Simulation

Emission Region

When the supersonic matter is decelerated abruptly to settle onto the surface of an accreting white dwarf, a strong accretion shock is formed. The shock heats the accreting matter to a temperature  keV, causing it to ionise and to emit bremsstrahlung X-rays. Bremsstrahlung cooling is generally efficient as the shock-heated matter has very high temperatures ( K) and densities (). For white dwarfs with a strong (> 1 MG) magnetic field, cyclotron cooling is also important, and for systems with low accretion rates and very strong ( MG) magnetic fields, it may be the more important process. The cooling processes determine the density and temperature structures of the shock-heated region and hence the properties of the radiation emitted from the region.

In this study we assume a simple one-dimensional planar model for the shock-heated emission regions of accreting magnetic white dwarfs. We use the hydrodynamic formulation given in Wu, Chanmugam & Shaviv (1994) (see also Wu 1994, and Cropper, Ramsay & Wu 1998 for the correction) for accretion flow with a composite cooling process to determine the density and temperature structures of the emission region. We assume that only bremsstrahlung and cyclotron cooling are important, and ignore other cooling processes. We divide the shock-heated emission region into 200 vertically stratified zones. The sizes of the zones are chosen such that the difference between the flow velocities at the zone boundaries is 1/200 of the pre-shock free-fall velocity in order to avoid unphysical weighing of the emission from the dense bottom zones near the white dwarf surface. The local effective temperature and density are calculated from the mean flow velocity of the zones.

We assume the coronal condition (Wilson 1962; Mewe 1990), so that the line and continuum radiation emitted from each zone can be calculated using the MEKAL opacity code (Mewe, Gronenschild & van den Oord 1985, Mewe, Kaastra & Liedahl 1995) from XSPEC (Arnaud 1996). The total emission is the sum of the contributions from all zones in the shock-heated region.

To avoid unnecessary complication in this demonstration study, we ignore effects due to absorption by the cool material surrounding the shock-heated region (Done, Osborne & Beardmore 1995; Mukai, Ishida & Osborne 1997) and effects due to reflection from the white-dwarf surface (van Teeseling, Kaastra & Heise 1996). These effects, which are strongly source dependent, may be important and should be considered in analysing the actual data (e.g., Cropper, Ramsay & Wu 1998).

We consider cases for white dwarfs with masses (M) of 0.5  and 1.0-. We use the Nauenberg (1972) mass-radius relation to determine the white dwarf radius. The relative strengths of the bremsstrahlung and cyclotron cooling processes are determined by the white-dwarf magnetic field and the accretion rate; and they are specified by a parameter , which is the ratio of the bremsstrahlung-cooling timescale to the cyclotron-cooling timescale at the accretion-shock surface. For , only bremsstrahlung cooling is present; for , both bremsstrahlung and cyclotron cooling have equal strength at the shock surface; for , cyclotron cooling is the dominated process at the shock surface. We fix the specific accretion rate to be 1 g cm s; large corresponds to strong white-dwarf magnetic field. (If we fix the magnetic field instead, then larger correspond to lower accretion rates. See Wu, Chanmugam & Shaviv 1994 for the dependence of on the white-dwarf magnetic field and the accretion rate.) We set the cross-section area of the emission region to be  cm and the distance of the system, 100 pc, and assume solar abundances.

Spectral Synthesis

We calculate the raw input spectra, using the temperature and density structures determined by the hydrodynamic calculations and the MEKAL code for the X-ray emission. Fig. 1 shows the raw spectra of the systems with a 1.0-M white dwarf and = 0, 1, and 100. As the resolution of the spectra is limited mainly by the binning process, the emission lines all appear to be sharp and precisely resolved. The K lines of H- and He-like ions of O, Mg, Si, S, Ar, Ca and the Fe lines are clearly seen. The Fe L lines are prominent, with hints that the strength of the lines increase with , the efficiency of cyclotron cooling relative to bremsstrahlung cooling. In Fig. 2 the raw spectra of the 0.5-M accreting white dwarfs are shown. The general features in the spectra of the 0.5-M white dwarfs are similar to those in the spectra of the 1.0-M white dwarfs, except that the emission lines below 2 keV are generally stronger and the continua are weaker. Moreover, the strength of the Fe L lines are also stronger for = 100 than for = 0 and 1.

The system parameters we have assumed in our simulation are similar to the system AM Herculis itself, whose white-dwarf mass is about 1 M (Cropper, Ramsay & Wu 1998), magnetic field is about 20 MG (Chanmugam 1992), distance is about 75 pc (Cropper 1990). To verify the normalisation in our simulation we consider the case for the 1.0-M white dwarf and fold the raw spectra through the EXOSAT ME response. We obtain the count rates 4.1, 3.1 and 1.6 ct/s at 1 - 10 keV for 0, 1 and 100 respectively. These count rates are consistent with the count rate of 4.5 ct/s, derived from the EXOSAT ME observation of the system AM Herculis itself in Aug 10, 1983 (data were obtained from the High Energy Astrophysics Science Archive Research Center).

In Fig. 3 we show the simulated HEG spectra of white dwarfs with parameters (M/M, ) = (0.5, 0), (0.5, 1) and (1.0, 100) for an integration time of 100 ksec. The photon counts and the corresponding Poisson noise of the spectra are simulated. The K lines of Mg, Si, S, Ar, Ca and Fe are well resolved in the spectra. In Fig. 4 the MEG spectra for the same `observing' condition are shown. The MEG, which offers better effective area below about 4 keV, clearly resolves the O, Mg and the Fe L lines.

For comparison, we also simulate the X-ray spectra for an instrument without gratings. We use the ASCA SIS as a demonstration. We fold the raw spectra through the ASCA SIS response function, for an integration time of 100 ksec. The K lines of Si, S and Ar are still visible (Fig. 5), but are not as obvious as those in the AXAF grating spectra. The Mg lines now blend with the lower excitation Fe lines; the Ca and O lines are no longer clearly visible, and the Fe L lines are smeared beyond the resolution of the instrument.

© Copyright Astronomical Society of Australia 1997