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

Abstract

We critically examine the basic paradigm for the origin of the 2-3 hr period gap in cataclysmic variables (CVs). We carry out an extensive population synthesis study of CVs starting from ~ 3 x 10^6 primordial binaries, and evolving some ~ 2 x 10^4 surviving systems through their CV phase. In particular we study current-epoch distributions of CVs in the $\dot M-P_{orb}$, R_{2}-P_{orb}, M_{2}-P_{orb}, q-P_{orb}, T_{eff}-P_{orb}, and L_{2}-P_{orb} planes, where $\dot M$ is 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 ~ 50% lower than would be inferred if one assumes a main-sequence radius-mass relation for the donor star.