A SIMPLE ACCRETION MODEL OF A ROTATING GAS SPHERE ONTO A SCHWARZSCHILD BLACK HOLE

E. A. Huerta & S. Mendoza

Instituto de Astronomía, Universidad Nacional Autónoma de México, Apdo. Postal 70–264, 04510 México, D. F., Mexico (eahuerta@astroscu.unam.mx, sergio@astroscu.unam.mx)

Received 2006 October 18
Accepted 2007 January 17

RESUMEN

Construimos un modelo simple de acreción para una esfera de gas que cae hacia un agujero negro de Schwarzschild. Mostramos cómo construir soluciones analíticas en términos de las funciones elípticas de Jacobi. Esta construcción representa una generalización relativista del modelo de acreción Newtoniano primeramente propuesto por Ulrich (1976). De la misma manera en que ocurre para el caso Newtoniano, el flujo predice naturalmente la existencia de un disco de acreción ecuatorial alrededor del agujero. Sin embargo, el radio del disco se incrementa monotónicamente sin límite a medida que el flujo alcanza su mínimo momento angular para este caso en particular.

ABSTRACT

We construct a simple accretion model of a rotating gas sphere onto a Schwarzschild black hole. We show how to build analytic solutions in terms of Jacobi elliptic functions. This construction represents a general relativistic generalisation of the Newtonian accretion model first proposed by Ulrich (1976). In exactly the same form as it occurs for the Newtonian case, the flow naturally predicts the existence of an equatorial rotating accretion disc about the hole. However, the radius of the disc increases monotonically without limit as the flow reaches its minimum allowed angular momentum for this particular model.

Key Words: ACCRETION, ACCRETION DISKS — HYDRODYNAMICS — RELATIVITY

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ACKNOWLEDGEMENTS

We dedicate the present article to the vivid memory of Sir Hermann Bondi who pioneered the studies of spherical accretion. We would like to thank William Lee for providing his numerical Paczynsky & Wiita pseudo–Newtonian results in order to make comparisons with the exact analytic solution presented in this article. The authors gratefully acknowledge financial support from DGAPA–Universidad Nacional Autónoma de México (IN119203).

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