## 6. Bolometric light curves of time-dependent standard accretion disk: power lawIn order to calculate the luminosity of the disk, we assume the quasi-stationary accretion rate as it is at . For these most luminous parts of the disk we take given by (20). The overall emission of the disk is defined by the gravitational energy release , where is the efficiency of the process. At early As the temperature decreases, the law of decline switches to: The mass of the disk can be derived by integrating over its surface: The constant is the same as in
the previous section. These solutions give an asymptotic law for the
disk We remark that the observed X-ray light curves can have
## 6.1. Luminosity - accretion disk parameters dependenceIt is essential to point out that in formulae (36), (37) the
parameters cannot be changed to
describe how luminosity depends on them. Indeed, these expressions
were found as a result of solution of differential Eq. (6) with
the constant coefficient Thus the increase in gives the
increase in
## 6.2. Thomson opacity - free-free opacity transitionThe temperature of the disk decreases with time, and eventually the free-free and free-bound opacity supersedes the Thomson one. It is possible to connect two regimes at the point (, ), where and (indexes 1, 2 denote different opacity regimes) - two conditions allowing us naturally to define both and : The right top indexes of and indicate the opacity regimes. As the profiles of are very close in these two regimes (see Fig. 1), and parameters vary slightly with radius (being roughly constant in the region where the substantial mass of the disk is enclosed), the physical parameters of the disk (, , etc.) calculated in the two solutions are sufficiently accurately equal. At the time the free-free absorption coefficient calculated in the Thomson opacity regime and in the free-free opacity regime takes the form: The closeness of to
cm Fig. 2 represents the bolometric light curve of the disk for , . Hereafter we substitute with their typical values in a self-consistent way. The transfer between Thomson and free-free regimes begins at the moment , - arrow A at in Fig. 2. We intersect the curves at what corresponds to and for (left small arrow). We call "moment of transition". The transition ends at the time when the solutions match at - arrow B at in Fig. 2. This picture is reliable and useful, even though it implies the existence of two separate regimes, which is evidently not quite true. Indeed, at any epoch the inner part of the disk would be scattering dominated, the lower the accretion rate, the smaller this part. Obtaining of an exact solution needs consideration of combined free-free and Thomson opacity of the gas. There is some The second intersection of the curves in Fig. 2 at (right small arrow) corresponds to the other intersection of functions , meanwhile the physical parameters of the disk calculated using formulae (26)-(35) are different. Thus the disk is at the same (free-free) opacity regime as before. When decreases to the value K, the convection (which presumably appeares in the zones of partial ionization) starts to influence the disk's structure, and the diffusive type of radiation transfer, which we use, is no longer valid. For and this happens at : . For investigation of the disk evolution on larger time-scales see e.g. Cannizzo et al. (1995), Cannizzo (1998), Kim et al. (1999). © European Southern Observatory (ESO) 2000 Online publication: March 28, 2000 |