The Breakdown of Nuclear Quasi-Equilibrium in Highly Compact Binaries

Abstract

We have calculated the secular evolution of a highly compact binary, composed of a degenerate-dwarf primary and a low-mass main-sequence secondary, using the techniques developed by Rappaport, Joss, and Webbink (1982). Our new calculations (see Fig. 1) take into account the combined effects of (i) the gradual breakdown of quasi-equilibrium of the ³He abundance in the interior of the secondary, and (ii) the progressive mixture of fresh ³He into the core of the secondary due to the increasing depth of the stellar surface convection zone (see also D’Antona and Mazzitelli 1982). We find that these effects can cause the nuclear energy generation rate to pass through a sharp maximum at, the time when the secondary becomes fully convective. The resultant variations in the radius of the secondary, the binary orbital period, and the mass transfer rate tend to enhance the discovery probability of systems whose orbital periods are greater than ∿3^h, relative to shorter-period systems. This result may provide a natural explanation for the apparent sharp decrease in the discovery probability of h a see cataclysmic variable as its orbital period decreases through ∿3^h (see Fig. 2). However, the effects that we consider do not account for the relatively large number of observed cataclysmic variables with orbital periods between ∿80^m and ∿2^h, so that the overall distribution of orbital periods among cataclysmic variables is not yet fully understood.