Auxiliary tables for a paper OGLE-3 (AJ, 115, 1135, 1998) on long-period (>1 day) contact systems in the OGLE sample

Read Me First

The tables are in plain unformatted ASCII.

The tabulation is as follows:
inclination 30 (2.5) 90 degr
mass-ratio 0.05 (0.05) 1.0
degree of contact 0 (0.5) 1

Note: All the calculations here are for the gravity brightening exponent equal to von Zeipel's (Teff ~ g1.0) at high effective temperatures (32,000 K) in the Cousins I-band (as used by OGLE). These calculations have an exploratory nature and are not meant to be used for any particular system. The adopted bracketing atmospheres (34,500 and 30,250 K) were characterized by relative fluxes 1.078 and 0.922 and by the linear limb darkening coeffecients 0.20 and 0.23.
Of note are the following properties, which distinguish the results for hot contact systems from those for the solar-type (W UMa) case:

  1. Since the I-band is far redward of the spectrum peak for hot stars, the relative fluxes in the bracketing atmospheres differ rather moderately;
  2. Because of the same reason, the limb darkening coefficients are small;
  3. These two effects over-compensate the influence of the stronger gravity brightening producing similar perhaps even slightly less deep eclipses than for typical solar-type systems.

There are two tables for the hot systems:

coef 138278 bytes, 13 columns 7 characters wide
Each line contains the value of inclination (degr), mass-ratio, and eleven cosine coefficients a0 to a10 (in light units, not magnitudes!). There are three successive tables of the coeffecients for three values of the degree of contact: f=0 (inner), f=0.5, f=1 (outer).

depth of minima 43589 bytes, 4 columns 7 characters wide
Each line of the table contains the value of inclination (degr), mass-ratio, and the depth of both minima (in maximum light units), 1-l(00) and 1-l(1800), for eclipses of more- and less-massive components, respectively. Therefore, eg. to find the magnitude drop at the eclipse of the more massive component, do not use the depth tabulated here, but the light l(00), according to: m(0) = -2.5 log l(00). The division into three parts of the table, for the three values of the degree of contact, is the same as for "coef_hot".

Note: 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(1800) using the tables of the depth of secondary minima 1-l(1800)).