Introduction to accretion and accretion disks

As we have discussed in §2.2 and §2.3, many of the observable effects from black hole systems arise due to the accretion of gas. At its most basic level, gravitational potential energy can be released from the accreting matter and produce electromagnetic radiation or power bi-polar outflows or jets. More exotic is the possibility that accreting matter may produce and support magnetic fields which interact with the rotating black hole thereby facilitating the extraction of its spin energy via, for example, the process elucidated by Roger Blandford and Roman Znajek [107].

In any realistic scenario, matter will be accreting from a substantial distance and will possess significant angular momentum. In this case, we expect the accreting gas to form a rotationally-flattened structure orbiting the black hole, an accretion disk. A particular element of gas in the accretion disk will then lose angular momentum through a process which is loosely referred to as viscosity, thereby allowing it to flow slowly inwards towards the black hole and eventually accrete. While the nature of this angular momentum transport was mysterious for some time, we now believe it to be due to magneto-hydrodynamical (MHD) turbulence driven by a well-studied instability, the magnetorotational instability (MRI). In this section, we shall present the ``standard'' black hole accretion disk model and discuss these MHD phenomena. We then proceed to discuss disk atmospheres and the X-ray spectral signatures that result from these surface layers. Readers who are already familiar with accretion disk physics and X-ray reflection may wish to skip to §4. An excellent review of disk hydrodynamics and MHD, with emphasis on turbulent transport within astrophysical disks, is given by Steven Balbus and John Hawley [108].

Before launching into a detailed discussion of accretion disks, we must introduce the concept of the Eddington limit. Consider spherically-symmetric accretion onto an object of mass $M$, producing a radiative luminosity of $L$. If the accreting material is totally ionized, its opacity will be dominated by electron-scattering. If $L$ exceeds a critical luminosity (the Eddington luminosity) given by

$$L_{\rm Edd}=\frac{4\pi c G M \mu_e}{\sigma_{\rm T}},$$ 4

where $\mu_e$ is the mass per electron and $\sigma_{\rm T}$ is the electron scattering cross section, then the outward pressure of radiation will exceed the inward force of gravity making prolonged accretion an impossibility. While the Eddington luminosity strictly applies to spherically-symmetric systems, it also probably sets a practical limit for the luminosity of disk-like accretion flows (although there are recent suggestions that MHD processes may allow the limit to be somewhat violated [109]).