An exploration of the paradigm for the 2-3 hour period gap in cataclysmic variables

We critically examine the basic paradigm for the origin of the 2-3 hr period gap in cataclysmic variables (CVs), i.e., binary systems in which a white dwarf accretes from a relatively unevolved, low-mass donor star. The observed orbital period distribution for similar to 300 CVs shows that these systems typically have orbital periods, P-orb, in the range of similar to 80 minutes to similar to8 hr but a distinct dearth of systems with 2 less than or similar to P-orb(hr) less than or similar to 3. This latter feature of the period distribution is often referred to as the period gap. The conventional explanation for the period gap involves a thermal bloating of the donor star for P-orb greater than or similar to 3 hr due to mass transfer rates that are enhanced over those that could be driven by gravitational radiation (GR) losses alone (e.g., magnetic braking). If for some reason the supplemental angular momentum losses become substantially reduced when P-orb decreases below similar to3 hr, the donor star will relax thermally and shrink inside of its Roche lobe. This leads to a cessation of mass transfer until GR losses can bring the system into Roche lobe contact again at P-orb similar to 2 hr. We carry out an extensive population synthesis study of CVs, starting from similar to3 x 10(6) primordial binaries and evolving some similar to2 x 10(4) surviving systems through their CV phase. In particular we study current-epoch distributions of CVs in the (M)over dot-P-orb, R-2-P-orb, M-2-P-orb, q-P-orb, T-eff-P-orb, and L-2-P-orb planes, where is (M)over dot the mass transfer rate, q is the mass ratio M-2/M-1, and M-2, R-2, T-eff, and L-2 are the donor star mass, radius, effective temperature, and luminosity, respectively. This work presents a new perspective on theoretical studies of the long-term evolution of CVs. In particular, we show that if the current paradigm is correct, the secondary masses in CVs just above the period gap should be as much as similar to 50% lower than would be inferred if one assumes a main-sequence radius-mass relation for the donor star. We quantify the M-2-P-orb relations expected from models wherein the donor stars are thermally bloated. Finally, we propose specific observations, involving the determination of secondary masses in CVs, that would allow for a definitive test of the currently accepted model (i.e., interrupted thermal bloating) for the period gap in CVs.