In the study of accretion disks in cataclysmic variable stars (CVs),
the analysis of light curves plays an important role.
In particular the analysis of eclipse light curves provides
information on the disk's brightness structure on scales as small
that will probably never be resolved by direct imaging techniques.
By far the most powerful technique for detailed eclipse light curve
analysis is called eclipse mapping, developed by Horne
(1985). Classical model fitting techniques, as opposed to
reconstruction techniques such as eclipse mapping, dictate the intensity
structure on the accretion disk to obey some functional shape.
Eclipse mapping, on the other hand, treats the accretion disk as
being composed of a large number of elements.
The brightness values of these elements are adjusted independently to
fit the light curve, without the need to enforce
some functional dependence.
The only information that is required to
reconstruct a brightness map of the surface of the accretion
disk is the geometry of the binary system, from which the visibility
of each part of the disk at any time during the orbital phase is
deduced.
The maximum-entropy optimization scheme is used to
obtain the smoothest possible brightness distribution.
After several years of experience, eclipse mapping has now become a well established tool (see the reviews by Horne 1993 and Warner 1995). Eclipse mapping relies on a number of basic assumptions, such as the shape and brightness of the secondary star (which is usually assumed to be dark and filling its Roche lobe), and the shape of the accretion disk (which is usually assumed to be geometrically thin, and flat). Some of these model assumptions can in principle be changed. For example, the brightness of the secondary star has been included in models (Rutten et al. 1994), and some have incorporated limited three-dimensional disk shapes (such as flaring disks and disk rims; Wood et al. 1991; Rutten et al. 1992; Billington 1996).
In this paper, a general-purpose 3D light curve fitting program is presented which not only allows the use of nearly any three-dimensional disk shape, but also incorporates the surface of the Roche-lobe filling secondary star. This generalization allows us to extract information from the complete light curve rather than just the eclipse, as in the case of standard eclipse mapping. It also renders the program applicable to the analysis of a large range of light curves, such as, for example, light curves of geometrically thick disks, tilted disks, ellipsoidal variations, heating by irradiation, or any combination of these.
The problem of reconstructing the brightness distribution of flaring accretion disks from eclipse light curves is studied in Sect. 4 (click here) as an example of the use of the 3D light curve program. Doubt has been raised in the literature as to whether the radial temperature profile of accretion disks, deduced using the standard flat-disk eclipse mapping technique, is correct. Smak (1994) suggested that the flat radial dependence of the effective temperature observed in the disks of some systems (e.g. Rutten et al. 1992; Wood et al. 1992) is due to the fact that eclipse mapping does not take the correct three dimensional disk shape into account. This particular problem will be explored in some detail here by using the standard eclipse mapping method to fit light curves that are calculated for flared disks with a known brightness distribution, and comparing the reconstructed disks' brightness distribution with the original one.