## An analytic study of Bondi-Hoyle-Lyttleton accretion## I. Stationary flows
We prove that the sonic surface of axisymmetric meridional stationary flows is always attached to the accretor, however small, if the adiabatic index of the gas is . Using local expansions near a point-like accretor, we extend Bondi's classification of spherically symmetric flows to axisymmetric flows, introducing the possibility of angular sectors reached by no flow lines, and singular directions of infinite mass flux, in addition to the angular regions of subsonic and supersonic accretion. For , we show the impossibility of subsonic accretion onto a point-like accretor when the entropy of the flow is not uniform. The special case is treated separately. We analyse the influence of the adiabatic index and Mach number of the flow at infinity on the mass accretion rate of shocked spherical flows. We propose an interpolation formula for the mass accretion rate of axisymmetric flows as a function of the Mach number and the adiabatic index, in the range .
## Contents- 1. Introduction
- 2. Equations of a stationary flow in a gravitational potential
- 3. The sonic surface of axisymmetric stationary flows
- 4. Asymptotic expansions near the accretor
- 5. Mass accretion rate for a spherically symmetric flow with non-vanishing kinetic and thermal energies at infinity
- 6. An interpolation formula for the mass accretion rate of an axisymmetric flow with
- 7. Conclusions
- Acknowledgements
- Appendix
- Appendix A: third order partial differential system for an axisymmetric stationary flow
- Appendix B: proof of the property of the axisymmetric sonic surface of Type F flows
- Appendix C: linearized partial differential equation for
- Appendix D: linearized partial differential equation for
- Appendix E: approximation of the orbits within the supersonic region by hyperbolae
- Appendix F: entropy gradient produced by a detached shock in the vicinity of the axis of symmetry
- References
© European Southern Observatory (ESO) 1997 Online publication: July 3, 1998 |