The TDE Population from First-Principles Models of Stellar Disruption and Debris Dynamics

TL;DR

This work presents a physically grounded TDE population framework that ties peak luminosity to first-principles hydrodynamic disruption simulations, eliminating free emission parameters. By combining a calibrated $L_{ m peak}(M_*,M_{ m BH})$ with parametric stellar mass functions $dN_*/dM_*$ and BH-rate distributions $d{ m R}_{ m BH}/dM_{ m BH}$, the authors infer the underlying stellar population and disruption rates using MCMC against the ManyTDE data. The results favor an old, low-mass-dominated nuclear population with a near-flat $d{ m R}_{ m BH}/dM_{ m BH}$ and show that partial disruptions contribute a substantial fraction (~30%) of detectable events, shaping the observed $M_{ m BH}$–$L_{ m peak}$ distribution. The analysis also predicts a large, largely undetected population of low-luminosity TDEs, suggesting the true volumetric TDE rate may exceed current estimates by up to an order of magnitude. Overall, the study demonstrates strong statistical consistency between hydrodynamics-based predictions and observed demographics, while highlighting key sensitivities to the stellar mass–radius relation and the need to treat high-mass BH regimes separately.

Abstract

We present a physically-grounded population model for optical tidal disruption events (TDEs) that combines first-principles hydrodynamic simulations of stellar disruption with statistical inference of the underlying stellar and black hole populations. The model's prediction of peak luminosity is based directly on recent global simulations that follow the disruption self-consistently and contains no tunable parameters related to the emission physics. We construct the predicted joint distribution of peak luminosity and black hole mass, including both full and partial disruptions, and compare it to a sample of observed TDEs using Bayesian inference and Markov chain Monte Carlo sampling. We find that the model reproduces the distribution in the ($M_{BH},L_{peak}$) plane for the bulk of the observed TDE population with good statistical consistency. The data strongly favor an old stellar population, with a sharp suppression of stars above $M_* \simeq 1.5 - 2 M_\odot$. They also indicate that, at fixed stellar mass, the volumetric TDE rate is nearly independent of black hole mass. Partial disruptions contribute a substantial fraction ($\sim 30\%$) of detected events in flux-limited samples and are essential for reproducing the observed distribution. The inferred population properties are robust to different approximations to the stellar mass-radius relation, although the event rate at high luminosity is sensitive to the form of this relation for massive stars. We predict a large population of difficult to detect low luminosity TDEs, implying that the true volumetric TDE rate may exceed that inferred from present samples by up to an order of magnitude.

Figures (11)

• Figure 1: The observed data points in the ManyTDE sample MvV. $L_{\rm peak}$ is in erg s$^{-1}$ and $M_{\rm BH}$ has units of $M_\odot$. As discussed in the text, events with $M_{\rm BH} \gtrsim 10^8 M_\odot$ must have dynamics qualitatively different from those involving lower-mass black holes.
• Figure 2: Luminosities of full disruptions with stellar masses $M_*=0.1, 0.3, 0.5, 1, 3, 10, 30 M_\odot$ as functions of $M_{\rm BH}$. Solid lines are calculated using the single power-law mass-radius relation and dashed lines are calculated from the modified one. Also shown are the curves of luminosity our model would predict for $R_T=6 r_g$ and $R_T = 4r_g$; extreme TDEs occur when $4r_g < r_p < 6r_g$Ryu+2023; direct capture ensues when $r_p < 4 r_g$ (an exact result for Schwarzschild spacetime, the angle-averaged result for Kerr Krolik+2020). The luminosities of partial disruptions of a given $M_*$ form a family lying below the curve for a full disruption of such a star.
• Figure 3: The event rate density in the $\log M_{\rm BH} \times \log L_{\rm peak}$ plane for flux-limited samples: full disruptions (left) and partial disruptions (right). In both cases, the stellar mass function's shape is the Salpeter IMF, and $\alpha_{\rm BH} = 0.$ Rates are shown on a linear scale calibrated by the colorbar; these scales are the same to make it easy to gauge the ratio of partial events to full.
• Figure 4: The total (full + partial) event rate density in the $\log M_{\rm BH} \times \log L_{\rm peak}$ plane for flux-limited samples. Both panels assume that the stellar mass function is proportional to a Salpeter IMF, but in the left panel $\alpha_{\rm BH} = -0.5$ and in the right panel $\alpha_{\rm BH} = +0.5$. Rates (in arbitrary units) are shown on a linear scale calibrated by the colorbar.
• Figure 5: The total (full + partial) event rate density in the $\log M_{\rm BH} \times \log L_{\rm peak}$ plane for flux-limited samples. Both plots have $\alpha_{\rm BH} = 0$, but the left utilizes a Salpeter IMF mass function, cut-off at $1M_\odot$, i.e., $\alpha_1 = 2.35$, $\alpha_2 = 4$, and $M_b = 1M_\odot$, whereas the right has no cut-off: $\alpha_1 = \alpha_2 = 2.35$. Rates (arbitrary units) are shown on a linear scale calibrated by the colorbar.