
7
16.2
8
16.2
9
16.3
16.3
1
16.3
2
16.3
3
16.3
4
16.3
5
16.3
6
16.3
7
16.3
8
16.3
9
16.4
16.4
1
16.4
2
16.4
3
16.4
4
16.4
5
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1522+122 Histogram
189
0
2
4
6
8
10
12
14
1616
.06
16.1
2
16.1
8
16.2
4
16.3
16.3
6
16.4
2
16.4
8
16.5
4
16.6
16.6
6
16.7
2
16.7
8
16.8
4
16.9
16.9
6
17.0
2
17.0
8
17.1
4
17.2
17.2
6
17.3
2
17.3
8
17.4
4
17.5
17.5
6
17.6
2
17.6
8
17.7
4
17.8
17.8
6
17.9
2
17.9
8
18.0
4
18.1
18.1
6
18.2
2
18.2
8
18.3
4
18.4
18.4
6
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1550+131 (NN Ser) Histogram
190
0
10
20
30
40
50
60
70
80
90
100
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1617+150 Histogram
191
0
10
20
30
40
50
60
7012
.79
12.8
6
12.9
3
13
13.0
7
13.1
4
13.2
1
13.2
8
13.3
5
13.4
2
13.4
9
13.5
6
13.6
3
13.7
13.7
7
13.8
4
13.9
1
13.9
8
14.0
5
14.1
2
14.1
9
14.2
6
14.3
3
14.4
14.4
7
14.5
4
14.6
1
14.6
8
14.7
5
14.8
2
14.8
9
14.9
6
15.0
3
15.1
15.1
7
15.2
4
15.3
1
15.3
8
15.4
5
15.5
2
15.5
9
15.6
6
15.7
3
15.8
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1639+338 Histogram
192
0
2
4
6
8
10
12
14
16
18
16.0
416
.05
16.0
616
.07
16.0
816
.09
16.1
16.1
116
.12
16.1
316
.14
16.1
516
.16
16.1
716
.18
16.1
916
.216
.21
16.2
216
.23
16.2
416
.25
16.2
616
.27
16.2
816
.29
16.3
16.3
116
.32
16.3
316
.34
16.3
516
.36
16.3
716
.38
16.3
916
.416
.41
16.4
216
.43
16.4
416
.45
16.4
616
.47
16.4
8M
ore
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1657+656 Histogram
193
0
2
4
6
8
10
12
14
16
18
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 1710+567 Histogram
194
0
10
20
30
40
50
60
70
Fre
qu
en
cy o
f d
ata
po
ints
approx. V data points (magnitudes)
PG 1712+493 Histogram
195
0
10
20
30
40
50
60
70
80
9013
.65
13.6
8
13.7
1
13.7
4
13.7
7
13.8
13.8
3
13.8
6
13.8
9
13.9
2
13.9
5
13.9
8
14.0
1
14.0
4
14.0
7
14.1
14.1
3
14.1
6
14.1
9
14.2
2
14.2
5
14.2
8
14.3
1
14.3
4
14.3
7
14.4
14.4
3
14.4
6
14.4
9
14.5
2
14.5
5
14.5
8
14.6
1
14.6
4
14.6
7
14.7
14.7
3
14.7
6
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 2200+085 Histogram
196
0
5
10
15
20
25
30
35
40
45
5015
.76
15.7
9
15.8
2
15.8
5
15.8
8
15.9
1
15.9
4
15.9
7
16
16.0
3
16.0
6
16.0
9
16.1
2
16.1
5
16.1
8
16.2
1
16.2
4
16.2
7
16.3
16.3
3
16.3
6
16.3
9
16.4
2
16.4
5
16.4
8
16.5
1
16.5
4
16.5
7
16.6
16.6
3
16.6
6
16.6
9
16.7
2
16.7
5
16.7
8
16.8
1
16.8
4
16.8
7
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 2240+193 Histogram
197
0
5
10
15
20
25
30
35
40
12.2
2
12.2
5
12.2
8
12.3
1
12.3
4
12.3
7
12.4
12.4
3
12.4
6
12.4
9
12.5
2
12.5
5
12.5
8
12.6
1
12.6
4
12.6
7
12.7
12.7
3
12.7
6
12.7
9
12.8
2
12.8
5
12.8
8
12.9
1
12.9
4
12.9
7
13
13.0
3
13.0
6
13.0
9
13.1
2
13.1
5
13.1
8
13.2
1
13.2
4
13.2
7
13.3
13.3
3
13.3
6
Mo
re
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 2300+166 Histogram
198
0
10
20
30
40
50
60
70
80
13.1
9
13
.3
13.4
1
13.5
2
13.6
3
13.7
4
13.8
5
13.9
6
14.0
7
14.1
8
14.2
9
14
.4
14.5
1
14.6
2
14.7
3
14.8
4
14.9
5
15.0
6
15.1
7
15.2
8
15.3
9
15
.5
15.6
1
15.7
2
15.8
3
15.9
4
16.0
5
16.1
6
16.2
7
16.3
8
16.4
9
16
.6
16.7
1
16.8
2
16.9
3
17.0
4
17.1
5
17.2
6
17.3
7
17.4
8
17.5
9
17
.7
17.8
1
Fre
qu
ency
of
dat
a p
oin
ts
