The Evolution of X-ray Spectra in Tidal Disruption Events

Abstract

The study of the evolution of X-ray spectra in tidal disruption events (TDEs) is an important approach for understanding the physical processes occurring near a supermassive black hole. Observations show that the X-ray spectra of TDEs are very soft at the peak after the outburst, followed by a spectral hardening on a timescale of years. Theoretically, TDEs are suggested to undergo super-Eddington accretion around the time of the outburst. In this paper, we construct a new disc-corona model to explain the observed X-ray spectral hardening in TDEs. In our model, there is a transition radius \(r_{\rm tr}\). For \(r < r_{\rm tr}\), the accretion flow exists in the form of a slim disc, whose emission is dominated by soft X-rays. For \(r > r_{\rm tr}\), the accretion flow exists in the form of a traditional sandwiched disc-corona, in which a harder X-ray spectrum is produced. Our calculations show that \(r_{\rm tr}\) decreases with decreasing mass accretion rate \(\dot{M}\), which naturally predicts the hardening of the X-ray spectra since the relative contribution of the outer disc-corona to the inner slim disc increases as \(\dot{M}\) decreases. Our model has been applied to explain the observed X-ray spectral hardening in the TDE candidate AT 2019azh, in which \(\dot{M}\) is assumed to decrease proportionally to \(t^{-5/3}\). Potential applications of the model for explaining the X-ray spectral evolution in upcoming rich TDE observations are also expected.

Figures (11)

• Figure 1: Gas pressure-dominated solution for $\dot{m}=0.3$ (top row) and $\dot{m}=1.6$ (bottom row). In this calculation, we fix $M=10^{6}M_{\odot}$, $\alpha=0.3$, $\beta=1$. Left panels: Fraction of energy dissipated in the corona ($f_{\rm c}$) and in the disc ($1-f_{\rm c}$). Middle panels: Radial profiles of temperature ($T/10^9$ K), number density ($n/10^{11}$ cm$^{-3}$), optical depth ($\tau$), Compton $y$-parameter, and Alfvén speed ($V_A/c$). Right panels: Emergent spectra corresponding to the two accretion rates. The light blue shading marks the 0.3-10 keV band.
• Figure 2: Mass accretion rate $\dot m$ as a function of radius $R/R_{\rm S}$ by setting $c_1 = 4/27$ for $M=10^{6}M_{\odot}$ (blue solid line) and $M=10^{7}M_{\odot}$ (orange dashed line) respectively, i.e. the critical (minimum) $\dot m$ for the existence of the radiation pressure-dominated solution at a fixed radius for $M=10^{6}M_{\odot}$ and $M=10^{7}M_{\odot}$ respectively. The region above the curve of $\dot m$ as a function of $R/R_{\rm S}$ corresponds to the radiation pressure-dominated solution, and the region below the curve of $\dot m$ as a function of $R/R_{\rm S}$ corresponds to the gas pressure-dominated solution.
• Figure 3: Radiation pressure-dominated solution for $\dot{m}=6$ (top row) and $\dot{m}=20$ (bottom row). In this calculation, we fix $M=10^{6}M_{\odot}$, $\alpha=0.3$, $\beta=1$. Left panels: Fraction of energy dissipated in the corona ($f_{\rm c}$) and in the disc ($1-f_{\rm c}$). Middle panels: Radial profiles of temperature ($T/10^9$ K), number density ($n/10^{11}$ cm$^{-3}$), optical depth ($\tau$), Compton $y$-parameter, and Alfvén speed ($V_A/c$). Right panels: Emergent spectra corresponding to the two accretion rates. The blue solid curves show the emergent spectra calculated from the new disc-corona model in this paper, the grey dashed curves show the emergent spectra using the disc-corona model in 2003ApJ...587..571L. The light blue shading marks the 0.3-10 keV band.
• Figure 4: Composite solutions (inner radiation pressure-dominated solution + outer gas pressure-dominated solution) for $\dot{m}=1.6$. In this calculation, we fix $M=10^{6}M_{\odot}$, $\alpha=0.3$, $\beta=1$. Left panel: Fraction of energy dissipated in the corona ($f_{\rm c}$). Middle panels: Radial profiles of temperature ($T/10^9$ K), number density ($n/10^{11}$ cm$^{-3}$), optical depth ($\tau$), Compton $y$-parameter, and Alfvén speed ($V_A/c$). Right panels: Emergent spectra. The blue solid curve shows the total spectrum. The red dashed curve shows the spectrum from the inner radiation pressure-dominated region, the orange dashed curve shows the spectrum from the outer gas pressure-dominated region. The light blue shading marks the 0.3-10 keV band.
• Figure 5: Gas pressure-dominated solution (orange dashed line) and composite solutions (blue solid line) for $\dot{m}=1.6$. In this calculation, we fix $M=10^{6}M_{\odot}$, $\alpha=0.3$, $\beta=1$.