Thin accretion disks onto brane world black holes

C. S. J. Pun, Z. Kovács, and T. Harko

Phys. Rev. D 78, 084015 – Published 9 October 2008

Abstract

The brane-world description of our universe entails a large extra dimension and a fundamental scale of gravity that might be lower by several orders of magnitude as compared to the Planck scale. An interesting consequence of the brane-world scenario is in the nature of the vacuum solutions of the brane gravitational field equations, with properties quite distinct as compared to the standard black-hole solutions of general relativity. One possibility of observationally discriminating between different types of black holes is the study of the emission properties of the accretion disks. In the present paper we obtain the energy flux, the emission spectrum and accretion efficiency from the accretion disks around several classes of static and rotating brane-world black holes, and we compare them to the general relativistic case. Particular signatures can appear in the electromagnetic spectrum, thus leading to the possibility of directly testing extra-dimensional physical models by using astrophysical observations of the emission spectra from accretion disks.

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Received 8 April 2008

DOI:https://doi.org/10.1103/PhysRevD.78.084015

Authors & Affiliations

C. S. J. Pun^1,*, Z. Kovács^2,3,†, and T. Harko¹

¹Department of Physics and Center for Theoretical and Computational Physics, The University of Hong Kong, Pok Fu Lam Road, Hong Kong
²Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
³Department of Experimental Physics, University of Szeged, Dóm Tér 9, Szeged 6720, Hungary

^*jcspun@hkucc.hku.hk
^†zkovacs@mpifr-bonn.mpg.de
^‡harko@hkucc.hku.hk

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Vol. 78, Iss. 8 — 15 October 2008

