Stability of Accretion Shocks with a Composite Cooling Function

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

Next Section: Perturbation Analysis
Title/Abstract Page: Stability of Accretion Shocks
Previous Section: Introduction
Contents Page: Volume 14, Number 2

Accretion onto Magnetic White Dwarfs

The height of accretion shocks (i.e. the thickness of post-shock regions), tex2html_wrap_inline549, of magnetic white dwarfs are generally tex2html_wrap_inline551, where tex2html_wrap_inline553 is the white dwarf radius. For typical accretion rates (tex2html_wrap_inline555), the ram pressure of the accretion matter near the white dwarf surface is less than the magnetic stress. As the accretion flow is channelled by the field lines, it can be approximated by a one-dimensional planar model. The time-dependent continuity and momentum equations are therefore
equation26
and
equation34
where P is the pressure and v is the velocity. If we assume that the temperature of the accretion matter is proportional to tex2html_wrap_inline561 and the matter has an adiabatic index of 5/3, the energy equation is then
eqnarray42

equation54
(cf. Wu 1994), where tex2html_wrap_inline563 is the effective ratio of the bremsstrahlung cooling timescale to the cyclotron cooling timescale at the shock surface. In the above equation and hereafter, the subscript ``s'' denotes parameters and variables at the shock surface. The coefficient tex2html_wrap_inline567tex2html_wrap_inline569tex2html_wrap_inline571 corresponding to bremsstrahlung cooling, where tex2html_wrap_inline573 is the Boltzmann constant, h the Planck constant, c the velocity of light, e the electron charge, tex2html_wrap_inline581 the electron mass, tex2html_wrap_inline583 the proton mass, tex2html_wrap_inline585 the mean molecular weight of the gas and tex2html_wrap_inline587 the Gaunt factor (see Rybicki & Lightman 1979). The numerical value of tex2html_wrap_inline589 is tex2html_wrap_inline591 in c.g.s. units, assuming that tex2html_wrap_inline593 and tex2html_wrap_inline595. For typical parameters of AM Herculis systems, tex2html_wrap_inline597 and tex2html_wrap_inline599 (Appendix A).

We assume a `stationary wall' boundary condition at the white dwarf surface, so that the lower boundary condition is v = 0. At the shock surface, we assume the strong shock condition, so that tex2html_wrap_inline603, tex2html_wrap_inline605 and tex2html_wrap_inline607, where tex2html_wrap_inline609 is the free-fall velocity at the white dwarf surface and tex2html_wrap_inline611 is density above the shock. With the boundary conditions specified, a closed-form steady state solution tex2html_wrap_inline613 to equations (1), (2) and (3) and a steady state shock height tex2html_wrap_inline615 can be obtained. (Wu, Chanmugam & Shaviv 1994, see also Aizu 1973 and Chevalier & Imamura 1982 for the cases of single power-law form cooling functions).


Next Section: Perturbation Analysis
Title/Abstract Page: Stability of Accretion Shocks
Previous Section: Introduction
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