Tidal disruption event Calorimetry: Observational constraints on the physics of TDE optical flares

TL;DR

This work applies a calorimetric framework to early-time optical/UV TDE flares, extracting the peak luminosity and total radiated energy and tying them to black hole mass across a large sample. By compiling and evaluating ten theoretical models, the authors demonstrate that most proposed mechanisms fail to reproduce the observed positive scaling of both $L_{ m pk}$ and $E_{ m rad}$ with $M_ullet$, ruling out efficient fallback accretion and apocenter-stream shocks as primary drivers. The analysis favors models in which compact disk formation and subsequent reprocessing (or cooling-envelope energy release) power the optical flare, with radiation likely near the Eddington limit on relevant timescales. An important conclusion is that the early-time emission arises from a disk-formation/cooling envelope process with possible reprocessing, rather than a direct, fallback-rate–powering mechanism, and that a full, self-consistent treatment of fallback, disk formation, and radiative transport across BH masses remains an open problem with implications for TDE demographics and accretion physics.

Abstract

Tidal disruption events are routinely discovered as bright optical/UV flares, the properties of which are now well categorized on the population level. The underlying physical processes that produce the evolution of their X-ray emission and their long-lasting UV/optical plateau are well understood; however, the origin of their early-time optical/UV emission remains the subject of much debate and uncertainty. In this paper we propose and perform ``Calorimetric'' tests of published theories of these optical flares, contrasting theoretical predictions for the scaling of the radiated energy and peak luminosity of these flares with black hole mass (something which is predicted by each theory), with the observed (positive) black hole mass scaling. No one theory provides a satisfactory description of observations at all black hole mass scales. Theories relating to the reprocessing of an Eddington-limited compact accretion disk, or emission (energy) released in the formation of a Keplerian disk near the circularisation radius, perform best, but require extending. Models whereby the optical/UV flare are directly produced by shocks between debris streams (e.g., TDEmass), or the efficient reprocessing of the fallback rate (e.g., MOSFIT, or any other model in which $L \propto \dot{M}_{\mathrm{fb}}$), are ruled out at high $(>5σ)$ significance by the data.

Figures (15)

• Figure 1: The observed correlation between (i) the energy radiated in the TDE optical/UV flare and (ii) the peak bolometric luminosity of the TDE optical/UV flare and the black hole mass in the center of the event. The upper panels show the explicit correlations, with the black hole masses inferred from the late-time UV luminosity (which produces the scaling relationships with the least scatter). Typical uncertainties in the black hole masses are shown by the error bar in the lower right hand corner of each plot. The red curve shows the posterior median correlation, while the three shaded regions show $1, 2$ and $3\sigma$ contours respectively. The lower panel shows the posterior distributions of the power-law fits under different assumptions regarding how the black hole mass should be constrained (UV-plateau in blue, $M_\bullet-\sigma$ in green, $M_\bullet-M_{\rm gal}$ in red and $M_\bullet-M_{\rm bulge}$ in orange). All four black hole mass estimation techniques provide consistent results.
• Figure 2: The scaling with black hole mass of the peak blackbody luminosity expected to be observed from the optical/UV flare in a TDE, for the seven models collated in this work. Shown by a dashed curve is the result for $m_\star = 0.5$, and the degree of expected variance in the models is shown by the shaded regions which denote the range for stellar mass $m_\star = 0.3-0.7$. By points we show the observed TDE values. Different models are labeled on each plot. Typical uncertainties in the black hole masses are shown by the error bar in the lower right hand corner of each plot.
• Figure 3: The scaling with black hole mass of the radiated energy expected to be observed in the optical/UV flare in a TDE, for the ten models collated in this work. Shown by a dashed curve is the result for $m_\star = 0.5$, and the degree of expected variance in the models is shown by the shaded regions which denote the range for stellar mass $m_\star = 0.3-0.7$. By points we show the observed TDE values. Different models are labeled on each plot. Typical uncertainties in the black hole masses are shown by the error bar in the lower right hand corner of each plot.
• Figure 4: The scaling with black hole mass of the late time ($\Delta t > 1\, {\rm yr}$) optical/UV luminosity expected to be observed after the initial optical/UV flare in a TDE, for disk formation scenarios at different radial scales. Shown by a dashed curve is the result for $m_\star = 0.5$, and the degree of expected variance in the models is shown by the shaded regions which denote the range for stellar mass $m_\star = 0.3-0.7$. By points we show the observed TDE values, with black hole masses inferred from galactic scaling relationships ($M_\bullet-\sigma$ where available, and $M_\bullet-M_{\rm bulge}$ otherwise). Typical uncertainties in the black hole masses are shown by the error bar in the lower right hand corner of each plot.
• Figure 5: The fallback rate (black dashed curve) and the black hole accretion rate (colored solid lines) for four different viscous timescales (denoted on plot) for the full disruption of a $m_\star = 0.5$ star about a $10^6M_\odot$ black hole (left) and a $10^7M_\odot$ black hole (right). The accretion rate onto the black hole is generically suppressed with respect to the fallback rate, with a degree of suppression which depends on the ratio of $t_{\rm visc}/t_{\rm fb}$. Note that the late time evolution of the accretion rate (the power law fall off at late times) is set by the microphysics of accretion (the index $n$) not the index in the fallback rate.