Light curves of time-dependent accretion disk in tidal disruption events

TL;DR

The paper develops a 1D time-dependent accretion-disk model for tidal disruption events, with continuous mass injection at the circularization radius following $\dot{M}_{\rm inject} \propto t^{-3/2}$ (equivalently $t^{-5/3}$ for fallback) and coupled mass, angular momentum, and energy evolution. It demonstrates that radiation pressure instability arises when the injection rate approaches the Eddington rate $\dot{M}_{\rm Edd}$, producing oscillatory light curves whose period decreases with increasing $\alpha$ and increases with $M_{\rm BH}$, while larger outer radii or smaller $\alpha$ can suppress oscillations and yield a steep drop followed by a flat late-time phase. The authors apply a photosphere reprocessing model to fit UV light curves of ASASSN-15oi and ASASSN-14ae, finding that early strong reprocessing implies large photosphere radii that recede toward the disk size as the emission becomes disk-dominated; the fits favor modest $\alpha$ and $\dot{M}_{\rm ini} \sim 2\dot{M}_{\rm Edd}$ with $M_{\rm BH}$ consistent with bulge-based estimates. The work suggests that radiation-pressure-driven disk evolution, combined with photospheric reprocessing, can explain key features of UV/optical TDE light curves and motivates future extensions to winds, disk spreading, and X-ray modeling for a fuller multi-band interpretation.

Abstract

Tidal disruption events (TDEs) are believed to be an ideal laboratory for studying the evolution of accretion flow around a supermassive black hole (BH). In general, the mass feeding rate to the BH is suggested to be super-Eddington initially, and evolves to be sub-Eddington on timescales of years. In this paper, we carry out calculations of the time-dependent evolution of accretion disk in the standard environment of TDE, i.e., injecting matter at the circularization radius of the stellar debris in the form of $\dot M_{\rm inject} \propto t^{-5/3}$. One of the main findings is that when $\dot M_{\rm inject}$ evolves to a value around the Eddington accretion rate, the radiation pressure instability occurs. We test the influence of the model parameters on the light curves, such as the BH mass $M_{\rm BH}$, viscosity parameter $α$, and mass-injecting radius $R_{\rm{out}}$, all of which are found to affect the light curves to some extent. In most cases, we find that the light curves oscillate significantly due to the radiation pressure instability. As an exception, when $α$ is small or $R_{\rm{out}}$ is large, we find that the oscillations are completely suppressed. In this case, the light curve drops steeply and then becomes flat in the late-time evolution, which we apply to explain the observed ultraviolet (UV) light curves of ASASSN-15oi and ASASSN-14ae together with the assumption of a photosphere. Finally, we discuss the potential applications of our time-dependent accretion disk model to explaining multi-band light curves of TDEs in the future.

Figures (11)

• Figure 1: Upper panel: The light curve. The colorful light curve refers to the results calculated with the time-dependent accretion disk by setting $M_{\rm{BH}}=10^{6}M_{\odot}$, $M_{\star} =M_{\odot}$, $R_{\star} =R_{\odot}$, $\alpha=0.01$, $\dot M_{\rm inject}=\dot M_{\rm fb}$ as equation (\ref{['M_dot_fb']}) and $R_{\rm out}=R_{\rm c}=47.5R_{\rm S}$ as equation (\ref{['Rc']}). The black dashed line is plotted by converting $\dot M_{\rm inject}$ to luminosity with $L=0.1\dot{M}_{\rm{inject}}c^{2}$. Lower panel: $T_{\rm eff}-\Sigma$ diagram. The black S-shaped curves in the left panel, middle panel and the right panel are calculated with the thermal equilibrium equation (\ref{['steady energy balance']}) at $5R_{\rm{S}}$, $20R_{\rm{S}}$ and $40R_{\rm{S}}$ respectively. The evolution of accretion disk in $T_{\rm{eff}}-\Sigma$ diagram is plotted in multiple colors in the left panel, middle panel and the right panel for $5R_{\rm{S}}$, $20R_{\rm{S}}$ and $40R_{\rm{S}}$ respectively. The same color in the upper and lower panels represents the same evolution stage.
• Figure 2: Light curves for different $M_{\rm{BH}}$, i.e., $M_{\rm{BH}}=10^{6}M_{\odot}$, $10^{6.5}M_{\odot}$ and $10^{7}M_{\odot}$. We set $\alpha=0.01$, $\dot M_{\rm inject}=\dot M_{\rm fb}$ as equation (\ref{['M_dot_fb']}) and $R_{\rm out}=R_{\rm c}$ as equation (\ref{['Rc']}).
• Figure 3: Light curves for different $\alpha$, i.e., $\alpha=0.001$, $0.01$ and $0.1$. We set $M_{\rm{BH}}=10^{6}M_{\odot}$, $\dot M_{\rm inject}=\dot M_{\rm fb}$ as equation (\ref{['M_dot_fb']}) and $R_{\rm out}=R_{\rm c}$ as equation (\ref{['Rc']}).
• Figure 4: Upper panel: The light curve. The colorful light curve refers to the $\alpha=0.001$ case in Figure \ref{['alpha']}. The black dashed line is plotted by converting $\dot M_{\rm inject}$ to luminosity with $L=0.1\dot{M}_{\rm{inject}}c^{2}$. Lower panel: $T_{\rm eff}-\Sigma$ diagram. The black S-shaped curves in the left panel, middle panel and the right panel are calculated with the thermal equilibrium equation (\ref{['steady energy balance']}) at $5R_{\rm{S}}$, $20R_{\rm{S}}$ and $40R_{\rm{S}}$ respectively. The evolution of accretion disk in $T_{\rm{eff}}-\Sigma$ diagram is plotted in multiple colors in the left panel, middle panel and the right panel for $5R_{\rm{S}}$, $20R_{\rm{S}}$ and $40R_{\rm{S}}$ respectively. The same color in the upper and lower panels represents the same evolution stage.
• Figure 5: Light curves for different $R_{\rm{out}}$, i.e., $R_{\rm{out}}=0.5R_{\rm{c}}$, $R_{\rm{c}}$ and $2R_{\rm{c}}$, where $R_{\rm{c}}$ is calculated as equation (\ref{['Rc']}). We set $M_{\rm{BH}}=10^{6}M_{\odot}$, $\alpha=0.01$ and $\dot M_{\rm inject}=\dot M_{\rm fb}$ as equation (\ref{['M_dot_fb']}).