Quasi-normal acoustic oscillations in the Michel flow

TL;DR

This paper investigates the quasi-normal acoustic oscillations in the Michel flow, modeling a black hole analogue with fluid dynamics, and computes their frequencies demonstrating a dependency on horizon radii and surface gravity.

Contribution

It introduces a new numerical method to compute quasi-normal mode frequencies in the Michel flow and compares these results with independent simulations, confirming their accuracy.

Findings

Quasi-normal frequencies depend on horizon radii and angular momentum.

Frequencies scale with surface gravity when the sonic horizon is large.

Good agreement between numerical methods confirms the results.

Abstract

We study spherical and nonspherical linear acoustic perturbations of the Michel flow, which describes the steady radial accretion of a perfect fluid into a nonrotating black hole. The dynamics of such perturbations are governed by a scalar wave equation on an effective curved background geometry determined by the acoustic metric, which is constructed from the spacetime metric and the particle density and four-velocity of the fluid. For the problem under consideration in this article the acoustic metric has the same qualitative features as an asymptotically flat, static and spherically symmetric black hole, and thus it represents a natural astrophysical analogue black hole. As for the case of a scalar field propagating on a Schwarzschild background, we show that acoustic perturbations of the Michel flow exhibit quasi-normal oscillations. Based on a new numerical method for determining the solutions of the radial mode equation, we compute the associated frequencies and analyze their dependency on the radii of the event and sonic horizons and the angular momentum number. Our results for the fundamental frequencies are compared to those obtained from an independent numerical Cauchy evolution, finding good agreement between the two approaches. When the radius of the sonic horizon is large compared to the event horizon radius, we find that the quasi-normal frequencies scale approximately like the surface gravity associated with the sonic horizon.