Astron. Astrophys. 318, 73-80 (1997)

1. Introduction

Luminous X-ray sources with very soft spectra had already been found with the IPC detector of the EINSTEIN X-ray observatory. The ROSAT observations now led to the discovery of many new sources of this kind, and a separate class, the supersoft sources (SSS), has been established. The SSS are luminous X-ray objects with very soft spectra (more than 90% of the observed photons below 0.5 keV). This corresponds to a blackbody temperature of K. The bolometric luminosity is close to the Eddington limit which for a star is erg/s. Up to now about 25 to 30 objects have been found in our galaxy, in the Magellanic Clouds and the Andromeda Nebula.

Such luminosities and temperatures correspond to blackbody surfaces of typical white dwarf dimension, cm. The very soft spectra can originate from different kinds of objects where we might expect a hot and possibly accreting white dwarf as in novae, planetary nebulae, symbiotic binaries but possibly even from neutron stars surrounded by an appropriate cocoon of gas (for recent reviews see Hasinger (1994), Kahabka et al. (1994)). From the different behaviour of the observed SSS (variability, on- and off-states) one might conclude that they do not form one unique class of objects.

Optical counterparts of several SSS were found, mainly blue objects. It was argued that the irradiated accretion disk around the compact object would be the dominant optical light source (van den Heuvel et al. 1992, later referred to as vdH). For several systems orbital periods are known: e.g. CAL 83 (25 hr, Smale et al. 1988), CAL 87 (10.6 hr, Callanan et al. 1989) and RX J0019 (15.8 hr, Beuermann et al. 1995). The periods give constraints on the geometry of the binary system. Especially for CAL 87 important information comes from the optical and X-ray eclipse light curves (Cowley et al. 1990, Schmidtke et al. 1993, Kahabka et al. 1994).

In an earlier attempt to model the optical light curve Callanan & Charles (1989) used a numerical code of Hellier & Mason (1989) for a simulation of CAL 87 as a LMXB. They already found an elevated disk rim as useful for such a simulation.

The aim of our present investigations is to determine a theoretical light curve for CAL 87, based on the model of vdH for steady nuclear burning on accreting white dwarfs. We model the contributions from the accretion disk, hot spot spray and the secondary star, each of them illuminated by the central hot white dwarf. Following the results of vdH we have a narrow range of possible mass accretion rates, white dwarf masses and secondary star masses. We obtained values listed in Table 1. Additionally, as shown later, the well observed optical light curve puts severe constraints on the theoretical model.

Table 1. The system parameters

In Sect. 2 we discuss the observed light curve, especially the asymmetry in the ingress and egress of the primary minimum in connection with the interaction between the accretion stream and the disk. This lets us consider a cold clumpy spray which is illuminated by the white dwarf and whose brightness varies for the observer with orbital period. We compare this feature with the signature of the interaction of accretion stream and disk in light curves of eclipsing nova-like cataclysmic variables.

In Sect. 3 we describe how we model the visual radiation from secondary star, accretion disk and spray. We take the source of illumination, the white dwarf, as a point source. The radiation from the secondary star is evaluated as resulting from surface elements on the equipotential surface of a Roche lobe filling star. The disk height is determined consistently with the irradiation. The efficiency of reprocessing to thermal radiation is taken as a parameter. We used an angle resolution of for the surface elements of the star and 200 concentric rings and also resolution in azimuth for the disk. For the shape of the spray we included information from ballistic trajectories.

In Sect. 4 we present the results of our modelling. Comparing with the observed light curve we find that it is necessary to include both, essential energy transport from the bright side of the secondary to non-illuminated parts and a large volume of the spray. We show four models to explain the different effects: model a (simple), b (including the spray), c (with energy transport to un-illuminated parts of the secondary) and d (with modifications of model b and c together).

The discussion in Sect. 5 summarizes what we can learn from modelling the observed light curve for the SSS CAL 87. Studying how this system would appear if we would see it under different inclinations, we find that these other light curves are quite similar to the light curves of CAL 83 and RX J0019.

© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998
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