= Wind-limited black-hole binary merger window
{title2=$a_f=a_iM_i/M_f$}
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 $M_{\rm BH}$, $a_f=a_iM^0/M_{\rm BH}$. 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.
Back to article page