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Figure 1
The effective potential of a DMPR black hole with total mass $M$ and tidal charge $Q$ for the specific angular momentum $\tilde{L} = 4 M$ . The solid line is the effective potential for a Schwarzschild black hole with the same total mass. The values of $Q$ are $Q = - M^{2}$ (long dashed line), $Q = - 0.5 M^{2}$ (short dashed line), $Q = 0.5 M^{2}$ (dotted line) and $Q = M^{2}$ (dot-dashed line), respectively.Reuse & Permissions
Figure 2
Figure on the left: The time-averaged flux radiated by the accretion disk around a DMPR black hole for different values of the tidal charge parameter $Q$ : $Q = - M^{2}$ (long dashed line), $Q = - 0.5 M^{2}$ (short dashed line), $Q = 0.5 M^{2}$ (dotted line) and $Q = M^{2}$ (dot-dashed line), respectively. The flux for a Schwarzschild black hole is plotted with a solid line. The mass accretion rate is $2 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ . Figure on the right: The time-averaged flux radiated by the accretion disk around a DMPR black hole and tidal charge $Q = - M^{2}$ for different values of the mass accretion rate ${\dot{M}}_{0}$ : $1.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (long dashed line), $1.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (short dashed line), $= 2.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (solid line), $2.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dotted line), and $3.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dot-dashed line), respectively. The total mass of the black hole is $2.5 \times 10^{6} M_{⊙}$ .Reuse & Permissions
Figure 3
Figure on the left: The emission spectrum of the accretion disk around a DMPR black hole for different values of the tidal charge parameter $Q$ : $Q = - M^{2}$ (long dashed line), $Q = - 0.5 M^{2}$ (short dashed line), $Q = 0.5 M^{2}$ (dotted line) and $Q = M^{2}$ (dot-dashed line), respectively. The solid line represents the disk spectrum for a Schwarzschild black hole. The mass accretion rate is $2 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ . Figure on the right: The emission spectrum of the accretion disk around a DMPR black hole with tidal charge $Q = - M^{2}$ for different values of the mass accretion rate ${\dot{M}}_{0}$ : $1.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (long dashed line), $1.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (short dashed line), $2.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (solid line), $2.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dotted line), and $3.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dot-dashed line), respectively. The total mass of the black hole is $2.5 \times 10^{6} M_{⊙}$ .Reuse & Permissions
Figure 4
Figure on the left: The time-averaged flux radiated by an accretion disk around a first class CFM black holes for various values of $η$ : $η = - 10$ (long dashed line), $η = - 5$ (short dashed line), $η = 5$ (dotted line) and $η = 10$ (dot-dashed line). The flux for a Schwarzschild black hole is plotted with a solid line. The mass accretion rate is $2 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ . Figure on the right: The time-averaged flux radiated by the accretion disk around a first class CFM black hole for $η = - 10$ and for different values of the mass accretion rate ${\dot{M}}_{0}$ : $1.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (long dashed line), $1.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (short dashed line), $2.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (solid line), $2.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dotted line), and $3.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dot-dashed line), respectively. The total mass of the black hole is $2.5 \times 10^{6} M_{⊙}$ .Reuse & Permissions
Figure 5
Figure on the left: The emission spectrum of the accretion disk around a first class CFM black hole for different values of $η$ : $η = - 10$ (long dashed line), $η = - 5$ (short dashed line), $η = 5$ (dotted line) and $η = 10$ (dot-dashed line). The spectrum for a Schwarzschild black hole is plotted with a solid line. The mass accretion rate is $2 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ . Figure on the right: The emission spectrum of the accretion disk around a first class CFM black hole for $η = - 10$ and for different values of the mass accretion rate ${\dot{M}}_{0} : = 1.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (long dashed line), $1.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (short dashed line), $= 2.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (solid line), $2.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dotted line), and $3.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dot-dashed line), respectively. The total mass of the black hole is $2.5 \times 10^{6} M_{⊙}$ .Reuse & Permissions
Figure 6
The effective potential of the thin accretion disk around a CFM black hole of the second class with a total mass of $M$ and $\tilde{L} = 4 M$ for different values of the parameter $η$ . The potential $V (r)$ corresponding to the Schwarzschild black hole is plotted with a solid line. The values of $η$ are $η = - 0.8$ (long dashed line), $η = - 0.4$ (short dashed line), $η = 0.4$ (dotted line) and $η = 0.8$ (dot-dashed line), respectively.Reuse & Permissions
Figure 7
Figure on the left: The time-averaged flux radiated by an accretion disk around a second class CFM black hole for different values of $η$ : $η = - 0.8$ (long dashed line), $η = - 0.4$ (short dashed line), $η = 0.4$ (dotted line) and $η = 0.8$ (dot-dashed line). The flux for a Schwarzschild black hole is plotted with a solid line. The mass accretion rate is $2 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ . Figure on the right: The time-averaged flux radiated by the accretion disk around a second class CFM black hole with the parameter $η = 0.8$ for different values of the mass accretion rate ${\dot{M}}_{0}$ : $1.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (long dashed line), $1.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (short dashed line), $2.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (solid line), $2.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dotted line), and $3.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dot-dashed line), respectively. The total mass of the black hole is $2.5 \times 10^{6} M_{⊙}$ .Reuse & Permissions
Figure 8
