Energetic particle acceleration in spherically symmetric accretion flows - Importance of a momentum-dependent diffusion coefficient

Details Energetic particle acceleration in spherically symmetric accretion flows - Importance of a momentum-dependent diffusion coefficient Energetic particle acceleration in spherically symmetric accretion flows - Importance of a momentum-dependent diffusion coefficient

Dec 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989apj...347..496s&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 347, Dec. 1, 1989, p. 496-504.

Statistics

Computation

10

Diffusion Coefficient, Galactic Cosmic Rays, Particle Acceleration, Transport Theory, Black Holes (Astronomy), Computational Astrophysics, Radiation Distribution, Stellar Mass Accretion

Scientific paper

We study the transport of suprathermal particles in steady spherical accretion flows under the assumption that the flow velocity V(r) ∝ - r-α, and that the spatial diffusion coefficient κ(r, p) ∝ rβpγ, can be expressed as power laws. We derive the solution of the transport equation for arbitrary combinations of the parameters (α, β, γ), thereby generalizing previous work on this subject. In addition, a collisional loss term is also taken into account. Two different boundary conditions are considered: either, there is a monoenergetic injection of particles into the flow, or there are no sources at finite radius, but the distribution function is required to match smoothly onto a prescribed ambient energetic particle population at infinity. We find that the parameter space (α, β, γ) divides naturally into three regions that reflect the nature of the particle transport in the vicinity of the singularity located at the origin. If α + β < 1 then all injected particles are absorbed by the singularity at the origin. If α + β > 1 and γ exceeds the critical value y* = y*(α, β), then no particles are absorbed by the origin. In the remainder of the parameter space some fraction of the particles are advected into the origin and the remainder escape to infinity.
The emergent particle flux is a power law for large momenta, with the hardest spectra being obtained for γ ˜ γ*. In contrast with the previously studied Comptonization case where (in the nonrelativistic limit) γ = 0 and the compression of the accretion flow amplifies the emergent luminosity by only a small factor, drastic enhancements are possible when γ is asymptotically equal to γ*. The possible implication of our results for cosmic-ray acceleration in our Galaxy is briefly discussed.

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