Evolution of Quasi-Periodic Eruptions in the post-TDE Accretion Disk Perturbed by an Orbiting Star

Abstract

Quasi-periodic eruptions (QPEs) are a recently discovered class of highly variable X-ray bursts originating in galactic nuclei. These high-amplitude bursts exhibit periodicity ranging from tens of minutes to several days. QPEs are also characterized by variable peak amplitudes that can vary by a factor of few. While multiple physical models have been proposed to explain QPE light curves, none can fully account for all the observed features. A possible connection between QPEs and tidal disruption events (TDEs) has been suggested, particularly due to the past optical/UV outbursts that can be traced back for several sources, the long-term decay in the continuum luminosity, and the soft, thermal-dominated X-ray spectrum. Our primary goal is to verify whether the long-term decrease in eruption amplitudes detected for some QPE sources is consistent with the accretion disk being formed following a TDE. In this work, we adopt a simplified extreme mass ratio inspiral (EMRI) scenario, where a Solar-type star orbits a supermassive black hole (SMBH) and collides with an accretion disk twice per orbit, generating eruptions. We assume a post-TDE disk that follows a temporal power-law decline in mass accretion ($\propto t^{-p}$, $p>0$). As our aim is to develop a toy-model scenario, we have used purely analytical methods without considering all intervening processes in their full generality. Indications are that (i) the observed long-term decline in QPE amplitudes can be reproduced if the first monitored epoch occurs years to a few decades after the tidal disruption, (ii) stellar mass loss caused by ablation can play an important role in the evolution of QPE amplitudes in systems with heavy main-sequence (MS) stars.

Figures (11)

• Figure 1: Scheme of an EMRI system. A body of mass $M_{\star}\ll M_{\bullet}$ follows an inclined, elliptical trajectory, on which it intersects the accretion disk twice per orbit (generally at two different radii, shown with red plumes). These collisions ablate the stellar atmosphere and push the gaseous material out of the disk plane.
• Figure 2: Surrogate light curve evolution during 3 years at equidistant time intervals modeled using a quasi-Gaussian profile with a given duration and an amplitude given by Eq. \ref{['Lqpe']}.
• Figure 3: The theoretical ratio of the peak luminosities $\mathcal{R}(T)$. A thin solid red line corresponds to alternative parameters: $M_{\bullet,6} = 0.1, M_\text{dis} = 10$, the remaining lines correspond to $M_{\bullet,6} = 1,\, M_\text{dis} = 1$. Luminosities $L_1-L_3$ are power-law functions of $\dot{m}$ while the accretion rate is expected to drop by $\dot{m} \propto t^{-p}$, where $p \in \{9/4, 1/2, 6/5\}$ and the corresponding accretion rates are $\dot{m}_1$, $\dot{m}_2$, and $\dot{m}_3$, respectively. The solid green thick line shows the decline of the surface density of the disk due to viscous spreading, $\Sigma$, and the thick dashed line represents the combined effect of the $\Sigma$ decline and canonical ($-1.2$) $\dot{m}$ decline that crosses the value of 2 at $40\,t_\text{fb}$. The blue rectangle covers values 2-10. The minimum value of $T$ is at $10\,t_\text{fb}$. The value of $\mathcal{R} = 1.1$ corresponds to our minimum expected detectable ratio and crosses the $S_\text{c}$ line at 310$\,t_\text{fb}$. The markers on the left side show the decline values for individual sources listed in the second column of Table \ref{['table']}; x, v, - belong to the eRO-QPE1, eRO-QPE3, and GSN 069, respectively.
• Figure 4: In analogy to Fig. \ref{['Amplitude ratio']}, a long-term X-ray amplitude decline is shown here for the monitoring delay of 3 years. The fiducial parameters are as follows: $M_{\bullet} = 10^6\,M_\odot$, $M_\star = 1\,M_\odot$, $P_\text{QPE} = 24\,$h, $M_{\text{dis},\star} = 1\,M_\odot$, $p = 1$, $\alpha = 0.1$; see also Appendix \ref{['apendixb']} for details.
• Figure 5: The ablation rate of the stellar mass after $t_\text{vis}$. Top: The remaining stellar mass scaled to $M_{\star} = M_1(0)$ evolves with time. Bottom: The mass of the debris lost during the disk passages, scaled to $M_{\star}$ again. The curves that reach the half on the $y$-axis (top panel) do not continue further since the star lost a significant amount of mass. We started the mass loss after $t_\text{vis}$, which is a point in time where $\rho_{\rm d}$ in a post-TDE disk starts to decay with a power-law of $n$. The first 4 curves are for the $M_{\rm dis} = 1$ but the last one for $M_{\rm dis} = 5$ and $M_{\bullet,6} = 1, M_1 = 1$.