Curtis J. Saxton , Kinwah Wu , Helen Pongracic, PASA, 14 (2), in press.
Next Section: Results and Discussions Title/Abstract Page: Stability of Accretion Shocks Previous Section: Accretion onto Magnetic White | Contents Page: Volume 14, Number 2 |
Perturbation Analysis
Following Chevalier & Imamura (1982), we consider a perturbation
where is the perturbed velocity of the shock surface, taken to be real, and 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
where . We also assume that the perturbed variables are given by
where . Substituting equations (6), (7) and (8) into equations (1), (2) and (3) and considering the dimensionless variables , , , and , we obtain three complex, linear perturbed equations
and
where
Equations (9), (10) and (11) can be separated into six real decoupled linearised equations. With the boundary conditions, at the white dwarf surface, and , and at the shock surface (see Appendix B), the eigenvalues , and hence , 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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