approx. V data points (magnitudes)
PG 2315+071 Histogram
APPENDIX C: POWER LAW PLOTS OF CVS AND NON-CVS
200
y = 0.2848x + 14.226
14
14.2
14.4
14.6
14.8
15
15.2
15.4
15.6
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PX And Power Law
201
y = 0.5555x + 13.822
13
13.5
14
14.5
15
15.5
16
16.5
17
17.5
18
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
AY Psc Power Law
202
y = 0.3382x + 14.125
14
14.5
15
15.5
16
16.5
17
17.5
18
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
WX Ari Power Law
203
y = 0.4449x + 12.063
y = 2.63x + 9.2601
11
11.5
12
12.5
13
13.5
14
14.5
15
15.5
16
0 0.5 1 1.5 2 2.5
ap
pro
x. V
(m
agn
itu
de
s)
log(rank)
SU UMa Power Law
204
y = 0.2466x + 14.652
14
14.5
15
15.5
16
16.5
17
17.5
18
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
ud
es)
log(rank)
BH Lyn Power Law
205
y = 0.2004x + 13.996
13.8
14
14.2
14.4
14.6
14.8
15
15.2
15.4
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
EI UMa Power Law
206
y = 0.7783x + 14.586
10
11
12
13
14
15
16
17
18
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
ud
es)
log(rank)
BZ UMa Power Law
207
y = 0.2784x + 10.945
y = 2.3171x + 7.0194
10
10.5
11
11.5
12
12.5
13
13.5
14
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
SY Cnc Power Law
208
y = 0.0952x + 14.012
13.95
14
14.05
14.1
14.15
14.2
14.25
14.3
14.35
14.4
14.45
14.5
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
BP Lyn Power Law
209
y = 0.3825x + 13.604
13
13.5
14
14.5
15
15.5
16
16.5
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
BK Lyn Power Law
210
y = 0.7511x + 12.43
12
12.5
13
13.5
14
14.5
15
15.5
16
16.5
0 0.5 1 1.5 2 2.5
ap
pro
x. V
(m
agn
itu
de
s)
log(rank)
ER UMa Power Law
211
y = 0.243x + 14.042
14
14.5
15
15.5
16
16.5
17
17.5
18
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
RZ LMi Power Law
212
y = 0.1341x + 15.048R² = 0.9756
14.8
15
15.2
15.4
15.6
15.8
16
16.2
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
ud
es)
log(rank)
LN UMa Power Law
213
y = 0.4237x + 13.972R² = 0.965
12
12.5
13
13.5
14
14.5
15
15.5
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
ud
es)
log(rank)
CH UMa Power Law
214
y = 0.1992x + 14.119R² = 0.9148
13.5
14
14.5
15
15.5
16
16.5
17
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
SW Sex
215
y = 0.4427x + 13.383R² = 0.9472
13.5
14
14.5
15
15.5
16
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
ud
es)
log(rank)
DW UMa Power Law
216
y = 0.2101x + 15.296R² = 0.8945
y = 0.7645x + 14.632R² = 0.9903
y = 1.8964x + 12.693R² = 0.9886
15
15.5
16
16.5
17
17.5
18
18.5
19
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
DO Leo Power Law
217
y = 0.4549x + 15.224R² = 0.9535
14
14.5
15
15.5
16
16.5
17
17.5
18
18.5
19
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
AN UMa Power Law
218
y = 1.0464x + 13.599R² = 0.9963
10
11
12
13
14
15
16
17
18
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
QZ Vir Power Law
219
y = 0.3928x + 12.163R² = 0.8778
y = 3.3583x + 8.6974R² = 0.9705
y = 1.5735x + 12.627R² = 0.9949
12
13
14
15
16
17
18
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
TW Vir Power Law
220
y = 0.2152x + 17.274R² = 0.9307
17
17.5
18
18.5
19
19.5
