Stability of Accretion Shocks with a Composite Cooling Function

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

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Title/Abstract Page: Stability of Accretion Shocks
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Perturbation Analysis

Following Chevalier & Imamura (1982), we consider a perturbation
equation81
where tex2html_wrap_inline617 is the perturbed velocity of the shock surface, taken to be real, and tex2html_wrap_inline619 is the complex eigenvalue which determines the stability. (Hereafter, the subscripts ``0'' and ``1'' denote the steady state and the perturbed quantities respectively.) The time-dependent shock height is
equation87
where tex2html_wrap_inline621. We also assume that the perturbed variables are given by
eqnarray93
where tex2html_wrap_inline623. Substituting equations (6), (7) and (8) into equations (1), (2) and (3) and considering the dimensionless variables tex2html_wrap_inline625, tex2html_wrap_inline627, tex2html_wrap_inline629, tex2html_wrap_inline631 and tex2html_wrap_inline633, we obtain three complex, linear perturbed equations
equation103

equation116
and
eqnarray125

eqnarray137

eqnarray144
where
equation151

Equations (9), (10) and (11) can be separated into six real decoupled linearised equations. With the boundary conditions, tex2html_wrap_inline635 at the white dwarf surface, and tex2html_wrap_inline637, tex2html_wrap_inline639 and tex2html_wrap_inline641 at the shock surface (see Appendix B), the eigenvalues tex2html_wrap_inline643, and hence tex2html_wrap_inline619, can readily be obtained.


Next Section: Results and Discussions
Title/Abstract Page: Stability of Accretion Shocks
Previous Section: Accretion onto Magnetic White
Contents Page: Volume 14, Number 2

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