Equal-mass tidal-capture threshold
= Equal-mass tidal-capture threshold
{title2=$pv<[32G^2m_g^2\langle r^2\rangle/3]^{1/4}$}
Two equal galaxies each receive the <tidal impulse heating of a spherical galaxy>, while their relative orbital energy at infinity is $m_gv^2/4$. Transfer of more internal energy than that orbital energy gives $pv<[32G^2m_g^2\langle r^2\rangle/3]^{1/4}$. Slow encounters require <adiabatic shielding of tidal encounters>, so the impulsive inequality does not apply there.