Angular Momentum Losses and the Orbital Period Distribution of Cataclysmic Variables below the Period Gap: Effects of Circumbinary Disks

The population synthesis of cataclysmic variable binary systems at short orbital periods (<2.75 hr) is investigated. A grid of detailed binary evolutionary sequences has been calculated and included in the simulations to take account of additional angular momentum losses beyond that associated with gravitational radiation and mass loss, due to nova outbursts, from the system. As a specific example, we consider the effect of a circumbinary disk to gain insight into the ingredients necessary to reproduce the observed orbital period distribution. The resulting distributions show that the period minimum lies at about 80 minutes, with the number of systems monotonically increasing with increasing orbital period to a maximum near 90 minutes. There is no evidence for an accumulation of systems at the period minimum, which is a common feature of simulations in which only gravitational radiation losses are considered. The shift of the peak to about 90 minutes is a direct result of the inclusion of systems formed within the period gap. The period distribution is found to be fairly flat for orbital periods ranging from about 85 to 120 minutes. The steepness of the lower edge of the period gap can be reproduced, for example, by an input of systems at periods near 2.25 hr due to a flow of cataclysmic variable binary systems from orbital periods longer than 2.75 hr. The good agreement with the cumulated distribution function of observed systems within the framework of our model indicates that the angular momentum loss by a circumbinary disk or a mechanism that mimics its features, coupled with a weighting factor to account for selection effects in the discovery of such systems and a flow of systems from above the period gap to below the period gap, is an important ingredient for understanding the overall period distribution of cataclysmic variable binary systems.