Computer Science – Sound
Scientific paper
Mar 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982phdt........18f&link_type=abstract
Thesis (PH.D.)--CALIFORNIA INSTITUTE OF TECHNOLOGY, 1982.Source: Dissertation Abstracts International, Volume: 43-03, Section: B
Computer Science
Sound
Scientific paper
First we formulate a general set of equations governing stationary spherical accretion into black holes. The equations are fully general relativistic and are applicable to optically thick regions, optically thin regions, and the transition regions which join them. By the phrase "optically thick" it is meant that (1) radiative energy transport can be adequately described by the diffusion approximation and (2) the photons are everywhere in local energy equilibrium with the accreting gas particles. Then we present the mathematical theory of stationary spherical optically thick accretion into black holes. We analyze the integral curves of the differential equations describing the problem. We find a one-parameter family of critical points, where the inflow velocity equals the isothermal sound speed. Physical solutions must pass through one of these critical points. We obtain a complete set of boundary conditions which the solution must satisfy at the horizon of the black hole, and show that these, plus the requirement that the solution pass through a critical point, determine a unique solution to the problem. This analysis leads to a generalization of the well-known Bondi critical point constraint, which arises in the adiabatic accretion problem and which is effective at the point where the inflow velocity equals the adiabatic sound speed. We show that this point can be regarded as a "diffused critical point" in our problem. The analysis also yields a simple expression for the diffusive luminosity at radial infinity. We find a satisfying explanation for the peculiar critical point structure of this problem in an analysis of the characteristics and sub-characteristics present in the problem and in a "hierarchical" analysis of the waves which propagate along them. Finally, we apply the theory over a wide range of different accretion regimes. We consider gas pressure dominated solutions, radiation pressure dominated solutions, and solutions in which the radiation energy density dominates the rest-mass energy density of the gas particles. Numerical solutions are presented and their physical properties are discussed. We find the dimensionless number which governs the importance of energy diffusion in this problem. We also discuss the stability of these solutions against convection.
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