Gravitational drag on a point mass in hypersonic motion through a gaseous medium

TL;DR

This paper presents an analytic model for gravitational drag on a point mass moving hypersonically through gas, validated by simulations, and clarifies the lower cut-off distance in dynamical friction calculations.

Contribution

The paper introduces a fully analytic ballistic orbit model that accurately predicts gravitational drag and accretion rates, removing ambiguity in the lower cut-off distance for dynamical friction.

Findings

Analytic model matches simulation results for drag force.

Ballistic models effectively predict accretion rates.

Clarifies the lower cut-off distance in dynamical friction calculations.

Abstract

We explore a ballistic orbit model to infer the gravitational drag force on an accreting point mass M, such as a black hole, moving at a hypersonic velocity v_{0} through a gaseous environment of density \rho_{0}. The streamlines blend in the flow past the body and transfer momentum to it. The total drag force acting on the body, including the nonlinear contribution of those streamlines with small impact parameter that bend significantly and pass through a shock, can be calculated by imposing conservation of momentum. In this fully analytic approach, the ambiguity in the definition of the lower cut-off distance $r_{\rm min}$ in calculations of the effect of dynamical friction is removed. It turns out that $r_{\rm min}=\sqrt{e}GM/2v_{0}^{2}$. Using spherical surfaces of control of different sizes, we carry out a successful comparison between the predicted drag force and the one obtained from a high resolution, axisymmetric, isothermal flow simulation. We demonstrate that ballistic models are reasonably successful in accounting for both the accretion rate and the gravitational drag.