Stability of Accretion Shocks with a Composite Cooling Function

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

Next Section: APPENDIX B. The perturbed
Title/Abstract Page: Stability of Accretion Shocks
Previous Section: References
Contents Page: Volume 14, Number 2

APPENDIX A. The composite cooling function

We assume that the local total cooling function in the post-shock region is given by
where tex2html_wrap_inline775 is bremsstrahlung cooling function, tex2html_wrap_inline777 the effective cyclotron cooling function, tex2html_wrap_inline779 the bremsstrahlung cooling timescale, tex2html_wrap_inline781 the cyclotron cooling timescale, the subscript ``s'' denotes the values at the shock surface, and tex2html_wrap_inline563, tex2html_wrap_inline787 and tex2html_wrap_inline789 are constants to be determined. The bremsstrahlung cooling function is tex2html_wrap_inline791 (eg. Rybicki & Lightman 1979), and the bremsstrahlung cooling timescale is
where tex2html_wrap_inline793 and tex2html_wrap_inline795 are the electron and proton number density respectively.

We assume that the optically thick cyclotron radiation has a Rayleigh-Jean spectrum up to a critical frequency tex2html_wrap_inline797, and the photons with frequencies beyond tex2html_wrap_inline797 have insignificant contribution to the cooling process and can be neglected. The angle-averaged cyclotron luminosity is therefore
(Langer, Chanmugam & Shaviv 1982), where c is the speed of light, and A and x are the effective area and the thickness of the emission region respectively. For parameters appropriate for accretion shocks in magnetic cataclysmic variables
(Wada et al. 1980), where tex2html_wrap_inline807 is the dimensionless plasma size parameter, tex2html_wrap_inline809 the cyclotron frequency, tex2html_wrap_inline581 the electron mass, and e the electron charge. The effective cyclotron cooling time scale is therefore
(see Langer, Chanmugam & Shaviv 1982). As tex2html_wrap_inline815,
If we assume that tex2html_wrap_inline817, then tex2html_wrap_inline819 and tex2html_wrap_inline821. It follows that
Since tex2html_wrap_inline823 and tex2html_wrap_inline825, we have
Thus, tex2html_wrap_inline827, tex2html_wrap_inline829 and tex2html_wrap_inline831, the ratio of the bremsstrahlung cooling timescale to the cyclotron cooling time scale at the shock surface. In terms of the parameters at the shock surface, the ratio is
(Wu, Chanmugam & Shaviv 1994), where B is the magnetic field, tex2html_wrap_inline835 the shock temperature, tex2html_wrap_inline837 the electron number density at the shock surface, and tex2html_wrap_inline549 the shock height.

Next Section: APPENDIX B. The perturbed
Title/Abstract Page: Stability of Accretion Shocks
Previous Section: References
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