Assess the predictive value of encounter velocity

Investigate whether the relative velocity at characteristic separations provides predictive information about binary capture outcomes when considered alongside first-periapsis depth and gas mass in eccentric black-hole encounters embedded in active-galactic-nucleus discs.

Background

The simulations identify first-periapsis distance as the strongest predictor of direct capture, while the gas mass within the binary Hill sphere provides only limited additional separation between captures and flybys. The authors note that relative velocity at the separation of twice the binary Hill radius is relevant for interpreting individual outcomes, particularly because fast, gas-poor encounters can fail despite reaching a deep periapsis.

A systematic assessment of relative velocity at characteristic distances, jointly with periapsis depth and gas mass, was not performed in the reported simulation suite. Establishing its predictive value could improve classification of capture outcomes and clarify the physical causes of exceptional failures.