Numerical Simulation of Rotating Accretion Disk Around the Schwarzschild Black Hole Using GRH Code

TL;DR

This paper presents 2D numerical simulations of thin accretion disks around Schwarzschild black holes using GRH equations solved with HRSC schemes, revealing spiral shock wave formation dependent on adiabatic index.

Contribution

First to model spiral shock waves in accretion disks around Schwarzschild black holes using GRH equations with HRSC schemes.

Findings

Spiral shocks form for adiabatic indices less than 5/3.

Shock location is around 10M from the black hole.

Lower gamma results in more tightly wound spirals.

Abstract

The 2D time dependent solution of thin accretion disk in a close binary system have been presented on the equatorial plane around the Schwarzschild black hole. To do that, the special part of the General Relativistic Hydrodynamical(GRH) equations are solved using High Resolution Shock Capturing (HRSC) schemes. The spiral shock waves on the accretion disk are modeled using perfect fluid equation of state with adiabatic indices $\gamma = 1.05, 1.2$ and 5/3. The results show that the spiral shock waves are created for gammas except the case $\gamma=5/3$. These results consistent with results from Newtonian hydrodynamic code except close to black hole. Newtonian approximation does not give good solution while matter closes to black hole. Our simulations illustrate that the spiral shock waves are created close to black hole and the location of inner radius of spiral shock wave is around $10M$ and it depends on the specific heat rates. We also find that the smaller $\gamma$ is the more tightly the spiral winds.