Stability of Accretion Shocks with a Composite Cooling Function

Curtis J. Saxton , Kinwah Wu , Helen Pongracic, PASA, 14 (2), in press.

Title/Abstract Page: Stability of Accretion Shocks
Previous Section: APPENDIX A. The composite
Contents Page: Volume 14, Number 2

APPENDIX B. The perturbed boundary conditions

Consider a reference frame which is co-moving with the shock surface. Let the subscripts ``1'' and ``2'' denote the quantities in the pre-shock and the post-shock regions respectively, and the `prime' and `un-prime' denote the observers' and the new reference frame (co-moving with the shock surface) respectively. If the velocity in the observer's frame is u, then the velocity in the new reference frame is
eqnarray309
From eqn (4), we therefore obtain the velocity of the accretion matter
eqnarray313
From the continuity equation we have
eqnarray317
Since tex2html_wrap_inline843 (where tex2html_wrap_inline611 is the density above the shock surface), we have tex2html_wrap_inline847. For a strong shock, tex2html_wrap_inline849. It follows that
eqnarray319
and
eqnarray325
On the other hand, we have
eqnarray333
and
eqnarray337
Hence,
eqnarray341
The gas pressure of the pre-shock gas near the shock surface is given by
eqnarray345
Since
eqnarray361
we have
eqnarray364


Title/Abstract Page: Stability of Accretion Shocks
Previous Section: APPENDIX A. The composite
Contents Page: Volume 14, Number 2

Welcome... About Electronic PASA... Instructions to Authors
ASA Home Page... CSIRO Publishing PASA
Browse Articles HOME Search Articles
© Copyright Astronomical Society of Australia 1997
ASKAP
Public