An Exploration of the Paradigm for the 2–3 Hour Period Gap in Cataclysmic Variables

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Abstract
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 ~300 CVs shows that these systems typically have orbital periods, Porb, in the range of ~80 minutes to ~8 hr but a distinct dearth of systems with 2 Porb(hr) 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 Porb 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 Porb decreases below ~3 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 Porb ~ 2 hr. We carry out an extensive population synthesis study of CVs, starting from ~3 × 106 primordial binaries and evolving some ~2 × 104 surviving systems through their CV phase. In particular we study current-epoch distributions of CVs in the Porb, R2-Porb, M2-Porb, q-Porb, Teff-Porb, and L2-Porb planes, where is the mass transfer rate, q is the mass ratio M2/M1, and M2, R2, Teff, and L2 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 ~50% lower than would be inferred if one assumes a main-sequence radius-mass relation for the donor star. We quantify the M2-Porb 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.