Michel accretion of a polytropic fluid with adiabatic index $\gamma \gt 5/3$: global flows versus homoclinic orbits - INSPIRE

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Michel accretion of a polytropic fluid with adiabatic index $\gamma \gt 5/3$ : global flows versus homoclinic orbits

Nov 24, 2015

17 pages

Published in:

Class.Quant.Grav. 33 (2016) 10, 105016

Published: Apr 27, 2016

e-Print:

1511.07728 [gr-qc]

DOI:

10.1088/0264-9381/33/10/105016

View in:

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Abstract: (IOP)

We analyze the properties of a polytropic fluid that is radially accreted into a Schwarzschild black hole. The case where the adiabatic index γ lies in the range of

1\lt \gamma \leqslant 5/3

has been treated in previous work. In this article, we analyze the complementary range of

5/3\lt \gamma \leqslant 2

. To this purpose, the problem is cast into an appropriate Hamiltonian dynamical system, whose phase flow is analyzed. While, for

1\lt \gamma \leqslant 5/3

, the solutions are always characterized by the presence of a unique critical saddle point, we show that, when

5/3\lt \gamma \leqslant 2

, an additional critical point might appear, which is a center point. For the parametrization used in this paper, we prove that, whenever this additional critical point appears, there is a homoclinic orbit. Solutions corresponding to homoclinic orbits differ from standard transonic solutions with vanishing asymptotic velocities in two aspects: they are local (i.e., they cannot be continued to arbitrarily large radii), the dependence of the density or the value of the velocity on the radius is not monotonic.

Note:

13 pages, 3 figures

04.20.-q
04.70.-s
98.62.Mw
accretion flows
black holes
Hamiltonian dynamical systems

References(23)

Figures(3)

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