1 Introduction

The thermal structure of the accretion columns on accreting magnetic white dwarfs can be derived analytically for a single-particle fluid and sufficiently simple assumptions on the radiative cooling (Aizu 1973; Chevalier & Imamura 1982; Wu et al. 1994). For the more general case of the optically thick frequency and angle-dependent radiative transfer in a two-fluid plasma, the coupled hydrodynamic and radiative transfer equations have to be solved numerically (Woelk & Beuermann 1996, henceforth WB96). In this paper, we present results which are improved and expanded over those of WB96. We obtain the temperature and density profiles for plane-parallel post-shock cooling flows and derive fit formulae for the peak electron temperature $T_{\max}$, the column density $x_{\rm s}$, and the geometrical shock height $h_{\rm sh}$ as functions of the magnetic field strength B and the mass flow density (accretion rate per unit area) $\dot m$. For low $\dot m$ and high B, we show that the shock solution merges into the non-hydrodynamic bombardment solution for an atmosphere which is heated by a stream of fast ions and cools by cyclotron radiation (Woelk & Beuermann 1992, 1993, henceforth WB92, WB93).

Our treatment of radiation-hydrodynamics is onedimensional and stationary. The one-dimensionality implies that our solutions are strictly applicable only to pillbox-shaped emision regions with a width $D \gg$ $h_{\rm sh}$ and a stand-off distance $h_{\rm sh}$ $\ll$ $R_{\rm wd}$, where $R_{\rm wd}$ is the white dwarf radius. 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).