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1230+226 Power Law
221
y = 0.2776x + 13.818R² = 0.9261
y = 2.3034x + 10.945R² = 0.9922
y = 0.9047x + 13.629R² = 0.9819
13
13.5
14
14.5
15
15.5
16
16.5
17
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
HS Vir Power Law
222
y = 0.4094x + 14.626R² = 0.8739
14.8
15
15.2
15.4
15.6
15.8
16
16.2
16.4
16.6
16.8
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
ud
es)
log(rank)
ES Dra Power law
223
y = 0.3324x + 14.425R² = 0.9141
14
14.5
15
15.5
16
16.5
17
17.5
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
MR Ser Power Law
224
y = 0.1099x + 14.936R² = 0.8082
14.5
15
15.5
16
16.5
17
17.5
18
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
V849 Her Power Law
225
y = 0.3701x + 11.172R² = 0.9559
11
11.5
12
12.5
13
13.5
14
14.5
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
AH Her Power Law
226
y = 0.2505x + 12.542R² = 0.9927
12.4
12.6
12.8
13
13.2
13.4
13.6
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
V795 Her Power Law
227
y = 0.2418x + 13.452R² = 0.9387
13
13.5
14
14.5
15
15.5
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
V825 Her Power Law
228
y = 0.134x + 14.219R² = 0.9576
14
14.2
14.4
14.6
14.8
15
15.2
15.4
15.6
15.8
16
16.2
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
LQ Peg Power Law
229
y = 0.1855x + 13.375R² = 0.9856
13.4
13.5
13.6
13.7
13.8
13.9
14
14.1
14.2
14.3
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
V378 Peg Power Law
230
y = 0.2141x + 12.732R² = 0.8544
12
12.5
13
13.5
14
14.5
15
15.5
16
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
HX Peg Power Law
231
y = 1.1641x + 17.116R² = 0.9745
14
15
16
17
18
19
20
21
22
0 0.5 1 1.5 2 2.5 3
ap
pro
x. V
(m
agn
itu
de
s)
log(rank)
BG Ari Power Law
232
y = 0.6598x + 17.303R² = 0.9722
13
14
15
16
17
18
19
20
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
MM Hya Power Law
233
y = 0.4066x + 16.078R² = 0.9861
15
15.5
16
16.5
17
17.5
18
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
HM Leo Power Law
234
y = 0.1129x + 14.667R² = 0.954
y = 1.5095x + 12.401R² = 0.9072
14
15
16
17
18
19
20
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
NY Ser Power Law
235
y = 0.2777x + 15.918R² = 0.9571
15.5
16
16.5
17
17.5
18
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
e)
log(rank)
CT Ser Power Law
236
y = 0.1869x + 16.182R² = 0.9254
14
14.5
15
15.5
16
16.5
17
17.5
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 0008+186 Power Law
237
y = 0.0739x + 15.803R² = 0.9397
15.6
15.8
16
16.2
16.4
16.6
16.8
17
17.2
17.4
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
Log(rank)
PG 0240+066 Power Law
238
y = 0.0912x + 16.007R² = 0.9495
14.8
15
15.2
15.4
15.6
15.8
16
16.2
16.4
16.6
16.8
17
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 0248+054 Power Law
239
y = 0.0452x + 15.246R² = 0.9253
14.6
14.8
15
15.2
15.4
15.6
15.8
16
0 0.5 1 1.5 2 2.5 3
Ap
pro
x. V
(m
agn
itu
de
s)
log(rank)
PG 0322+078 Power Law
240
y = 0.0914x + 16.907R² = 0.9683
16.8
16.9
17
17.1
17.2
17.3
17.4
17.5
17.6
17.7
0 0.5 1 1.5 2 2.5 3
ap
pro
x. V
(m
agn
itu
de
s)
log(rank)
PG 0947+036
241
y = 0.0279x + 13.354R² = 0.879
13.3
13.35
13.4
13.45
13.5
13.55
