Perturbative analysis of two-temperature radiative shocks with multiple cooling processes

Abstract

The structure of the hot downstream region below a radiative accretion shock, such as that of an accreting compact object, may oscillate because of a global thermal instability. The oscillatory behaviour depends on the functional forms of the cooling processes, the energy exchanges of electrons and ions in the shock‐heated matter, and the boundary conditions. We analyse the stability of a shock with unequal electron and ion temperatures, where the cooling consists of thermal bremsstrahlung radiation which promotes instability, plus a competing process which tends to stabilize the shock. The effect of transverse perturbations is considered also. As an illustration, we study the special case in which the stabilizing cooling process is of order 3/20 in density and 5/2 in temperature, which is an approximation for the effects of cyclotron cooling in magnetic cataclysmic variables. We vary the efficiency of the second cooling process, the strength of the electron–ion exchange and the ratio of electron and ion pressures at the shock, to examine particular effects on the stability properties and frequencies of oscillation modes.

Effects of Lower Boundary Conditions on the Stability of Radiative Shocks

“…The conditions on the perturbed variables are derived in the frame that is comoving with the shock (Imamura et al 1996; see also appendices of Saxton, Wu, & Pongracic 1997), λ ζ = 0, λ τ = −3, and λ π = λ e = 2. The system parameters are the same as defined in Saxton & Wu (1999): s is the efficiency of cyclotron cooling relative to bremsstrahlung cooling at the shock; σ s is the ratio of electron to ion pressures at the shock; ψ ei specifies the efficiency of electron-ion energy exchange relative to the total efficiency of radiative cooling. The shock boundary conditions are the same in all cases studied; alternative conditions at the lower boundary are considered.…”

“…The perturbed electron pressure and total pressure variables always meet at the same value at the lower boundary, regardless of the boundary condition, because the electron and ion temperatures equilibrate at the lower boundary. For comprehensive discussion of the eigenfunctions, see Saxton (1999) and Saxton & Wu (2001). Saxton (1999, Sections 5.4.1-5.4.2) considered the relationships between eigenvalues and local features of the corresponding eigenfunctions.…”

“…Chevalier & Imamura 1982;Imamura et al 1996;Saxton et al 1997Saxton et al , 1998Saxton & Wu 1999, 2001. When bremsstrahlung emission is the only cooling process the fundamental mode is stable, and the overtones are unstable, with instability δ R tending to increase with harmonic number.…”

“…When cyclotron cooling is very efficient, so that the electron-ion exchange process is unable to maintain strong thermal coupling between electrons and ions, the modes are more like those of a doubly-closed or doubly-open pipe, f ∝ n (Saxton & Wu 1999). The standard analytic treatment defines the lower boundary as the place where the flow velocity becomes zero in the time-independent solution and does not oscillate in the time-dependent response to perturbation (e.g.…”

Accretion physics of AM Herculis binaries

“…The stationarity implies that our solutions describe the mean properties of the shocks and that aspects like rapid fluctuations in the mass flow density and the stability against shock oscillations are left aside. Shock oscillations have been treated by a number of authors (Imamura et al 1996;Saxton & Wu 1999, and references therein) and generally suggest that cyclotron cooling stabilizes the flow and bremsstrahlung cooling destabilizes it. Observationally, optical oscillations have been found in a few polars, while the search for hard X-ray oscillations has so far yielded only upper limits (Larsson 1992;Wolff et al 1999;Imamura et al 2000, and references therein).…”