Stability properties of two-temperature radiative accretion shocks

Saxton & Wu (1999) presented calculations of the stability of the accretion shock which forms on the surface of an accreting magnetic white dwarf in AM Herculis type systems in an attempt to explain the observed properties of the quasi periodic oscillations sometimes seen in these systems. He showed that radiative cooling may cause thermal instability in the post-shock structure of the accretion flow settling onto a magnetic white dwarf. The stability and oscillatory properties depend on the functional forms and relative efficiencies of the cooling processes present, and also on the efficiency of energy exchange between the electrons and ions, which may in general have different temperatures. For conditions appropriate for accreting magnetic white dwarfs, we perform a linear stability analysis with unequal electron and ion temperatures and two competing cooling processes: bremsstrahlung cooling which promotes instability; and cyclotron cooling which tends to dampen oscillations. As with a single-temperature flow, the mode frequencies exhibit approximately linear quantisation. The frequency spacing depends mainly on the efficiency of cyclotron cooling. The modes' stabilities are sensitively dependent on the global parameters, and consecutive modes do not necessarily have similar stabilities. Except when the electron and ion pressures are very different at the shock, increasing the cyclotron cooling efficiency increases the stability of each mode. Transverse perturbations destabilise the modes over certain ranges of wavenumber, but these ranges are reduced when cyclotron cooling is important, unless the two fluid components' pressures differ greatly at the shock. Two-temperature conditions have little effect on the oscillatory properties when bremsstrahlung is the dominant cooling process, but a cyclotron-dominated shock is sensitive to the two-temperature parameters. When the electron-ion exchange is very weak, the lower boundary loses importance and the oscillatory properties are determined by the energy exchange rather than the cooling (Figure 5).

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