13.6
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1116+349 Power Law
242
y = 0.0951x + 16.148R² = 0.9764
16
16.2
16.4
16.6
16.8
17
17.2
17.4
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1200-095 Power Law
243
y = 0.0752x + 15.139R² = 0.9652
14.4
14.6
14.8
15
15.2
15.4
15.6
15.8
16
16.2
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1403-111 Power Law
244
y = 0.3559x + 15.606R² = 0.9877
15.5
16
16.5
17
17.5
18
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 2254+075 Power Law
245
y = 0.1197x + 16.367R² = 0.9803
15.9
16
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 2357+027 Power Law
246
y = 0.0401x + 14.996
14.95
15
15.05
15.1
15.15
15.2
15.25
15.3
15.35
15.4
15.45
15.5
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 0023+298 Power Law
247
y = 0.0541x + 14.019
13.7
13.8
13.9
14
14.1
14.2
14.3
0 0.5 1 1.5 2 2.5 3
ap
pro
x. V
(m
agn
itu
de
s)
log(rank)
PG 0048+091 Power Law
248
y = 0.0403x + 15.657R² = 0.9126
15.5
15.6
15.7
15.8
15.9
16
16.1
0 0.5 1 1.5 2 2.5 3
Ap
pro
x. V
(m
agn
itu
des
)
log(rank)
PG 0051+169 Power Law
249
y = 0.0534x + 16.214R² = 0.9517
15.9
16
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
0 0.5 1 1.5 2 2.5 3
Ap
pro
x. V
(m
agn
itu
des
)
log(rank)
PG 0914+120 Power Law
250
y = 0.117x + 16.312R² = 0.9593
15
15.5
16
16.5
17
17.5
0 0.5 1 1.5 2 2.5 3
Ap
pro
x. V
(m
agn
itu
des
)
log(rank)
PG 0935+087 Power Law
251
y = 0.0313x + 14.714R² = 0.9307
14.55
14.6
14.65
14.7
14.75
14.8
14.85
14.9
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 0947+462 Power Law
252
y = 0.0241x + 15.046R² = 0.866
14.98
15
15.02
15.04
15.06
15.08
15.1
15.12
15.14
15.16
15.18
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1002+506 Power Law
253
y = 0.0301x + 15.378R² = 0.9357
15.2
15.25
15.3
15.35
15.4
15.45
15.5
15.55
15.6
15.65
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1038+270 Power Law
254
y = 0.05x + 14.599R² = 0.9654
14.6
14.65
14.7
14.75
14.8
14.85
14.9
14.95
15
15.05
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1104+022 Power Law
255
y = 0.028x + 14.618
14.6
14.62
14.64
14.66
14.68
14.7
14.72
14.74
14.76
14.78
14.8
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1114+187 (HK Leo) Power Law
256
y = 0.0353x + 15.706R² = 0.8904
y = 0.075x + 15.889R² = 0.9648
15.6
15.7
15.8
15.9
16
16.1
16.2
16.3
16.4
16.5
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1119+147 Power Law
257
y = 0.0339x + 14.284R² = 0.9476
13.95
14
14.05
14.1
14.15
14.2
14.25
14.3
14.35
14.4
14.45
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1128+098 Power Law
258
y = 0.0475x + 15.279R² = 0.9632
15.2
15.4
15.6
15.8
16
16.2
16.4
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1136+581 Power Law
259
y = 0.0303x + 14.853R² = 0.9115
14.8
14.85
14.9
14.95
15
15.05
15.1
15.15
15.2
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1146+228 Power Law
260
y = 0.0531x + 14.462
y = 2.8441x + 9.5118
14
15
16
17
18
19
20
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1155+492 (BE UMa) Power Law
261
y = 0.021x + 13.362R² = 0.8927
13.35
13.4
13.45
13.5
13.55
13.6
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
du
e)
log(rank)
