Smak (1994) studied the problem of the reconstruction of the radial temperature distribution of accretion disks from eclipse light curves. His study suggested that particularly at the highest inclinations flat radial temperature profiles were obtained with eclipse mapping. He concluded that this was an artefact of the standard eclipse mapping technique which incorrectly assumes that the disk is flat and thin, although actually no calculations with the standard eclipse mapping code were used to corroborate that conclusion. The present paper conducts experiments to test how well standard eclipse mapping reproduces the disk radial brightness profile (and thus the radial temperature profile) in the case of flared, thick disks.
First, we define a three-dimensional accretion disk surface
with a fixed opening angle and a well-defined outer rim, similar
to that shown in Fig. 1 (click here).
Second, we calculate the brightness distribution of the
disk, following the canonical steady-state disk model
(see Frank et al. 1992) based on 
, and assuming a mass transfer rate
of 
.
The secondary star does not contribute to the light curve.
Third, the light curve of this flaring disk is calculated by
summing intensities from all the visible parts of the disk
in the appropriate proportions,
as a function of orbital phase (see Sect. 2 (click here)).
Random noise at a level of one percent is added.
Finally, the resulting light curve is fitted using the standard
thin-disk eclipse mapping method (Horne 1985; Rutten et al.
1992), assuming the correct values
for the mass ratio, orbital period and orbital inclination.
From the resulting brightness profile the radial temperature
profile is calculated and compared with the original temperature
profile of the model.
Figure 4: Model light curve of an eclipsing binary system with a tilted accretion
disk. The solid curve shows the case for a transparent disk, while the
dash-dotted line traces the light curve for an optically thick disk which
obscures the secondary star around phase 0.5. The dash-dotted and dashed
curves separate out the contributions of the secondary star and of the
accretion disk respectively
This experiment is conducted for a range of disk opening angles varying from 0 to 15 degrees (as measured from the orbital plane), and orbital inclinations between 70 and 90 degrees. These tests include rather extreme eclipse situations where in some cases the disk is only partly eclipsed, and in other cases the rim of the thick disk obscures the inner disk. Three examples of the reconstructed radial temperature profiles are shown in Fig. 6 (click here), two for the case where the disk opening angle is 5 degrees, and an orbital inclination of respectively 80 and 85 degrees, and a third case with an opening angle of 10 degrees viewed a an inclination of 80 degrees. In the latter two cases the front part of the disk surface is just at the verge of being obscured by the disk rim. These examples show good agreement between the reconstructed temperature profile and the theoretical profile for the standard steady-state accretion disk, as indicated by the full curves in Fig. 6 (click here). The deviation of the fit from the model in the center of the disk is due to smearing of the flux, which is inherent to the maximum entropy optimization scheme. At the cool and faint outer edge of the disk the fit deviates slightly from the model at the point where the thick, flaring disk is rounded off and edges. These examples are representative for the other reconstructions for different inclinations and disk opening angles, with the exception of situations where the inner disk is completely obscured by the outer disk rim. In the those cases the reconstruction does exhibit a flat temperature structure.
Figure 5: Model light curve of an eclipsing CV with a thick accretion disk,
a bright spot and a conspicious white dwarf
This experiment shows that the standard thin-disk eclipse mapping technique reproduces the radial temperature distribution of accretion disks reasonably accurately, even in cases when the disk is flaring. The reason for the discrepancy between this result and that presented by Smak (1994) is not immediately obvious, except for the fact that that paper did not actually employ a standard maximum entropy eclipse mapping code. The present invesitgation does agree with Smak's work in the case where the disk is thick enough to self obscure its inner parts. In such situation the radial temperature profile can obviously not be reconstructed, since no information on the inner disk is available in the light curve.