## 1. IntroductionWe investigate analytically the problem of time-dependent accretion, closely related to the phenomena of flares widely observed in binary systems. In this paper we will concern ourselves with the emission of the flaring source which is generated by the accretion disk. We suppose the light curve to be regulated by the accretion rate variations. Such sources are typified by the low-mass X-ray binaries and cataclysmic variables. After Weizsäcker (1948) who considered the evolution of a protoplanetary cloud, the analytical investigations of non-stationary accretion were carried out by Lüst (1952), Lynden-Bell & Pringle (1974), Lyubarskii & Shakura (1987, hereafter LS87) as applied to accretion disks. A brief overview is presented in the book by Kato et al. (1998). LS87 suggested three stages of evolution of a time-dependent accretion disk (see also Sect. 5.1). Initially a finite torus of the increased density is formed around a gravitational centre. Viscosity causes the torus to spread and develop into the disk (1st stage). After the disk approaches the centre, the accretion rate reaches the maximum value (2nd stage) and begins to descend (3rd stage). During this stage the total angular momentum of the disk is conserved. Ogilvie (1999) presented a time-dependent self-similar analytical solution for a quasi-spherical advection-dominated flow with conserved total angular momentum. In a binary system, variations of accretion rate can be due to the non-stationary exchange of mass between the components of the binary (mass-overflow instability model) or due to the disk instability processes (see Kato et al. 1998and references therein). At some time the accretion rate onto the centre begins to augment. We assume that the maximum accretion rate through the inner boundary of the disk corresponds to a peak of outburst and the accretion rate decreases afterwards. In this study we particularly focus on the stage soon after the outburst. In Sect. 2 we outline the general equations of time-dependent accretion. The basic equation relates surface density of the disk and viscous stresses in it. Thus the specific structure of the disk influences greatly the run of the process. Sect. 3 introduces the investigation of time-dependent Keplerian -disks. The vertical structure of standard Keplerian disk is considered in Sect. 4. In a binary system the third stage of LS87 cannot be realized because the accretion disk around a primary would be confined by the gravitational influence of a secondary. Such disks do not preserve their angular momentum, transferring it to the orbital motion. We suggest the particular conditions at the outer boundary of the disk which allow the acquisition of new solutions characterized by faster decays than in LS87. The procedure and the analytical solution are presented in Sect. 5. We calculate the resulting bolometric light curve taking into account the transition between the opacity regimes as accretion rate decreases (Sect. 6). We note that observed light curves can have different slopes due to unevenness of spectral distribution (Sect. 7). In Sect. 8 we discuss the case of advection-dominated accretion flow (ADAF) in which exponential variations with time of accretion rate possibly take place. In Sect. 9 we discuss application of our model to X-ray novae. © European Southern Observatory (ESO) 2000 Online publication: March 28, 2000 |