Diagnostic Capabilities

Because of temperature and density stratification in the emission region, emission lines of different elements are emitted from different heights above the white dwarf surface. The free-fall velocity at the surface of a 0.5-M white dwarf is . This will cause an energy shift of about 1 part in 100 for the centre energies of the emission lines. For typical mCV parameters (e.g., a specific accretion rate of about 1 g/cm/s), the emission from the shock-heated region are optically thick in the optical bands. The capability of optical spectroscopy is therefore limited, despite that it can provide a very high velocity resolution.

The keV emission lines, however, can be optically thin down to about 10 m above the white dwarf surface. The spectral resolving power () of 1000 provided by the AXAF gratings implies a velocity resolution of , which is sufficient to resolve the velocity shift of the lines from the post-shock matter of an accreting white dwarf.

We show in Fig. 6 the simulated MEG spectra over the energy range 0.5-1.2 keV with linear scales in photon counts and energy for accreting white dwarfs with the same parameters as those in Fig. 3 and 4. This demonstrates that in spite of the noise in the spectra shown in Fig. 4, lines such as the O VII Lyman- line (at 0.653 keV), and the O VII He4 and He5 lines (at 0.574 keV and 0.569 keV respectively) are actually strongly detected and well resolved by the MEG. The forbidden O VII He6 line (at 0.561 keV) is, however, undetected because it is suppressed (see e.g. Mewe 1990) by the high density ( g/cm) in the emission region. Since the line features in the three cases we consider are distinguishable, the grating spectra to be obtained by AXAF can be used to constrain the system parameters such as the white dwarf mass and the parameter . As depends on the accretion rate, the magnetic field and the mass of the white dwarf, if the mass and the magnetic field are known, one may also deduce the accretion rate.

In Fig. 7 we show the simulation of the O VII He4 and He5 lines emitted from a system with M = 1.0 M and . Although the two lines appear to have about the same amplitude, their fluxes are actually quite different. There are about 1000 counts in the He5 line and 1300 counts in the He4 line. The same apparent amplitude for the lines is due to the binning effect, i.e., the center of the He5 line is closer to the center of a bin, whereas the center of the He4 line is closer the boundary between two bins.

We model the lines with Lorentzians and the continuum with a constant term and obtain the 1  uncertainty in the location of the line centres of about 0.01 eV. The uncertainty in the mean is generally equal to the uncertainty in the population divided by the square root of the number of measurements. When the line dominates the continuum, each photon detection in the line is an independent measurement of the line center, i.e., each photon independently has a 68% chance of falling within one (instrumental) of the line center. Therefore, we have , where is the instrumental width, the uncertainty in the line center energy, and N the number of photons in the line. At the energy range  keV, is about 0.3 eV. Hence, for 1000 photons the uncertainty in the line center is 0.01 eV, consistent with what we have measured from the simulation.

We expect the systematic error of ACIS to be much less than 10%. If we increase the uncertainty in the flux for every point by 10% to allow for systematic errors, we find the the formal 1 uncertainty in the line position increases only to 0.04 eV. This value is still better than the instrumental resolution. Therefore, provided that there are enough counts to detect the line, say 10 or more, one should be able to locate the centre accurately.

The instrumental resolution at the O VII lines implies that the velocity of the accreting matter that emits the lines can be measured to an accuracy better than  cm/sec. With 1000 counts in the line and no systematic errors (i.e. an uncertainty of 0.01 eV), the velocity uncertainty is  cm/s. Thus, if we divide the data into 10 orbital phase bins (for the measurement of the variations in the velocity due to orbital motion) and allow the line flux to be weakened by a factor of a few, a velocity resolution of  cm/sec can still be achieved. As we have presented a very conservative estimate, higher velocity resolution is achievable if strong lines are used and/or the sums of several lines are considered. Our simulations therefore have shown that the AXAF gratings will be able to diagnose accretion flow in regions as close as 10 m above the white dwarf surface.

In summary, we have simulated AXAF grating spectra of accreting white dwarfs, using parameters appropriate for magnetic cataclysmic variables. Our simulations show that the High-Energy Transmission Grating of AXAF can resolve the keV X-ray emission lines that characterise the temperature, density and velocity profiles of the shock-heated emission regions of these systems. This will allow us to place constraints on the white-dwarf mass and the accretion rate. The high-resolution spectra will also enable us to directly measure the velocity of accretion flow in regions very close to the white-dwarf surface.

© Copyright Astronomical Society of Australia 1997