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Astron. Astrophys. 346, 82-86 (1999)

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4. Discussion

4.1. Variability of the optical light curves

The quiescent optical light curves of V616 Mon show a double-humped ellipsoidal modulation due to the changing projected area of the Roche-lobe filling mass donor star. Maxima occur at quadrature, corresponding to maximum projected area, and are hence expected to be symmetric. Minima occur at orbital conjunctions; in general they have differing depths due to limb- and gravity-darkening. The light from the secondary star is diluted by the flux from the accretion disc. Also the ellipsoidal light curve may be distorted by other variable contributions to the total light; the bright spot associated with the impact of the mass transfer stream on the edge of the disc (McClintock & Remillard 1990); star spots on the secondary; and variable disc emission, including the superhump phenomenon (Warner 1995).

Recently Leibowitz et al. (1998) have collated the optical light curves of V616 Mon obtained over the last 7 years. They find that the depth of the maxima and minima of the light curves vary with time. They observe a long term photometric behaviour of a few hundred days with a peak to peak amplitude of 0.3 mag. They suggest that the minimum in the light curve corresponding to when the red dwarf lies between the observer and the compact object (orbital phase 0.0) changes depth with time. Since in the standard precessing disc model one does not expect this minimum to change depth significantly (as at this phase the secondary star is least affected by X-ray illumination) they conclude that they cannot explain the variations in terms of a simple geometrical precessing accretion disc model (Heemskerk & van Paradijs 1989).

However, it should be noted that the main thrust of their conclusion lies in the interpretation of the varying component in the light curves. In the precessing disc model the depth of either minimum can vary with time, depending on the tilt of the accretion disc (Heemskerk and van Paradijs 1989). Also they have assumed that the maximum in the light curve (orbital phase 0.75) with respect to which the minima is measured remains constant. This is probably not the case as the observed optical light near this orbital phase is contaminated by the bright spot. Optical spectroscopy of V616 Mon shows the presence of a bright spot (MRW). Bright spots have been seen in the optical light curves of cataclysmic variables with similar mass ratios such as Z Cha and OY Car (Wood et al. 1986, 1989) where it is observed between orbital phase 0.6 and 1.1. Variations in the optical flux emitted by the bright spot as the result of clumpy mass transfer from the secondary star could easily give rise to variability in the optical flux observed at this orbital phase.

In the IR the effects of the variability discussed above are much less (SNC). The IR light curve of V616 Mon shows equal maxima; this is what is expected if the IR variations are due solely to the ellipsoidal modulation of the secondary star.


Table 2. Optimal Subtraction of the Companion Star

4.2. The Brackett-[FORMULA] emission line

Various authors have pointed out that the double-peaked emission line profiles can be interpreted as arising from an accretion disk viewed at high inclination. However, it should be noted that a double-peaked emission line profile can also arise from a system with an inclination as low as 15o (see the models of Horne & Marsh 1986). Assuming that the double-peaked lines arise entirely from the disk, we can estimate the binary inclination of V616 Mon by measuring the separation of the Br[FORMULA] emission-line peaks.

The Keplerian velocity of the outer edge of the disk ([FORMULA]) is given by [FORMULA]. Combining this with Kepler's third law, Paczynski's (1971) formula for the Roche lobe radius, and using the fact that the accretion disk fills 50 per cent of the compact object's Roche-lobe (MRW), gives [FORMULA] km s-1, where [FORMULA] is the mass of the black hole (in solar masses), and [FORMULA] is the orbital period (in hours). The separation of the Br[FORMULA] emission-line peaks measured from the summed spectrum of V616 Mon is 1204 km s-1, implying a projected velocity of the outer edge of the accretion disk of [FORMULA] 602 km s-1. Using the above formula with [FORMULA]=7.75 hrs (MRW) and [FORMULA] (SNC) gives a [FORMULA], which agrees well with that obtained by SNC.

