Numerical study of the tidal interaction of a star and a massive black hole

TL;DR

This paper develops a numerical framework using spectral methods and moving frames to accurately simulate the tidal interactions between a main sequence star and a massive black hole, improving computational efficiency and precision.

Contribution

It introduces a novel formalism combining symmetry, moving grids, and spectral methods for simulating star-black hole encounters with high accuracy.

Findings

Validated the affine model against full numerical simulations.

Achieved high-accuracy results within a few hours on standard workstations.

Demonstrated the effectiveness of the moving frame and spectral methods in hydrodynamical simulations.

Abstract

We present a formalism well adapted to the numerical study of the encounter of an ordinary main sequence star with a massive black hole. Symmetry considerations, the use of a well adapted moving grid and a well adapted moving frame along with integration of the partial differential equations by means of pseudo-spectral methods result in a very powerful and accurate tool. The hydrodynamical equations are written in a moving frame which mimics the bulk of the movement of the fluid, resulting in very small relative velocities and a well suited spatial resolution throughout the calculations. Therefore, the numerical calculations are considerably simplified, smoothing in particular the Courant condition. Typical runs are performed within a few hours on a workstation with the high accuracy linked to the spectral methods. Predictions of the so-called affine are tested against this full numerical simulation.