2010ApJ...721.1356S

The mass-loss rate of donor stars in cataclysmic variables (CVs) is of paramount importance in the evolution of short-period CVs. Observed donors are oversized in comparison with those of isolated single stars of the same mass, which is thought to be a consequence of the mass loss. Using the empirical mass-radius relation of CVs and the homologous approximation for changes in effective temperature T₂, orbital period P, and luminosity of the donor with the stellar radius, we find the semi-empirical mass-loss rate {{dot}M_2} of CVs as a function of P. The derived {{dot}M_2} is at ∼10^–9.5-10^–10 M_☉/yr and weakly depends on P when P>90 minutes, while it declines very rapidly toward the minimum period when P < 90 minutes, emulating the P-T₂relation. Due to strong deviation from thermal equilibrium caused by the mass loss, the semi-empirical {{dot}M_2} is significantly different from and has a less-pronounced turnaround behavior with P than suggested by previous numerical models. The semi-empirical P-{{dot}M_2} relation is consistent with the angular momentum loss due to gravitational wave emission and strongly suggests that CV secondaries with 0.075 M_☉< M₂< 0.2 M_☉ are less than 2 Gyr old. When applied to selected eclipsing CVs, our semi-empirical mass-loss rates are in good agreement with the accretion rates derived from the effective temperatures T₁ of white dwarfs, suggesting that {{dot}M_2} can be used to reliably infer T₂ from T₁. Based on the semi-empirical {{dot}M_2}, SDSS 1501 and 1433 systems that were previously identified as post-bounce CVs have yet to reach the minimal period.