Quasi-Periodic Eruptions as a Probe of Accretion Disk in Tidal Disruption Events

TL;DR

This work explores early-time quasi-periodic eruptions (QPEs) as probes of disk formation in tidal disruption events (TDEs) by modeling the interaction of an EMRI with a newly formed slim, super-Eddington accretion disk. Using two representative slim-disk frameworks (SQ and SS), the authors derive QPE observables—duration, luminosity, and temperature—and their time evolution, highlighting diffusion-driven durations of order $t_{ m QPE} \sim 10^{2}-10^{3}$ s and temperatures up to $T_{ m QPE} \sim 1-50$ keV, with a duty cycle $\lesssim 1\%$. They show that early QPEs are detectable with current X-ray telescopes but are challenging to observe due to wind obscuration and the short duty cycle, while providing a direct window into the disk formation physics of TDEs. The study suggests that prompt, long-term X-ray monitoring of optical TDEs could leverage QPE detections to constrain disk formation timescales and the SMBH accretion environment.

Abstract

Quasi-periodic eruptions (QPEs) are X-ray transients characterized by nearly regular recurring flares from galactic nuclei. Recent observations have confirmed that some QPEs occur in galactic centers that experienced a tidal disruption event (TDE) a few years earlier. This may be reasonably explained if QPEs are produced when a star orbiting a supermassive black hole passes through an accretion disk formed by the TDE. Based on this scenario, we investigate the expected QPE signatures in the early stages of TDEs, taking into account the time evolution of the accretion disk. In the early phase, the disk is in a super-Eddington accretion state. The interaction between the star and such a slim disk results in QPEs with durations of $\sim 100-1000\,{\rm s}$ and temperatures of $\sim 1-100\,{\rm keV}$, which are significantly shorter and hotter than those of the currently detected QPE population. These events are detectable with current X-ray telescopes, but their small duty cycle ($\lesssim1\,\%$) and the potential presence of a massive disk wind may make detection challenging. We encourage early-time and long-term monitoring TDEs showing X-rays to capture these QPEs, as such detections would provide valuable insights into the disk formation process in TDEs.

Figures (9)

• Figure 1: Schematic picture of an EMRI and thick disk system. The EMRI orbits around a SMBH with a semimajor axis $a$. The orbital plane is inclined from the equatorial plane by an angle $i$.
• Figure 2: (Top) Normalized cumulative number distribution of EMRIs as a function of the inclination angle $i$. EMRIs are assumed to distribute isotropically around the disk axis. EMRIs are in a prograde (retrograde) orbit for $i < (>) \pi/2$, and embedded in a thick disk for $i < \pi/4$ and $> 3\pi/4$ (shaded regions). (Bottom) The ratio of relative velocity between a EMRI and disk material to the disk sound speed for different inclination. A shock is not formed when the ratio is smaller than unity (the horizontal shaded region).
• Figure 3: Time evolution of the accretion rate (upper), surface density (middle), and scale height (lower) of the disk for the Strubbe&Quataert (SQ, blue) and self-similar (SS, orange) models. The parameters are $M_{\bullet} = 10^6 \, M_{\odot}$, $M_{\star,{\rm TDE}} = M_{\odot}$, $R_{\star,{\rm TDE}} = R_{\odot}$, $\alpha=0.1$, and $R = 100 \, R_{\rm g}$. The SQ model is reliable after the fallback time (Eq. \ref{['eq:fallback_time']}) and until the photon trapping condition (Eq. \ref{['eq:t_trap']}) is violated at square points (or left of the vertical dashed lines). The SS model is valid for $\dot{M} \gtrsim \dot{M}_{\rm Edd}$ and we extrapolate $\dot{M}$ with the same temporal index $\dot{M} \propto t^{-5/3}$ beyond diamond points.
• Figure 4: Time evolution of the QPE duration (upper), luminosity (middle), and characteristic temperature (lower) for the SQ model. The disk parameters are the same as Fig. \ref{['fig:Mdot']}, and the EMRI parameters are $R_{\star} = R_{\odot}$ and $i = \pi/2$. The photon trapping condition (Eq. \ref{['eq:t_trap']}) is satisfied to the left of the vertical dashed lines. In the upper panel, the expansion time is also plotted by the red line. The shaded regions around the thick green curves show the possible variation due to different inclination angles. The angles corresponding to the boundaries are shown explicitly. Dotted lines denote the scaling of the quantities in the slim-disk phase (see Eq. \ref{['eq:t_QPE_SQ']}). During the almost entire evolution, the temperature is larger than the blackbody one ($T_{\rm BB}$, purple) due to the insufficient thermalization.
• Figure 5: Time evolution of the critical photon energies for Comptonization. The solid and dashed curves show the photon energies above which photons can be upscattered without free-free absorption, and within the expansion timescale, respectively. The larger of the two determines the contribution of Comptonization. The blue and orange curves represent the SQ (blue) and SS (orange) models, respectively.