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Astron. Astrophys. 354, L37-L40 (2000)

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4. Light curve modelling

To test whether the model of a contracting and expanding white dwarf can quantitatively explain both the X-ray light curve and the dips in the optical light curve we have calculated a predicted optical light curve from our X-ray data. First we used LTE white dwarf model atmosphere spectra (van Teeseling et al. 1994) to determine the photospheric radius as a function of the HRI count rate, where we assumed a distance of 50 kpc, a bolometric luminosity of [FORMULA] erg s-1, and an absorption column of [FORMULA] cm-2 (Gänsicke et al. 1998). Then we used the binary light curve code BINARY++ (van Teeseling et al. 1998) to calculate the orbital average optical magnitude as a function of the photospheric radius [FORMULA] of the white dwarf. Since this code self-consistently calculates the amount of irradiation from an extended white dwarf on the accretion disk and companion, including all possible shielding effects, this calculation is more accurate than the semi-analytic approach we used in Reinsch et al. (1996) and allows us to investigate how the results depend on the various parameters. We assume a mass ratio of [FORMULA], an orbital separation [FORMULA] cm as appropriate for a quasi-main-sequence donor star and an orbital period [FORMULA] days, an orbital inclination of [FORMULA], a disk filling 80% of the average Roche-lobe radius, a uniform irradiation reprocessing efficiency of [FORMULA], a secondary temperature of 9000 K, and an accretion rate of [FORMULA].

Fig. 2 shows the resulting total absolute V magnitude as a function of [FORMULA], and individual magnitudes of the disk, the companion star and the white dwarf. For [FORMULA] or [FORMULA] cm, the expanded white dwarf is the dominant optical light source. With increasing [FORMULA] the disk first becomes brighter because of more effective irradiation, but becomes fainter again for [FORMULA] cm because an increasing part of the inner disk disappears inside the white dwarf envelope.

[FIGURE] Fig. 2. Absolute V magnitude as a function of the white dwarf photospheric radius [FORMULA] for the disk, the companion star, the white dwarf, and their sum.

In Fig. 1, we have plotted the predicted optical light curve over the combined MACHO light curve. For data points with only an upper limit for the X-ray count rate, we assume a radius [FORMULA] cm, which correctly reproduces the amplitude of the dip in the MACHO light curve. The [FORMULA] X-ray upper limit of 0.00014 cts/s for the X-ray off state requires a radius of [FORMULA] cm (using [FORMULA] erg s-1, [FORMULA] K, [FORMULA] cm-2) during the optical bright state. Our calculations show that it is relatively easy to reproduce the observed optical dips from the X-ray data, with the correct amplitude and surprisingly accurate absolute magnitudes. It also illustrates that when the X-rays become detectable, the white dwarf photosphere has almost reached its minimum size and the optical light curve has almost reached the level of the faint phase plateau. The difference between the observed and predicted optical light curve immediately after the optical decline could be explained by the initial lack of an optically thick inner disk after the white dwarf envelope has contracted to its minimal proportions.

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© European Southern Observatory (ESO) 2000

Online publication: January 31, 2000