Spherical accretion of a perfect fluid onto a black hole

Authors

DOI:

https://doi.org/10.31349.RevMexFisE.18.020206

Keywords:

numerical relativity -- black holes -- accretion -- relativistic astrophysics

Abstract

In this academic paper we present in detail the numerical solution of the accretion of a perfect fluid onto a black hole. The conditions are very simple, we consider a radial flux being accreted by a Schwarzschild black hole. We present two scenarios: 1) the test field case in which the fluid does not affect the geometry of the black hole space-time background, and 2) the full non-linear scenario, in which the geometry of the space-time evolves simultaneously with the fluid according to Einstein's equations.
In the two scenarios we describe the black hole space-time in horizon penetrating coordinates, so that it is possible to visualize that accretion actually takes place within the numerical domain.
For the evolution of matter we use the Valencia formulation of relativistic fluid dynamics. In the non-linear scenario we solve the equations of geometry using the ADM formulation of General Relativity, with very simple and intuitive gauge and boundary conditions, and include diagnostics related to the Apparent Horizon and Event Horizon growth.
In view of the recent spectacular discoveries by the Event Horizon Telescope collaboration and further discoveries to come, the aim of this paper is to provide the necessary tools for interested graduate students in Black Hole Astrophysics, to enter into the accretion modeling starting from a considerable advanced starting point.

Author Biographies

Francisco S Guzmán Murillo, IFM-UMSNH

Prof. Instituto de Física y Matemáticas. Universidad Michoacana de San Nicolás de Hidalgo

Iván Alvarez Ríos

M. Sc. student IFM-UMSNH

Alejandro Romero Amezcua

Undergrad. Student FCFM-UMSNH

José A González

Prof. IFM-UMSNH

References

Event Horizon Telescope Collaboration,

First M87 Event Horizon Telescope Results.

ApJ, 875, L1 (2019).

{it Ibid.} ApJ, 875, L2 (2019).

{it Ibid.} ApJ, 875, L3 (2019).

{it Ibid.} ApJ, 875, L4 (2019).

{it Ibid.} ApJ, 875, L5 (2019).

{it Ibid.} ApJ, 875, L6 (2019).

J. A. Gonz'alez, F. S. Guzm'an, Classification of a black hole spin out of its shadow using support vector machines.

Phys. Rev. D 99, 103002 (2019)

J. A. Font, J. M. Iba~nez, A. Marquina, J. M Mart'i,

Multidimensional relativistic hydrodynamics: Characteristic fields and modern high-resolution shock-capturing schemes.

A&A {bf 282}, 304-314 (1994).

F. Banyouls, J. A. Font, J. Ma. Iba~nez, L. Ma. Mar'i, J. A. Miralles.

Numerical {3 + 1} General Relativistic Hydrodynamics: A Local Characteristic Approach.

The Astrophysical Journal, 476, 221-231, (1997).

https://iopscience.iop.org/article/10.1086/303604/pdf

L. Rezzolla, O. Zanotti. Relativistic Hydrodynamics, Oxford 2013.

P. Harten, B. Lax, B. B. van Leer,

On Upstream Difference and Godunov-Type Schemes for Hyperbolic Conservation Laws.

SIAM Review, 25, 35-61 (1983). B. Einfeldt,

On godunov-type methods for gas dynamics.

Journal of Computational Physics, 25, 294-318 (1988).

F.S. Guzm'an, F.D. Lora-Clavijo, and M.D. Morales,

Revisiting spherically symmetric relativistic hydrodynamics

Rev. Mex. F'is. E 58, 84-98 (2012).

https://rmf.smf.mx/ojs/rmf-e/article/view/4683

J. M. Mart'i and E. M"uller,

Numerical Hydrodynamics in Special Relativity

Living Reviews in Relativity 6, 7 (2003).

J. W. Thomas.

Numerical Partial Differential Equations: Conservation Laws and Elliptic Equations Texts in Applied Mathematics, Springer 1995.

R. L. LeVeque,

Numerical Methods for Conservation Laws.

Lecture in Mathematics, Birkhauser (1992).

E. F. Toro,

Riemann Solvers and Numerical Methods for Fluid Dynamics.

Springer (1999).

H. Bondi,

On spherically symmetrical accretion.

MNRAS 112, 195-204 (1952).

Philippos Papadopoulos, Jose A. Font,

Relativistic Hydrodynamics around Black Holes and Horizon Adapted Coordinate Systems.

Phys.Rev. D58 (1998) 024005. https://arxiv.org/abs/gr-qc/9803087

F.C. Michel.

Accretion of matter by condensed objects.

Astrophysics and Space Science 15, 153-160, (1972).

M. Gracia-Linares, F. S. Guzm'an,

Accretion of supersonic winds onto black holes in 3D: stability of the shock cone.

The Astrophysical Journal, 812, 23 (2015)

F. D. Lora-Clavijo. Dr. Sc. Thesis. Universidad Michoacana de San Nicol'as de Hidalgo, 2013.

http://www.ifm.umich.mx/~guzman/LoraClavijoDrScThesis.pdf

In preparation.

M. Alcubierre,

Introduction to 3+1 Numerical Relativity.

Oxford Science Publications 2008.

T.W. Baumgarte and S. L. Shapiro, Numerical Relativity: Solving Einstein's Equations on the Computer, Cambridge University Press 2010.

J. Thornburg,

A 3+1 Computational Scheme for Dynamic Spherically Symmetric Black Hole Spacetimes -- II: Time Evolution.

https://arxiv.org/pdf/gr-qc/9906022.pdf

J. W. Thomas.

Numerical Partial Differential Equations: Finite Difference Methods. Texts in Applied Mathematics, Springer 1995.

Richard A. Matzner(1), H. E. Seidel, Stuart L. Shapiro, L. Smarr, W.-M. Suen, Saul A. Teukolsky, J. Winicour,

Science 270, 941-947, 1995.

https://science.sciencemag.org/content/270/5238/941

http://www.cactuscode.org

P. Diener.

A new general purpose event horizon finder for 3D numerical spacetimes. Class.Quant.Grav. 20, 4901-4918, (2003)

Downloads

Published

2021-07-02