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

From eqn (4), we therefore obtain the velocity of the accretion matter

From the continuity equation we have

Since (where is the density above the shock surface), we have . For a strong shock, . It follows that

and

On the other hand, we have

and

Hence,

The gas pressure of the pre-shock gas near the shock surface is given by

Since

we have

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