9. Discussion and conclusion
In this work, we presented the analytical solutions to time-dependent accretion in binary systems. During an outburst we propose the specific external boundary conditions on a disk confined due to tidal interactions. For two opacity regimes the full analytical time-dependent solutions for the Keplerian disk are obtained and an asymptotic light curve is calculated with smooth transition between opacity regimes. During the decline phase accretion disks around black holes appear to be dominated by the free-free and free-bound opacity in order to comply with the Eddington limit on luminosity. This phase is characterized by the power-law decay of accretion rate . It is shown that the decay time scale depends on the real energetic band of detector (Fig. 3).
The results obtained in this work can be applied to the accreting systems having variable emission of flare type if emission is essentially due to the fully ionized accretion disk around a black hole, or a neutron star, or a white dwarf.
Narayan & Yi (1994) accretion flows are shown to undergo exponential decays if the disk has infinite size. This notable result probably persists even when the advective disk is in a binary system. The latter suggestion is to be thoroughly considered in the accurate numerical investigation. If this is the case, the abrupt steep falls observed in several X-ray novae (Tanaka & Shibazaki 1996) in the last phase of the decay, at luminosity levels erg s-1, can be interpreted in terms of quickly depleting ADAF (Sect. 8) with relevant values of .
Using the results of this work, we can explain the general features of X-ray novae light curves in the early phase. Typical XN outburst light curves (see Tanaka & Shibazaki 1996; Chen at al. 1997 for a review) show quasi-exponential decay. To date several approaches have been used to account for XN features. The exponential decays were obtained in the framework of disk instability model (Cannizzo et al. 1995; Vishniac 1997; Cannizzo 1998) in which the large time-scale evolution of the disk is considered. Mineshige et al. (1993) argued that the exponential decays in XN can be reproduced if the mass and the angular momentum are efficiently removed from the inner portions of the disk at a constant rate, or wind mass loss or enhanced tidal dissipation could be substantial. King & Ritter (1998) took into account the irradiation of the disk by the central X-ray source and obtained the characteristic XN light curves.
We suggest an alternative reason to explain this remarkable feature, at least during the early stages of the outburst when the disk is fully ionized. Nearly exponential X-ray decays are obtained taking into account the fact that the X-ray light curves are observed in the energetic range where the spectrum of the disk has Wien-form. Black hole XN spectra typically are composed of an ultrasoft component and a hard power-law component (e.g. Tanaka 1992; Tanaka & Shibazaki 1996). At the first stages after outburst the ultrasoft component dominates and can be represented by a multicolor blackbody disk (Tanaka 1992). This component has an exponential fall-off, a decisive factor to produce observed exponential trends. The observed characteristic times can be obtained within reasonable intervals of parameters (Fig. 3, Sect. 7).
The secondary peak commonly observed in XN can be qualitatively analytically produced by certain reconstruction of viscosity mechanisms and corresponding increase of (Sect. 6.1). Possible mechanisms of reflares involving irradiation effects were investigated by Kim et al. (1994), Mineshige (1994), King & Ritter (1998) (see, however, Cannizzo 1998).
Of course, the accretion disk spectrum represents only one contribution to the total observed spectrum of the source. The corona around the disk is probably responsible for the other spectral components. In addition, taking into consideration the irradiation of the outer parts of the disk would affect evolution of the disk (see, e.g. King & Ritter 1998; Kim et al. 1999). Kim et al. (1999) constructed an optical light curve of a XN and found the direct irradiation of the disk by the inner layers to have only a small effect on the outer disk because of shadowing. The indirect irradiation (from a corona or a chromosphere above the disk) is found to affect the light curve more strongly. We suggest that the irradiation of the twisted warped disk could also result in important heating of the outer layers. Further investigation and applications to observed sources will be the basis of our future work.
© European Southern Observatory (ESO) 2000
Online publication: March 28, 2000