Supermassive black hole mass inference with the optical flares of tidal disruption events

TL;DR

TDEs offer a unique avenue to constrain SMBH masses using optical/UV emission, particularly as LSST-type surveys raise the number of detections. The authors introduce TDEFLARE, a fast, empirically calibrated framework that links black hole mass to three optical/UV observables—plateau luminosity $L_P$, peak luminosity $L_{ m pk}$, and radiated energy $E_g$—via robust scaling relations, then combines their mass posteriors using conflation, while accounting for relativistic Hills-mass effects. The approach yields mass constraints consistent with detailed disk models and known galactic scaling relations, works for full and partial (including repeating) TDEs, and remains effective with limited data near peak, which is crucial for large LSST samples. The work further discusses population-level implications, including the intrinsic TDE BH mass function, Malmquist-Hills biases, and LSST-driven population synthesis, highlighting both methodological strengths and biases to consider in interpreting TDE-based demographics.

Abstract

Tidal disruption events (TDEs) represent a truly unique, and potentially very powerful, probe of the quiescent supermassive black hole (SMBH) population. Given current observational survey capabilities the vast majority of the TDEs discovered in the next decade will be observed only across optical-UV wavelengths. A set of questions of broad scientific interest relating to SMBH demographics and SMBH-galaxy correlations could in principal be answered by using TDE emission as an efficient means to constrain SMBH masses. In this paper we argue for using well-understood elements of TDE emission (the thermal X-ray continuum and late-time UV plateau) to derive empirical relationships between the more poorly understood early optical/UV flare and the black hole mass, before using these empirical relationships to measure TDE black hole masses simply and rapidly. We provide a publicly available code TDEFLARE which does this, showing (i) it produces results consistent with disk codes containing far more physics, (ii) it reproduces galactic scaling relationships at high ($>5σ$) significance, (iii) it produces reliable mass estimates for both partial and full disruptions, and (iv) it does not require late time data to derive mass constraints. We provide 89 TDE black hole mass constraints, derive the intrinsic black hole mass function implied by the current TDE population, and discuss the Malmquist-Hills bias, an important confounding factor in TDE science.

Figures (11)

• Figure 1: The scaling relationships employed by TDEFLARE between the black hole mass and the radiated $g$-band energy (upper left), the peak $g$-band luminosity (upper right) and the $g$-band plateau luminosity (lower). The lower panel plots black hole masses as inferred from galactic scaling relationships ($M_\bullet-\sigma$ where available, and if not $M_\bullet-M_{\rm bulge}$ where available, and otherwise $M_\bullet-M_{\rm gal}$) against observed plateau luminosities, while the curve and shaded region is derived from first principles disk theory. The upper two panels use the disk-theory informed black hole masses to calibrate empirical scaling relationships between the radiated energy/peak luminosity and the black hole mass. These curves are not based on a fundamental theory, but remain of practical use in constraining black hole masses from TDE data. In each plot the dashed curve represents the median of the scaling relationship, while the shaded region denotes the width of one $\epsilon_i$ scatter (in log space), for each of the three scaling relationships (see text).
• Figure 2: The optical flares from TDEs are, broadly speaking, simple to describe over their first decade of luminosity decay in the sense that they are well described by exponential profiles. Left: the optical ($g$-band) light curves of four TDEs (names on plot), chosen to span the full range of peak luminosities seen in TDEs. Right: these light curves "normalised", i.e., the observed luminosity normalised by their peak spectral luminosity, and with time axis normalised by a simple exponential decay timescale $\tau$ (fit to each TDEs first $\sim 100$ days of $g$-band data). The inset shows the first decade of decay, which by definition takes $\ln(10)\approx 2.3$ decay times. Brighter TDEs decay more slowly (the opposite of what would be expected from fallback arguments). This implies that the initial flare from TDEs can be described by two numbers in an exponential profile (with minimal "hidden" variables), both of which can be related to the black hole mass in the system.
• Figure 3: An example of the TDEFLARE fitting process and results. Upper left: the observed and modeled multi wavelength light curves of AT2019dsg, highlighting that the phenomenological model reproduces the data well. Upper right: the posterior distributions of the fitted parameters, showing that the three important parameters can be constrained well. Lower left: the three individual posterior distributions of the black hole mass, from the different observed parameters (blue, green and purple) and the conflated distribution (black). Lower right: a comparison of various black hole mass inference techniques, with varying degrees of physical content. All are consistent at $1\sigma$.
• Figure 4: The importance of including the physics of the Hills mass when constraining the black hole mass of bright (high mass) sources. The upper panel shows the light curve fits and posterior distributions of fits to the TDE eJ2344. The source is extremely bright, implying high mass posteriors (lower panel). If one does not include Hills mass physics one infers a mass which is above the typical Hills scale (black curve), when Hills mass physics is taken into account the mass posterior drops (red curve), bringing it into line with more complex models (numerical posterior from the FitTeD code shown as a grey histogram). The posterior is also consistent with the $M_\bullet-\sigma$ relationship (orange dashed curve).
• Figure 5: Fitting TDEFLARE to two successive flares of the repeating partial tidal disruption event AT2022dbl. The upper left and right panels show light curve modeling of the two successive flares, with parameter posteriors shown in the middle row. The first flare has sufficient data to constrain the plateau, while the second does not. The lowest panel shows black hole mass inference from each scaling relationship (green, purple and blue) techniques for flare 1 (dashed curves) and flare 2 (solid curves). The conflated distributions (black) are consistent between the two epochs, and are consistent with the $M_\bullet-\sigma$ mass at $1\sigma$.