Time-dependent Accretion Disks in Tidal Disruption Events: Long-term Light Curves

The time-dependent accretion disk has been applied to explain the light curves observed in tidal disruption events (TDEs). Radiation pressure instability is expected to be an important factor that can shape the evolution of the accretion disk. In this paper, we upgrade the time-dependent disk model in Guo $\&$ Qiao by incorporating an index $\mu$ (with the stress tensor $\propto p^{\mu}p^{1-\mu}_{\rm{gas}}$, where $p=p_{\rm{gas}} + p_{\rm{rad}}$) for the modified viscosity, and a parameter $f_{\rm{w}}$ for the strength of the wind. Meanwhile, we adopt a more realistic fallback rate to inject into the disk. After systematically testing the effects of the newly incorporated parameters, we find that $f_{\rm{w}}$ can affect the time when the instability occurs, while $\mu$ can influence the occurrence and variation magnitude of the radiation pressure instability. When $\mu<0.4$, the radiation pressure instability is completely removed from the disk, and the light curves evolve stably without large-scale magnitude variation. When $\mu>0.4$, the light curves can show oscillations caused by the instability, or drop steeply when the instability occurs and become flat in the late-time evolution, which mainly occurs when the viscous viscosity parameter $\alpha$ is small or the impact parameter $\beta$ is small. Since the drop magnitude can be modulated by $\mu$, we apply these `decay-to-flatten' light curves to some optical/UV observations in TDEs with different magnitudes of decline. Finally, we discuss the potential application of our model to some special TDEs that show oscillations in the light curves.