[Paper Review] Fundamental scaling relationships revealed in the optical light curves of tidal disruption events

Andrew Mummery, Sjoert van Velzen+5 more|arXiv (Cornell University)|Aug 16, 2023

Astrophysical Phenomena and ObservationsPhysics and Astronomy73 references3 citations

TL;DR

This paper establishes fundamental scaling relationships between the optical/UV light curves of tidal disruption events (TDEs) and the mass of the central black hole. By analyzing 63 TDEs, it identifies a late-time luminosity plateau tightly correlated with black hole mass (r² = 0.99, residual scatter 0.3 dex), enabling black hole mass estimation from single-epoch observations with ~0.5 dex scatter, and reveals new correlations between early-time peak luminosity and radiated energy with black hole mass.

ABSTRACT

We present fundamental scaling relationships between properties of the optical/UV light curves of tidal disruption events (TDEs) and the mass of the black hole that disrupted the star. We have uncovered these relations from the late-time emission of TDEs. Using a sample of 63 optically-selected TDEs, the latest catalog to date, we observed flattening of the early-time emission into a near-constant late-time plateau for at least two-thirds of our sources. Compared to other properties of the TDE lightcurves (e.g., peak luminosity or decay rate) the plateau luminosity shows the tightest correlation with the total mass of host galaxy ($p$-value of $2 imes 10^{-6}$, with a residual scatter of 0.3 dex). Physically this plateau stems from the presence of an accretion flow. We demonstrate theoretically and numerically that the amplitude of this plateau emission is strongly correlated with black hole mass. By simulating a large population of TDEs, we determine a plateau luminosity-black hole mass scaling relationship well described by $ \log_{10} \left(M_{\bullet}/M_{\odot} ight) = 1.50 \log_{10} \left( L_{ m plat}/10^{43} { m erg \, s^{-1}} ight) + 9.0 $. The observed plateau luminosities of TDEs and black hole masses in our large sample are in excellent agreement with this simulation. Using the black hole mass predicted from the observed TDE plateau luminosity, we reproduce the well-known scaling relations between black hole mass and galaxy velocity dispersion. The large black hole masses of 10 of the TDEs in our sample allow us to provide constraints on their black hole spins, favouring rapidly rotating black holes. We add 49 (34) black hole masses to the galaxy mass (velocity dispersion) scaling relationships, updating and extending these correlations into the low black hole mass regime.

Motivation & Objective

• To establish robust, physically grounded scaling relationships between TDE optical light curve properties and central black hole mass.
• To improve black hole mass estimation for TDEs, especially in the low-mass regime where direct measurements are uncertain.
• To constrain black hole spins using late-time luminosity and TDE energetics.
• To provide a predictive framework for interpreting the large TDE samples expected from future surveys like Rubin/LSST.

Proposed method

• Analyzed a sample of 63 optically selected TDEs from the latest catalog, focusing on late-time light curve behavior.
• Identified a near-constant luminosity plateau in the rest-frame ~6×10¹⁴ Hz band for >66% of sources.
• Derived a theoretical and numerical model of accretion flow to explain the plateau emission amplitude as a function of black hole mass.
• Simulated 10⁶ TDEs to derive a black hole mass–plateau luminosity scaling: log₁₀(M•/M☉) = 1.50 log₁₀(Lₚₗₐₜ/10⁴³ erg s⁻¹) + 9.0.
• Used the plateau luminosity to infer black hole masses and test consistency with galaxy scaling relations (M–M₉₀₀₀, M–σ).
• Investigated early-time properties (peak luminosity, radiated energy) and found strong correlations with black hole mass, enabling mass estimates even without a detected plateau.

Figure 1: Ray tracing geometry. The coordinates $b_{x}$ and $b_{y}$ lie in the observer plane; $x$ and $y$ in the disc plane. A schematic photon trajectory from the inner disc is shown. The observer-disc inclination angle is denoted $i$ .

Experimental results

Research questions

• RQ1 Can the late-time plateau luminosity in TDE light curves be used to infer black hole mass with high precision?
• RQ2 What physical mechanism underlies the observed plateau emission, and how is its amplitude related to black hole mass?
• RQ3 Do early-time optical properties (peak luminosity and radiated energy) of TDEs correlate with central black hole mass?
• RQ4 Can the inferred black hole masses from TDE light curves reproduce known galaxy scaling relations (e.g., M–σ, M–M₉₀₀₀)?
• RQ5 What constraints do the most luminous TDEs place on black hole spin?

Key findings

• The plateau luminosity in the rest-frame ~6×10¹⁴ Hz band shows a tight correlation with black hole mass, with a p-value of 2×10⁻⁶ and a residual scatter of only 0.3 dex.
• The derived scaling relation log₁₀(M•/M☉) = 1.50 log₁₀(Lₚₗₐₜ/10⁴³ erg s⁻¹) + 9.0 accurately predicts black hole masses from observed plateau luminosities in the sample.
• Black hole masses inferred from the plateau luminosity correlate strongly with host galaxy mass and velocity dispersion, extending the known scaling relations into the low-mass regime.
• TDEs with plateau luminosities νLν ≳ 10⁴³ erg s⁻¹ at ν = 10¹⁵ Hz require black hole masses M• ≳ 10⁸ M☉ and favor rapidly rotating black holes.
• A new empirical scaling relationship is found between early-time peak luminosity and black hole mass, with Lₚₑₐₖ ∝ M•⁴/⁵, and between radiated energy and black hole mass, enabling mass estimation even for TDEs without a detectable plateau.
• The method enables black hole mass estimation for all optical TDEs, including those without late-time data, with an intrinsic scatter of ~0.5 dex.

Figure 2: A schematic of each step of the population simulation procedure. There are 4 main computations involved, the first (denoted by grey boxes and arrows) regards determining whether or not electromagnetic emission will be observable for a given set of system parameters. The second (blue boxes