Cataclysmic-variable orbital-period distribution ($N(P)$)

Ordinary hydrogen-rich cataclysmic variables occur on both sides of a cataclysmic-variable period gap at approximately two to three hours, with a cataclysmic-variable period minimum near 82 minutes. Selection effects change the observed proportions. Knigge, Baraffe and Patterson's donor-based evolutionary study summarizes these empirical landmarks.

For a Roche lobe-filling donor with local radius response $R_2\propto M_2^{\zeta }$, the Roche-lobe-filling period-density relation gives $P\propto M_2^{(3\zeta -1)/2}$. As mass is lost, the period falls for $\zeta >1/3$ and rises for $\zeta <1/3$, with a minimum at the transition. The reversal is called a period bounce. Slow evolution near the turning point produces an accumulation in the period distribution: for a steady flow of systems along one evolutionary branch, $N(P)\propto 1/|\dot{P}|$.

The cataclysmic-variable period gap is the observed deficit of accreting, ordinary hydrogen-rich cataclysmic variables with periods around two to three hours. The disrupted magnetic braking model interprets it as a detached phase after the donor contracts inside its Roche lobe.