The possible existence of accretion disks was originally predicted from theoretical considerations. An accretion disk occurs, when gas with non-zero angular momentum accretes onto a compact central object. The gas particles, mainly electrons and ions, interact by collisions. In addition electromagnetic forces transport angular momentum outwards. A mean free path length X is used to describe these interactions. The gas particles move along the path length before they change their direction or velocity due to a collision with another particle. For a distant observer (r >> X), the accretion flow can be described by a fluid motion, characterized by the parameters velocity v, temperature T and density p at a certain position. The calculating of the accretion process onto a compact central object and the emitted radiation spectrum is complicated. First, solutions for the movement of particles in the gravitational potential of the central black hole have to be found. Such solutions result from the continuity equation, the equation of state for an ideal gas, and the Euler equation (Chap. 2, ). Assuming spherical symmetric accretion, and neglecting forces other than the gravitational force, solutions are shown in Fig. 22.1 of . In the calculation of the emitted spectrum, cooling and heating processes have to be considered. In addition, the influence of magnetic fields can be of importance. A detailed discussion of all these effects is given in Chap. 4 of .
Accretion onto a compact object is an effective process in the release of radiation. To first order, this radiation release can be approximated by the change in potential energy AEaccretion of a test particle with mass m, in the gravitational field of a black hole, as
The accretion luminosity Laccretion, which represents the emitted amount of energy per time unit, can be derived from AEaccretion as
Laccretion = Z--TT^- = Z ^- = 7T ■ Mc2 = n ■ Mc2
M is the accretion rate and n = 2 is the term which describes the efficiency of the accretion process. The efficiency of converting matter into radiation in the accretion process onto a non-rotating black hole is n = 0.057 . For accretion onto a rotating black hole the corresponding value is n = 0.29 . With an accretion rate of only one solar mass per year, a luminosity of 1046 erg s-1 is obtained (assuming n = 0.1). This is typical of values measured in high- luminosity active galaxies.
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