Model for Relaxation Oscillations of a Luminous Accretion Disk in GRS 1915+105: Variable Inner Edge

To understand the bursting behavior of the microquasar GRS 1915+105, wecalculate time evolution of a luminous, optically thick accretion disk around astellar mass black hole undergoing limit-cycle oscillations between the high-and low- luminosity states. We, especially, carefully solve the behavior of theinnermost part of the disk, since it produces significant number of photonsduring the burst, and fit the theoretical spectra with the multi-color diskmodel. The fitting parameters are $\Tin$ (the maximum disk temperature) and$\Rin$ (the innermost radius of the disk). We find an abrupt, transientincrease in $\Tin$ and a temporary decrease in $\Rin$ during a burst, which areactually observed in GRS 1915+105. The precise behavior is subject to theviscosity prescription. We prescribe the radial-azimuthal component ofviscosity stress tensor to be $T_{r \phi}=-\alpha \Pi (p_{\rm gas}/p)^{\mu}$,with $\Pi$ being the height integrated pressure, $\alpha$ and $\mu$ being theparameter, and $p$ and $p_{\rm gas}$ being the total pressure and gas pressureon the equatorial plane, respectively. Model with $\mu=0.1$ can produce theoverall time changes of $\Tin$ and $\Rin$, but cannot give an excellent fit tothe observed amplitudes. Model with $\mu=0.2$, on the other hand, gives theright amplitudes, but the changes of $\Tin$ and $\Rin$ are smaller. Althoughprecise matching is left as future work, we may conclude that the basicproperties of the bursts of GRS 1915+105 can be explained by our ``limit-cycleoscillation'' model. It is then required that the spectral hardening factor athigh luminosities should be about 3 at around the Eddington luminosity insteadof less than 2 as is usually assumed.Comment: 11 pages, 5 figures, accepted for publication in Ap