## 2. The 3d cataclysmic variable modelOur computer code CVMOD generates
The white dwarf is modelled as an approximated sphere, using surface elements of nearly constant area (G"ansicke et al. 1998). The secondary star is assumed to fill its Roche volume. Here, the surface elements are choosen in such a way that their boundaries align with longitude and latitude circles of the Roche surface, taking the -point as the origin. We generate the surface of the accretion stream in two parts, (a)
the ballistic part from to (a) For the ballistic part of the stream, we use single-particle trajectories. The equations of motion in the corotating frame are given by Eq. (3) has been added to Flannery's 1975 set of
two-dimensional equations. is the
mass fraction of the white dwarf,
and are the distances from the point
to the white dwarf and the
secondary, respectively, in units of the orbital separation If , the trajectories resulting
from the numerical integration of Eqs. (1) - (3) are restricted
to the orbital plane. However, calculating single-particle
trajectories with different initial velocity directions (allowing also
) shows that there is a region
approximately one third of the way downstream from
to We define a 3d version of the stream as a tube with a circular cross section with radius centred on the single-particle trajectory for . (b) When the matter reaches Our accretion stream model involves several assumptions: (1) The
cross section of the stream itself is to some extent arbitrary because
we consider it to be - for our current data, see below - essentially a
line source. (2) The neglect of the magnetic drag (King 1993; Wynn
& King 1995) on the ballistic part of the stream and the neglect
of deformation of the dipole field cause the model stream to deviate
in space from the true stream trajectory. While, in fact, the location
of In our current code, we restrict the possible brightness distribution so that for each stream segment, which consists of 16 surface elements forming a section of the tube-like stream, the intensity is the same, i.e. there is no intensity variation around the stream. For the current data, this is no serious drawback, since we only use observations covering a small phase interval around the eclipse. Our results refer, therefore, to the stream brightness as seen from the secondary. From the present observations we can not infer how the fraction of the stream illuminated by the X-ray/UV spot on the WD looks like. The required extension of our computer code, allowing for brightness variation around the stream, is straightforward. The present version of the code is, however, adapted to the data set considered here. © European Southern Observatory (ESO) 2000 Online publication: April 10, 2000 |