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Accretion onto Black Holes

  • Chapter
Introduction to Black Hole Astrophysics

Part of the book series: Lecture Notes in Physics ((LNP,volume 876))

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Abstract

This chapter presents a detailed account of all forms of accretion onto black holes. The basic expressions for spherical, cylindrical, and disk accretion are developed. Advection-dominated accretion is also discussed, as well as different accretion regimes in binary systems.

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Notes

  1. 1.

    There is a second term η B(∇⋅v)δ ij in the stress tensor. The coefficient η B is the bulk viscosity, that we shall assume to be zero.

  2. 2.

    It is a common practice in the study of fluid dynamics to work with the total or material derivative of a function f(x,t), defined as df/dt=∂f/∂t+(v⋅∇)f. The second term is called the convective derivative.

  3. 3.

    Notice that T∝r −1 and ρ∝r 3/2.

  4. 4.

    See, however, Foglizzo and Ruffert (1997, 1999) for some general analytical results.

  5. 5.

    These amounts to assuming that the mean free path of the particles is much larger than the characteristic length scale of the problem, given by the accretion radius and the size of the accretor.

  6. 6.

    See Edgar (2004) for a proof of this statement.

  7. 7.

    In 2D simulations the shock is always attached to the accretor, although calculations by Foglizzo et al. (2005) suggest that it should get detached for γ∼3.

  8. 8.

    Notice that for a disk in rigid rotation ∂Ω/∂R=0 and the internal torques vanish.

  9. 9.

    The same criterion applies to the global stability of the disk under axisymmetric perturbations with kR≫1, where k is the wavenumber of the perturbation.

  10. 10.

    There is another possible solution with v(θ=0)=−ε′/2α. This is a generalization of the spherically symmetric Bondi accretion to viscous flows.

  11. 11.

    Narayan and Yi (1995b) adopted a value of the Eddington accretion rate of \(\dot{M}_{\mathrm{Edd}}=L_{\mathrm{Edd}}/0.1c^{2}\approx1.39\times 10^{18} M/M_{\odot}\ \mbox{g\,s}^{-1}\).

  12. 12.

    The viscous timescales in the inner regions of the disk, where the neutrinos are emitted, are much shorter than the typical timescales of variation of the accretion rate in the outer disk (di Matteo et al. 2002). Furthermore, Kohri and Mineshige (2002) have shown that for sufficiently large temperature and density (T∼1011 K, ρ∼1013 g cm−3) the timescale of positron/electron capture by nucleons (see text) and the timescale for neutrino diffusion in the vertical direction are both shorter than the accretion timescale. Under these conditions, the steady-state approximation is justified.

  13. 13.

    Degenerate matter does not add to the entropy of the flow.

  14. 14.

    In the strong magnetic field (∼1015 G) expected to exist in the central engines of GRBs, neutrinos can also create pairs through the reaction ν→ν+e ++e −, see e.g. Gvozdev and Ognev (2001).

  15. 15.

    The Coriolis force is not included in Eq. (4.196).

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Romero, G.E., Vila, G.S. (2014). Accretion onto Black Holes. In: Introduction to Black Hole Astrophysics. Lecture Notes in Physics, vol 876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39596-3_4

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