The X-ray variability of tidal disruption events

Abstract

When a star is torn apart by the tidal forces of a supermassive black hole (a so-called TDE) a transient accretion episode is initiated and a hot, often X-ray bright, accretion disk is formed. Like any accretion flow this disk is turbulent, and therefore the emission from its surface will vary stochastically. As the disk has a finite mass supply (i.e., at most the initial mass of the disrupted star) the disk will also undergo long-timescale evolution, as this material is lost into the black hole. In this paper we combine theoretical models for this long time evolution of the disk with models for the stochastic variability of turbulent accretion flows which are correlated on short (orbital) timescales. This new framework allows us to demonstrate that (i) dimming events should be more prevalent than brightening events in long term TDE X-ray light curves (i.e., their log-luminosity distribution should be asymmetric), (ii) TDE X-ray light curves should follow a near- (but formally sub-)linear correlation between their root mean square variability and the mean flux, (iii) the fractional variability observed on short timescales across an X-ray observing band should increase with observing energy, and (iv) TDEs offer a unique probe of the physics of disk turbulence, owing to their clean spectra and natural evolutionary timescales. We confirm predictions (i) and (ii) with an analysis of the long timescale variability of two observed TDEs, and show strong support for prediction (iii) using the intra-observation variability of the same two sources.

Figures (13)

• Figure 1: Realistic accretion flows are turbulent, owing to the magnetorotational instability. This results in the temperature of these flows being highly stochastic on short ($\sim$ the orbital) timescales. As this orbital timescale is typical $\sim$ hours for a TDE, this will result in stochastic, multi-timescale, variability in the observed X-ray luminosity of these sources. The panels here show two slices through a realistic GRMHD simulation of an accretion flow, with data taken from MummeryStone24. The temperature of the accretion flow is displayed in code units on a logarithmic scale. Clearly, capturing this variability in TDE observations will provide important constraints on physical models of the turbulence which drives the accretion process.
• Figure 2: The distributions of the outliers of a series of $N$ observations of an accretion disk with temperature $k\mu_T = 90$ eV, with temperature variance $k\sigma_T = 20$ eV. The black hole mass was taken to be $M_\bullet = 10^6 M_\odot$. The left hand panel shows the distribution of the brightest outliers, while the right hand panel shows the distribution of the dimmest outliers. The black dashed curve on both panels is for $N = 1$ observations and, as it must be, is identical for both. Note that the distribution of the bright outliers saturates around $L_{X, \, {\rm max}} \sim 10^{44}$ erg/s, while the distribution of dimming episodes tends to zero without a saturating bound. This is a natural result of the shape of a typical disk spectrum and can be simply understood (see text). It is important to stress that this analysis assumes that each of the $N$ observations are uncorrelated with one another.
• Figure 3: On the left we show a single realisation of a short-timescale X-ray light curve, with luminosity measured above a series of different observing energies (colourbar), for a disk with mean temperature $k\mu_T = 120$ eV, temperature variance of $\sigma_T/\mu_T = 0.05$ and a correlation time $t_{\rm corr} = 100,000$ seconds. The observations where taken near-continuously (sampled $N=1000$ times) over $t_{\rm obs} = 200,000$ seconds. These parameters were chosen to simulate a detailed XMM observation across different energy channels. On the right we show the fractional variability of each of the light curves, showing how the fractional variability increases with observing energy. This is a generic prediction of the theory developed here, and while the values of $F$ vary on a case-by-case basis, the trend of $F$ with energy is a robust prediction of this theory. Both the energy dependence and short-timescale correlations are clear to see, by eye, in the left hand plot.
• Figure 4: Five random realisations of stochastic, short-timescale, X-ray light curves for different correlation times of the flow, each for mean disk temperature $k \mu_T = 120$ eV and for fractional temperature variability $\sigma_T/\mu_T = 0.1$. The (most variable) upper left plot has $t_{\rm corr} = 10^4$ seconds, the (less variable) upper right plot has $t_{\rm corr} = 5\times 10^4$ seconds, and the (least variable) lower plot has $t_{\rm corr} = 10^5$ seconds. Note that while each set of light curves are generated with fixed fractional temperature variability, short correlation timescales produce noticeably larger variance in a given observational window. Given that the orbital timescale of the inner regions of a supermassive black hole disk can be of order $t_{\rm orb} \sim {\cal O}(10^3-10^4)$ seconds, short-timescale observations of TDEs will likely provide an extremely interesting probe of the natural timescale of turbulent variability in accretion disks (in units of the orbital timescale), a question of fundamental interest in disk physics. Note that the vertical axes of each panel are the same. On the lower right plot we show the distribution of the ratio of each observed luminosity to the mean across the observing window (i.e., the distribution of $R=\{L_j\}/\left\langle \{L_j\}\right\rangle$ for a list of observations $\{L_j\}$), averaged over 500 random realisations of the light curves, as a function of the assumed correlation timescale of the flow (displayed on plot). All other parameters are the same as for the three other plots.
• Figure 5: The power spectral density plotted against frequency of five different realisations of stochastic, short-timescale, X-ray light curves for different correlation times of the flow (denoted on plot). These light curves are generated in an identical manner to those shown in Figure \ref{['fig:correlation_time']}. The amplitude of the PSDs are re-normalised by a multiplicative offset for visibility purposes, while the frequency axis is in physical units. Dashed lines show simple power-law fits to the PSD of each light curve. While all light curves are formally described by "red" noise, shorter correlation times (relative to the typical observing cadence) produce "whiter" noise (see text for more discussion).