Tidal capture of galaxies

Tidal capture converts sufficient relative orbital energy into internal tidal heating to leave two initially unbound galaxies on a bound orbit. For identical spherical galaxies of mass $m_g$, a distant rapid flyby of impact parameter $p$ and relative speed $v$ gives the approximate capture condition $pv<[(32/3)G^2{m}_g^2⟨r^2⟩{]}^{1/4}$. This requires the impulse approximation and weak gravitational focusing; it is not a general criterion for subsequent coalescence.