In the stream accreting white dwarfs the material falls freely down the magnetic field lines, converting all the gravitational potential energy into kinetic energy. The velocity at the white dwarf surface is GM/R= mv2/2 i.e. of order 2 per cent of the speed of light for a solar mass object. This kinetic energy is then re-radiated when the material hits the surface, abruptly decelerating in a strong shock. If the stream is dense enough then the shock buries itself into the white dwarf photosphere, releasing the energy in an optically thick environment and radiating more or less as a blackbody in the UV part of the spectrum. Otherwise the energy is dissipated above the photosphere, and the material heats up to X-ray temperatures, and cools by optically thin free-free emission from the gas stream as it smashes onto the white dwarf surface at the magnetic pole.
At the typical temperature of $\sim 10$ keV for the opticaly thin shock, the X-ray plasma itself is not completely ionised and so can give atomic features on the emission spectrum. The ionization state is determined by electrons colliding with atoms and ions in the gas, and the higher the electron temperature then the higher the ionization state of the plasma. As these ions recombine they produce line emission (and free-bound recombination radiation) which depends strongly on the ionization state. Thus the temperature of the gas can be measured in two ways, firstly from the shape of the free--free continuum radiation, and secondly from the characteristics of the recombination lines.
This X--ray emission (lines and all) should illuminate the white dwarf surface, producing a reflected continuum and additional fluorescent iron line emission. This was first observationally identified in polars by Andy Beardmore from the University of Leicester, UK, myself and collaborators in 1995, using data from the brightest polar, AM Her. The inclusion of the hard reflected spectrum means that the intrinsic emission from the shocked plasma is then at a rather lower temperature than was previously believed, with a mean temperature of $kT\sim 15$~keV rather than 30~keV. This resolves a long standing discrepancy between the apparently very hot plasma continuum temperature and the much lower temperature implied by the plasma line emission.
However, the X-ray spectrum should be more complex than just a single temperature plasma and its reflection. Firstly the accretion flow just above the shock should produce absorption, which is clearly seen in the observed X-ray spectra of these objects. In 1995 I led a calculation of simple models the expected absorption distribution of this column assuming that it was made up of neutral material. This fails to fit the observed absorption from the bright polar EF Eri, probably indicating that the material is partially ionised. This conclusion was reinforced with data from another bright polar BY Cam which I analysed in 1997. In these two studies we also realised that the shock itself should consist of multiple temperature components as the material cools in order to join onto the white dwarf photosphere. The main signature of this cooling is that we should see low temperature iron recombination lines at around 1 keV co--existing with high temperature recombination lines at 6.7 keV (Done, Osborne \& Beardmore 1995). The form of the expected cooling has been known theoretically for many years, but we detected this for the first time in the X--ray spectrum of BY Cam (see figure 5b)