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J/PASP/105/1433     Light Curves of W UMa Systems     (Rucinski 1993)
================================================================================
A Simple Description of Light Curves if W UMa Systems
   Rucinski S.M.
   <Publ. Astron. Soc. Pac. 105, 1433 (1993)>
   =1993PASP..105.1433R (SIMBAD/NED Reference)
================================================================================
ADC_Keywords: Stars, variable; Binaries, contact

Abstract:
   Fourier cosine coefficients a(1) to a(6) are tabulated and shown
   graphically for light curves of contract binary stars of one (solar)
   effective temperature, with orbital inclinations (i),
   30 deg.le.i.le.90deg., mass ratios (q), 0.05.le.q.le.1, and three
   values of the degree of contact, f=0, 0.5, 1. The coefficients, combined
   with additional tables of depths of minima, can be used for statistical
   estimates of ensemble properties of light curves of contact systems in
   stellar systems or for approximate determinations of orbital elements
   of individual contact binaries. Tables of all eleven coefficients a(0)
   to a(10) for all combinations of i and q are accessible using the ftp
   file-transfer mechanism.

Introduction:
   There is a need for a simple method to obtain essential parameters for
   contact binaries without the necessity for full light-curve synthesis
   solutions. A statistical method is also required to determine the
   expected distribution of variability amplitudes with observations.

   Only one set of temperature is given: the solar case with T(eff)=5770 K,
   for photometric band V, with gravity darkening exponent beta=0.08 in
   T(eff) proportional to g to the beta and bolometric albedo A=0.5.
   Nevertheless. the calculations should be applicable to a large range of
   effective temperatures. Light curves depend practically only on three
   parameters, the mass ratio, q, the inclination, i, and the degree of
   contact, f.

   The observed light curve should be expressed in light units, relative to
   the maximum at phases 0.25 or 0.75. (If the maxima are unequal, use the
   higher maximum.) A very good representation of a light curve can be
   usually obtained by calculating the Fourier series l = sum
   (ai*cos(2*pi*i*phase) and then truncating the curved part of the
   secondary (occultation) eclipse at the level l(180) using the tables of
   b the depth of secondary minima, 1-l(180)).


File Summary:
--------------------------------------------------------------------------------
 FileName        Lrecl       Records    Explanations
--------------------------------------------------------------------------------
ReadMe             80             .     This file
coef_f0.dat        91           500     Coefficients for f=0 (Inner Contact)
coef_f05.dat       91           500     Coefficients for f=0.5
coef_f1.dat        91           500     Coefficients for f=1 (Outer Contact)
min_f0.dat         28           500     Depth of minimum for f=0
min_f05.dat        28           500     Depth of minimum for f=0.5
min_f1.dat         28           500     Depth of minimum for f=1
--------------------------------------------------------------------------------

Byte-by-byte Description of file: coef_f0.dat, coef_f05.dat, coef_f1.dat
--------------------------------------------------------------------------------
 Bytes   Format  Units   Label     Explanations
--------------------------------------------------------------------------------
 1- 7    F7.3     deg     i        The inclination
 8-14    F7.3     ---     q        The mass ratio
15-21    F7.3     ---     a0       The coefficient, a(0)
22-28    F7.3     ---     a1       The coefficient, a(1)
29-35    F7.3     ---     a2       The coefficient, a(2)
36-42    F7.3     ---     a3       The coefficient, a(3)
43-49    F7.3     ---     a4       The coefficient, a(4)
50-56    F7.3     ---     a5       The coefficient, a(5)
57-63    F7.3     ---     a6       The coefficient, a(6)
64-70    F7.3     ---     a7       The coefficient, a(7)
71-77    F7.3     ---     a8       The coefficient, a(8)
78-84    F7.3     ---     a9       The coefficient, a(8)
85-91    F7.3     ---     a10      The coefficient, a(10)
--------------------------------------------------------------------------------

Byte-by-byte Description of file: min_f0.dat, min_f05.dat, min_f1.dat 
--------------------------------------------------------------------------------
 Bytes   Format  Units   Label     Explanations
--------------------------------------------------------------------------------
 1- 7    F7.3     deg     i        The inclination
 8-14    F7.3     ---     c        The mass ratio
15-21    F7.3     ---     l0       Depth of minimum for eclipse of more massive
                                      component
22-28    F7.3     ---     l180     Depth of minimum for eclipse of less massive
                                      component
--------------------------------------------------------------------------------

Each line contains the value of inclination (degr), mass-ratio, and two
depths of minima 1-l(0) and 1-l(180) for eclipses of more- and
less-massive components, respectively. The division into three parts
according to the degree of contact is the same as for "coef"

   Note that a very good representation of a light curve can be usually
   obtained by calculating the Fourier series l = sum (ai*cos(2*pi*i*phase)
   and then truncating the curved part of the secondary (occultation)
   eclipse at the level l0 using the tables of the depth of secondary
   minima, l180.
--------------------------------------------------------------------------------
(End)          Nancy G. Roman          [ADC/SSDOO]    Sep-6-1995