## 7. Observed light curvesAs we mentioned in Sect. 6, the observed light curves can have
a slope of decline which is To calculate the spectra, one can assume the quasi-stationary accretion rate in the inner parts of the disk because the variation is small there (, see Fig. 1). The outer parts of the disk, where accretion rate varies significantly, contributes to the low-frequency band of the spectrum. We discuss the X-ray band and the most luminous parts of the disk and, thus, we take given by (20). Provided each ring in the disk emits as a black body, the temperature of the ring can be found as follows: where is the Stephan-Boltzmann constant. Then In the last expression the stationary solution for is taken. The black-body approximation is satisfactory if . Then the outgoing spectrum is the sum of Planckian contributions of each ring of the disk and has the characteristic slope for photon energies , where is the maximum effective temperature of the disk (Lynden-Bell 1969). However, if the Thomson scattering on free electrons contributes substantially to the opacity, the outgoing spectrum is modified (Shakura & Sunyaev 1973). See e.g. Ross & Fabian (1996) for investigation of spectral forms of accretion disks in low-mass X-ray binaries. The light curve is simulated by integrating at each over the specific frequency range using (20) and (44), where
erg s is the Planck
constant. The numerical factor in (45) corresponds to the luminosity
outgoing from Explaining the observed faster-than-power decay of outbursts in soft X-ray transients, one must take into account the specificity of the energetic band of the detector. Naturally, the observed slope of the curve depends on width and location of the observing interval. The narrower this band, the more different the observed curve could look like in comparison with the expected bolometric light curve. Of course, this difference also reflects the spectral distribution of energy coming from the source. We show here how the slope of the curve changes in the simplest
case of multi-color black body disk spectrum according to which
spectral range is observed. Following (45) we calculate
and integrate it over three energy
ranges: 3-6 keV, 1-20 keV and that one in which practically
all energy is emitted. Fig. 3 shows the photon flux variations in
two X-ray energy ranges (those of
One can see an almost linear trend of the X-ray flux when
bolometric luminosity is under the Eddington limit (to the right of
the vertical line in Fig. 3), especially in intervals of
. The decline becomes closer to the
exponential one with time. The slope of the curve depends on
, The natural explanation of such a result is the following: because the spectral shape of the disk emission has Wien-form (exponential fall-off) at the considered X-ray ranges, the law of variation of X-ray flux is roughly proportional to . In the free-free regime of opacity we have (see Sect. 5.1). Consequently, the observed X-ray flux varies like , which is quite close to exponential behavior. We restrict ourselves to this brief and general discourse, as a detailed application of our model to observed sources is not a goal of this paper. © European Southern Observatory (ESO) 2000 Online publication: March 28, 2000 |