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
DESCARGAR ARTÍCULO EN FORMATO PDF
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).
]]>REFERENCES
Beloborodov, A. M., & Illarionov, A. F. 2001, MNRAS, 323, 167 [ Links ]
Birkhoff, G. 1923, Relativity and Modern Physics (Cambridge: Harvard Univ. Press) [ Links ]
Bondi, H. 1952, MNRAS, 112, 195 [ Links ]
_________. 2005, The Scientific Legacy of Fred Hoyle, ed. D. Gough (Cambridge: Cambridge Univ. Press), 55 [ Links ]
Cassen, P., & Moosman, A. 1981, Icarus, 48, 353 [ Links ]
Cayley, A. 1961, An Elementary Treatise on Elliptic Functions (New York: Dover) [ Links ]
Chandrasekhar, S. 1983, The Mathematical Theory of Black Holes (Oxford: Oxford Univ. Press) [ Links ]
Frank, J., King, A., & Raine, D. J. 2002, Accretion Power in Astrophysics (3th ed.; Cambridge: Cambridge Univ. Press) [ Links ]
Hancock, H. 1917, Elliptic Integrals (New York: Dover) [ Links ]
Landau, L., & Lifshitz, E. 1994a, Course of Theoretical Physics, Vol. 2, The Classical Theory of Fields (4th ed.; Oxford: Pergamon) [ Links ]
_________. 1994b, Course of Theoretical Physics, Vol. 1, Mechanics (4th ed.; Oxford: Pergamon) [ Links ]
Lawden, D. 1989, Elliptic Functions and Applications (New York: Springer Verlag) [ Links ]
Lee, W. H., & Ramirez–Ruiz, E. 2006, ApJ, 641, 961 [ Links ]
Mendoza, S., Cantó, J., & Raga, A. C. 2004, Rev Mex AA, 40, 147 [ Links ]
Michel, F. C. 1972, Ap & SS, 15, 153 [ Links ]
Misner, C. W., Thorne, K. S., & Wheeler, J. A. 1973, Gravitation (San Francisco: Freeman) [ Links ]
Novikov, I., & Frolov, V. 1990, Black Hole Physics (Netherlands: Kluwer Academic) [ Links ]
Paczynsky, B., & Wiita, P. J. 1980, A & A, 88, 23 [ Links ]
Stanyukovich, K. P. 1960, Unsteady Motion of Continuous Media (New York: Oxford Univ. Press) [ Links ]
Ulrich, R. K. 1976, ApJ, 210, 377 [ Links ]
Wald R. 1984, General Relativity (Chicago: Univ. Chicago Press) [ Links ] ]]>