Figure on the left: The emission spectrum of the thin accretion disk around a second class CFM black hole for different values of $η$ : $η = - 0.8$ (long dashed line), $η = - 0.4$ (short dashed line), $η = 0.4$ (dotted line), and $η = 0.8$ (dot-dashed line). The spectrum for a Schwarzschild black hole is plotted with a solid line. The mass accretion rate is $2 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ . Figure on the right: The emission spectrum of the accretion disk around a second class CFM black hole with parameter $η = 10$ for different values of the mass accretion rate ${\dot{M}}_{0}$ : $1.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (long dashed line), $1.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (short dashed line), $2.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (solid line), $2.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dotted line), and $3.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dot-dashed line), respectively. The total mass of the black hole is $2.5 \times 10^{6} M_{⊙}$ .Reuse & Permissions
Figure 9
The effective potential for BMD black holes of a fixed total mass $M$ for $\tilde{L} = 4 M$ and different values of $s$ . The solid line is the effective potential for a Schwarzschild black hole with the same total mass $M$ . The parameter $s$ is set to $s = 5$ (long dashed line), $s = 10$ (short dashed line), $s = 15$ (dotted line) and $s = 20$ (dot-dashed line).Reuse & Permissions
Figure 10
Figure on the left: The time-averaged flux radiated by an accretion disk around a BMD black hole for different values of $s$ : $s = 5$ (long dashed line), $s = 10$ (short dashed line), $s = 15$ (dotted line) and $s = 20$ , respectively. The flux for a Schwarzschild black hole is plotted with a solid line. The mass accretion rate is $2 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ . Figure on the right: The time-averaged flux radiated by the accretion disk around a BMD black hole with $s = 20$ for different values of the mass accretion rate ${\dot{M}}_{0}$ : $1.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (long dashed line), $1.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (short dashed line), $2.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (solid line), $2.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dotted line), and $3.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dot-dashed line), respectively. The total mass of the black hole is $2.5 \times 10^{6} M_{⊙}$ .Reuse & Permissions
Figure 11
Figure on the left: The emission spectrum of the thin accretion disk around a BMD black hole for different values of the parameter $s$ : $s = 5$ (long dashed line), $s = 10$ (short dashed line), $s = 15$ (dotted line), and $s = 20$ . The solid line represents the spectrum for the Schwarzschild black hole. The mass accretion rate is $2 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ . Figure on the right: The emission spectrum of the accretion disk around a BMD black hole with parameter $s = 20$ for different values of the mass accretion rate ${\dot{M}}_{0}$ : $1.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (long dashed line), $1.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (short dashed line), $= 2.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (solid line), $2.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dotted line), and $3.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dot-dashed line), respectively. The total mass of the black hole is $2.5 \times 10^{6} M_{⊙}$ .Reuse & Permissions
Figure 12
The effective potential of a rotating AG brane-world black hole of a total mass $2.5 \times 10^{6} M_{⊙}$ and with spin $a = 0.9982$ for the specific energy $\tilde{E} = 0.8$ and the specific angular momentum $\tilde{L} = 4 M$ . The solid line is the effective potential for a rotating Kerr black hole ( $β = 0$ ) with the same total mass. The different values of $β$ are $β = - 2 M^{2}$ (long dashed line), $β = - M^{2}$ (short dashed line), $β = M^{2}$ (dotted line) and $β = 2 M^{2}$ (dot-dashed line), respectively.Reuse & Permissions
Figure 13
Figure on the left: The time-averaged flux radiated by the accretion disk around a rotating AG brane-world black-hole with spin $a = 0.8892$ for different values of the tidal charge parameter $β$ : $β = - 2 \times 10^{- 3} M^{2}$ (long dashed line), $β = - 10^{- 3} M^{2}$ (short dashed line), $β = 10^{- 3} M^{2}$ (dotted line), and $β = 2 \times 10^{- 3} M^{2}$ (dot-dashed line), respectively. The flux for a Kerr black hole with the same total mass and spin is plotted with a solid line. The mass accretion rate is $2 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ . Figure on the right: The time-averaged flux radiated by the accretion disk around a rotating AG brane-world black hole with spin $a = 0.8892$ and tidal charge $β = - 2 \times 10^{- 3} M^{2}$ for different values of the mass accretion rate ${\dot{M}}_{0}$ : $1.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (long dashed line), $1.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (short dashed line), $= 2.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (solid line), $2.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dotted line), and $3.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dot-dashed line), respectively. The total mass of the black hole is $2.5 \times 10^{6} M_{⊙}$ .Reuse & Permissions
Figure 14
Figure on the left: The emission spectrum of the accretion disk around a rotating AG brane-world black hole with spin $a = 0.8892$ for different values of the tidal charge parameter: $β = - 2 \times 10^{- 3} M^{2}$ (long dashed line), $β = - 10^{- 3} M^{2}$ (short dashed line), $β = 10^{- 3} M^{2}$ (dotted line), and $β = 2 \times 10^{- 3} M^{2}$ (dot-dashed line), respectively. The flux for a Kerr black hole with the same total mass and spin is plotted with a solid line. The mass accretion rate is $2 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ . Figure on the right: The emission spectrum of the accretion disk around a rotating AG brane-world black hole with spin $a = 0.8892$ and tidal charge $β = - 2 \times 10^{- 3} M^{2}$ for different values of the mass accretion rate ${\dot{M}}_{0}$ : $1.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (long dashed line), $1.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (short dashed line), $= 2.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (solid line), $2.5 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dotted line), and $3.0 \times 10^{- 6} M_{⊙} {yr}^{- 1}$ (dot-dashed line), respectively. The total mass of the black hole is $2.5 \times 10^{6} M_{⊙}$ .Reuse & Permissions

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