Jeans-mode mass loss

In Jeans-mode mass loss, an isotropic wind escapes from one binary component carrying that star's specific orbital angular momentum. If the companion accretes negligibly, a circular binary obeys $aM=\text{constant}$ and $P{M}^2=\text{constant}$.

Integrating the slow isotropic wind law $da/dM=-a/M$ gives $aM=\mathrm{constant}$. For equal initial stellar masses $M^0$ and equal remnant masses $M_{\mathrm{BH}}$, $a_f=a_i{M}^0/M_{\mathrm{BH}}$. Combining a minimum initial noncontact separation with a maximum separation for merger within a chosen time gives a necessary overlap condition. The total-mass factors of two cancel; extra orbital evolution, kicks and explosive mass loss require their own treatment.