Mass-Loss Rate in Short-Period Cataclysmic Variables

The relationship between orbital periods of cataclysmic variables (CV) and mass-loss rates of their donor stars is an important subject of theoretical researches. The observed donor's radii are oversized in comparison with those of isolated unperturbed 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 Hayashi theory for changes in effective temperature, orbital period, and luminosity of the donor with the stellar radius, we find the mass-loss rate of CVs as a function of the orbital period P. The derived mass-loss rate is more or less constant at 10-9.6-10-10M$\odot$ yr-1 with P above 90 minutes and declines very rapidly with P below 90 minutes, reaching 10-10.3-10-11.7M$\odot$ yr-1 when P is close to the minimum period. The turnaround behavior of the mass-loss rate shape with P near the minimal period is much less pronounced than suggested by earlier numerical models, making observational detection of the turnaround highly unlikely. When applied to our new results, SDSS 1035, 1507, 1501 and 1433 systems, previously known as post-bounce CVs, are more likely to be systems that have yet to reach the minimal period.