PG 1156-037 Power Law
262
y = 0.0702x + 15.602R² = 0.9489
15.4
15.5
15.6
15.7
15.8
15.9
16
16.1
16.2
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1157+044 Power Law
263
y = 0.0454x + 15.079R² = 0.9317
15.05
15.1
15.15
15.2
15.25
15.3
15.35
15.4
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1217-067 Power Law
264
y = 0.0574x + 15.626R² = 0.9395
14.8
15
15.2
15.4
15.6
15.8
16
16.2
16.4
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1257+010 Power Law
265
y = 0.0339x + 15.696R² = 0.9328
15.7
15.72
15.74
15.76
15.78
15.8
15.82
15.84
15.86
15.88
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1314+041 Power Law
266
y = 0.0596x + 14.932R² = 0.9754
14.9
14.95
15
15.05
15.1
15.15
15.2
15.25
15.3
15.35
15.4
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1315-123 Power Law
267
y = 0.0544x + 15.861R² = 0.9262
15.8
15.85
15.9
15.95
16
16.05
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
du
es)
log(rank)
PG 1316+678 Power Law
268
y = 0.0371x + 15.706R² = 0.921
15.65
15.7
15.75
15.8
15.85
15.9
15.95
16
16.05
16.1
16.15
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1443+337 Power Law
269
y = 0.0583x + 14.617R² = 0.9315
14.55
14.6
14.65
14.7
14.75
14.8
14.85
14.9
14.95
15
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1459-026 Power Law
270
y = 0.0417x + 15.765R² = 0.9332
15.7
15.75
15.8
15.85
15.9
15.95
16
16.05
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1517+265 Power Law
271
y = 0.0734x + 15.425R² = 0.9574
14.9
15
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1520-050 Power Law
272
y = 0.0438x + 16.109R² = 0.965
16
16.05
16.1
16.15
16.2
16.25
16.3
16.35
16.4
16.45
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1522+122 Power Law
273
y = 0.098x + 16.034R² = 0.8914
y = 0.8479x + 14.651R² = 0.9888
15.5
16
16.5
17
17.5
18
18.5
19
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1550+131 Power Law
274
y = 0.0254x + 14.604R² = 0.8383
14.5
14.6
14.7
14.8
14.9
15
15.1
0 0.5 1 1.5 2 2.5 3
app
rox
V. (
mag
nit
ud
es)
log(rank)
PG 1617+150 Power Law
275
y = 0.0644x + 15.396R² = 0.8973
12
12.5
13
13.5
14
14.5
15
15.5
16
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1639+338 Power Law
276
y = 0.0574x + 16.078R² = 0.9633
16
16.05
16.1
16.15
16.2
16.25
16.3
16.35
16.4
16.45
16.5
16.55
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1657+656 Power Law
277
y = 0.0921x + 14.724R² = 0.9611
14.6
14.7
14.8
14.9
15
15.1
15.2
15.3
15.4
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1710+567 Power Law
278
y = 0.0329x + 13.548R² = 0.9321
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 1712+493 Power Law
279
y = 0.0354x + 13.78R² = 0.906
13.4
13.6
13.8
14
14.2
14.4
14.6
14.8
15
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 2200+085 Power Law
280
y = 0.0607x + 15.789R² = 0.971
15.5
16
16.5
17
17.5
18
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 2240+193 Power Law
281
y = 0.0471x + 12.769R² = 0.9462
12
12.2
12.4
12.6
12.8
13
13.2
13.4
13.6
0 0.5 1 1.5 2 2.5
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 2300+166 Power Law
282
y = 0.0429x + 13.88R² = 0.8065
12
13
14
15
16
17
18
0 0.5 1 1.5 2 2.5 3
app
rox.
