The White Dwarf Mass and Orbital Period Distribution in Zero-Age Cataclysmic Binaries

Extract

A zero-age cataclysmic binary (ZACB) we define as a binary system at the onset of interaction as a cataclysmic variable. We present here the results of calculations of the distributions of white dwarf masses and of orbital periods in ZACBs, due to binaries present in a stellar population which has undergone continuous, constant star formation for 10¹⁰ years.

Distributions of ZACBs were calculated for binaries formed t years ago, for log t = 7.4 (the youngest age at which viable ZACBs can form) to log t = 10.0 (the assumed age of the Galactic disk), in intervals of log t = 0.1. These distributions were then integrated over time to obtain the ZACB distribution for a constant rate of star formation. To compute the individual distributions for a given t, we require the density of systems forming (number of pre-cataclysmics forming per unit volume of orbital parameter space), n_£(t), and the rates at which the radii of the secondary and of its Roche lobe are changing in time, _s (t) and _{L, s} (t), respectively. In calculating n_f(t), we assume that the distribution of the orbital parameters in primordial (ZAMS) binaries may be written as the product of the distribution of masses of ZAMS stars (Miller and Scalo 1979), the distribution of mass ratios in ZAMS binaries (cf. Popova, et al., 1982), and the distribution of orbital periods in ZAMS binaries (Abt 1983). In transforming the the orbital parameters from progenitor (ZAMS) to offspring (ZACB) binaries, we assume that all of the orbital energy deposited into the envelope during the common envelope phase leading to ZACB formation goes into unbinding that envelope. R._{L, s} (t) is determined from orbital angular momentum loss rates due to gravitational radiation (Landau and Lifshitz 1951) and magnetic braking (γ = 2 in Rappaport, Verbunt, and Joss 1983). We turn off magnetic braking if the secondary is completely convective.