In cataclysmic variables there is observational evidence that the accretion disc contamination in the K-band is significant. The eclipse light curves of the dwarf nova OY Car, for example show that during quiescence the accretion disc can contribute about 30 percent of the flux at 2.2 µ (Sherrington et al. 1982). IR spectra of cataclysmic variables also show emission lines arising from the optically thin gas in the accretion disc (Ramseyer et al. 1993; Dhillon & Marsh 1995), such as HeI (2.0587 µ) and Br[FORMULA] (2.1655 µ). In contrast, the X-ray transients V404 Cyg (Shahbaz et al. 1996) and V616 Mon show only Br[FORMULA] in emission. It should also be noted that the mass accretion rate during quiescence in the X-ray transients is a factor of 10 lower than that in dwarf novae.

One expects the EW of the emission lines arising from the accretion disc to decrease as the orbital period of the binary increases. This is simply because larger systems will have larger, cooler accretion discs. If one looks at the H[FORMULA] EW in the SXTs, then one can find some evidence for this type of correlation; for Nova Per 1992 the H[FORMULA] EW is 205 Å, whereas for the larger systems such as Nova Mus 1991 and V404 Cyg it is 50 Å and 40 Å rrespectively. Also note that in all the SXTs the disc contamination near H[FORMULA] is in the range 6-16 percent, i.e. it is small despite the large H[FORMULA] EW. In V404 Cyg the Br-[FORMULA] EW of the accretion disc is 2.7 Å. One expects the Br-[FORMULA] EW of the accretion disc in the much shorter system V616 Mon to be higher; this is what is observed (see Sect. 2).

4.3. The effect on the mass of the black hole

SNC obtained an IR light curve of V616 Mon which showed a double humped feature characteristic of the ellipsoidal variations of the secondary star. They modelled these variations assuming all the IR flux was arising from the secondary star, and determined the most probable mass of the compact object to be 10 [FORMULA]. Justification for this assumption comes from the analysis of the IR light curve of the transient Cen X-4 (Shahbaz et al. 1993). The mass of the compact object in Cen X-4 is consistent with that of a canonical neutron star; which the compact object must be because of the type I X-ray bursts observed during outburst (Matsuoka et al. 1980). This provides indirect evidence that the contribution of the accretion disc to the observed IR flux is very small, at least from Cen X-4. This may also be the case for V616 Mon; an upper limit to the accretion disc contribution to the IR flux being 27 percent (Sect. 3).

The effects of any accretion disc contamination to the observed IR flux will be to dilute the actual ellipsoidal modulation, making the observed modulation smaller than the true value. Since the amplitude of the ellipsoidal modulation is correlated with the binary inclination (large amplitudes imply a high binary inclination), this means that modelling a contaminated light curve will underestimate i.

We have modelled the amplitude of the ellipsoidal variations as a function of i. We used the same parameters as SNC: Teff=4000 K, q=14.9 (MRW), a gravity darkening exponent of 0.08 (Lucy 1967), and the limb darkening coefficient from Al-Naimiy (1978). Fig. 2 shows the effect of differing amounts of contamination in the IR light curves on the binary inclination. If we take the 2-[FORMULA] limit to the disc contamination of 27 percent, we find that i increases by 7 degrees and the mass of the black hole decreases by 3.6 [FORMULA] (2-[FORMULA] limit). Note that this extreme value for i is still lower than that obtained by Haswell et al. (1993), and the implied mass of the compact object ([FORMULA] 6.4 [FORMULA]) still substantially exceeds the canonical maximum mass of a neutron star (3.2 [FORMULA]; Rhoades & Ruffini 1974).

[FIGURE] Fig. 2. The effect of the accretion disc contamination on the value for the binary inclination, derived by modelling the K-band ellipsoidal variations of the secondary star (SNC). The 2-[FORMULA] upper limits to the accretion disc contamination and inclination are shown. binary inclination respectively.

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Online publication: May 6, 1999