V (
mag
nit
ud
es)
log(rank)
PG 2315+071 Power Law
APPENDIX D: DATA TABLE FOR MASS TRANSFER RATE CALCULATION
284
Name parallax
(mas) p error (mas)
distance (pc)
Apparent mag (V)
Av (S&F)
Absolute mag (Mv)
Luminosity (erg/s)
m-dot (g/sμ)
power-law slope
Period (hr)
Power-law Index
PX And 1.232 0.044 811.688 14.861 0.102 5.211 2.702E+33 1.637E+16 0.285 3.512 1.300
Ay Psc 1.336 0.052 748.503 15.465 0.161 5.933 1.391E+33 8.426E+15 0.556 5.216 1.669
WX Ari 1.479 0.141 676.133 15.128 0.543 5.434 2.201E+33 1.334E+16 0.338 3.344 1.365
SU UMa 4.535 0.029 220.507 13.950 0.124 7.109 4.705E+32 2.851E+15 0.445 1.832 1.507
BH Lyn 1.277 0.051 783.085 15.318 0.107 5.743 1.657E+33 1.004E+16 0.247 3.741 1.255
EI UMa 0.883 0.037 1132.503 14.517 0.080 4.167 7.070E+33 4.285E+16 0.200 6.434 1.202
BZ UMa 6.557 0.064 152.509 15.907 0.135 9.856 3.749E+31 2.272E+14 0.778 1.632 2.047
SY Cnc 2.232 0.044 448.029 12.575 0.081 4.238 6.626E+33 4.015E+16 0.278 9.177 1.292
BP Lyn 1.435 0.043 696.864 14.227 0.041 4.970 3.373E+33 2.044E+16 0.095 3.667 1.091
BK Lyn 1.980 0.069 505.051 14.909 0.042 6.350 9.463E+32 5.734E+15 0.383 1.800 1.423
ER UMa 2.676 0.046 373.692 14.433 0.025 6.546 7.906E+32 4.791E+15 0.751 1.528 1.997
RZ LMi 1.376 0.084 726.744 15.465 0.036 6.122 1.168E+33 7.077E+15 0.243 1.402 1.251
LN UMa 1.031 0.034 969.932 15.377 0.254 5.189 2.758E+33 1.671E+16 0.134 3.466 1.131
CH UMa 2.676 0.021 373.692 14.563 0.148 6.552 7.861E+32 4.764E+15 0.424 8.236 1.478
DW UMa 1.704 0.037 586.854 14.210 0.026 5.341 2.398E+33 1.453E+16 0.443 3.279 1.504
DO Leo 0.683 0.100 1464.129 16.954 0.076 6.050 1.248E+33 7.563E+15 0.210 5.628 1.213
AN UMa 3.099 0.137 322.685 16.488 0.021 8.924 8.843E+31 5.359E+14 0.455 1.914 1.521 QZ Vir/T
Leo 7.814 0.069 127.975 15.675 0.057 10.083 3.041E+31 1.843E+14 1.046 1.412 2.621
TW Vir 2.317 0.117 431.593 15.803 0.048 7.580 3.049E+32 1.848E+15 0.393 4.384 1.436
HS Vir 2.837 0.056 352.485 15.615 0.131 7.749 2.610E+32 1.582E+15 0.278 1.846 1.292
285
ES Dra 1.480 0.031 675.676 15.419 0.049 6.221 1.066E+33 6.460E+15 0.409 4.238 1.457
MR Ser 7.590 0.049 131.752 15.770 0.106 10.065 3.092E+31 1.874E+14 0.332 1.891 1.358
V849 Her 0.936 0.041 1068.376 15.272 0.191 4.938 3.477E+33 2.107E+16 0.110 3.384 1.107
AH Her 3.084 0.030 324.254 12.619 0.116 4.948 3.443E+33 2.087E+16 0.370 6.195 1.406
V795 Her 1.697 0.039 589.275 13.113 0.090 4.172 7.038E+33 4.265E+16 0.251 2.598 1.260
V825 Her 0.927 0.027 1078.749 14.016 0.067 3.784 1.006E+34 6.098E+16 0.242 4.944 1.250
V378 Peg 1.061 0.033 942.507 13.818 0.248 3.699 1.088E+34 6.594E+16 0.186 3.326 1.187
HX Peg 1.715 0.056 583.090 13.852 0.128 4.896 3.613E+33 2.190E+16 0.214 4.819 1.218
BG Ari 1.503 0.659 665.336 19.475 0.190 10.170 2.805E+31 1.700E+14 1.164 1.978 2.921
MM Hya 2.774 0.235 360.490 18.575 0.136 10.654 1.797E+31 1.089E+14 0.660 1.382 1.837
HM Leo 1.983 0.180 504.286 17.085 0.118 8.454 1.363E+32 8.258E+14 0.407 4.483 1.455
NY Ser 1.294 0.051 772.798 16.471 0.103 6.927 5.562E+32 3.371E+15 0.113 2.347 1.110
CT Ser 0.231 0.063 4329.004 16.514 0.098 3.235 1.669E+34 1.011E+17 0.278 4.680 1.292
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