Uniform-separation merger delay-time distribution
= Uniform-separation merger delay-time distribution
{title2=$dN/dt\propto t^{-3/4}$}
If a circular compact binary has a <gravitational wave> coalescence delay $t=BA_0^4$ and $dN/dA_0$ is constant, then $dN/dt=(dN/dA_0)|dA_0/dt|\propto t^{-3/4}$. More generally $dN/dA_0\propto A_0^\beta$ gives a <delay-time distribution> proportional to $t^{(\beta-3)/4}$. A log-uniform separation distribution instead gives $t^{-1}$.