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1. A simple and accurate prescription for the tidal disruption radius of a star and the peak accretion rate in tidal disruption events

   https://doi.org/10.1093/mnrasl/slac106  

   Coughlin, Eric R; Nixon, C J (September 2022, Monthly Notices of the Royal Astronomical Society: Letters)

   ABSTRACT A star destroyed by a supermassive black hole (SMBH) in a tidal disruption event (TDE) enables the study of SMBHs. We propose that the distance within which a star is completely destroyed by an SMBH, defined rt,c, is accurately estimated by equating the SMBH tidal field (including numerical factors) to the maximum gravitational field in the star. We demonstrate that this definition accurately reproduces the critical βc = rt/rt,c, where rt = R⋆(M•/M⋆)1/3 is the standard tidal radius with R⋆ and M⋆ the stellar radius and mass, and M• the SMBH mass, for multiple stellar progenitors at various ages, and can be reasonably approximated by βc ≃ [ρc/(4ρ⋆)]1/3, where ρc (ρ⋆) is the central (average) stellar density. We also calculate the peak fallback rate and time at which the fallback rate peaks, finding excellent agreement with hydrodynamical simulations, and also suggest that the partial disruption radius – the distance at which any mass is successfully liberated from the star – is βpartial ≃ 4−1/3 ≃ 0.6. For given stellar and SMBH populations, this model yields, e.g. the fraction of partial TDEs, the peak luminosity distribution of TDEs, and the number of directly captured stars. 

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2. The Peak of the Fallback Rate from Tidal Disruption Events: Dependence on Stellar Type

   https://doi.org/10.3847/2041-8213/ad0388  

   Bandopadhyay, Ananya; Fancher, Julia; Athian, Aluel; Indelicato, Valentino; Kapalanga, Sarah; Kumah, Angela; Paradiso, Daniel A; Todd, Matthew; Coughlin, Eric R; Nixon, C J (January 2024, The Astrophysical Journal Letters)

   Abstract A star completely destroyed in a tidal disruption event (TDE) ignites a luminous flare that is powered by the fallback of tidally stripped debris to a supermassive black hole (SMBH) of massM_•. We analyze two estimates for the peak fallback rate in a TDE, one being the “frozen-in” model, which predicts a strong dependence of the time to peak fallback rate,t_peak, on both stellar mass and age, with 15 days ≲t_peak≲ 10 yr for main sequence stars with masses 0.2 ≤M_⋆/M_⊙≤ 5 andM_•= 10⁶M_⊙. The second estimate, which postulates that the star is completely destroyed when tides dominate the maximum stellar self-gravity, predicts thatt_peakis very weakly dependent on stellar type, with $t_{\mathrm{peak}}=\left(23.2\pm 4.0\mathrm{days}\right){\left(M_{•}/{10}^6{M}_{\odot }\right)}^{1/2}$for 0.2 ≤M_⋆/M_⊙≤ 5, while $t_{\mathrm{peak}}=\left(29.8\pm 3.6\mathrm{days}\right){\left(M_{•}/{10}^6{M}_{\odot }\right)}^{1/2}$for a Kroupa initial mass function truncated at 1.5M_⊙. This second estimate also agrees closely with hydrodynamical simulations, while the frozen-in model is discrepant by orders of magnitude. We conclude that (1) the time to peak luminosity in complete TDEs is almost exclusively determined by SMBH mass, and (2) massive-star TDEs power the largest accretion luminosities. Consequently, (a) decades-long extra-galactic outbursts cannot be powered by complete TDEs, including massive-star disruptions, and (b) the most highly super-Eddington TDEs are powered by the complete disruption of massive stars, which—if responsible for producing jetted TDEs—would explain the rarity of jetted TDEs and their preference for young and star-forming host galaxies. 

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3. Cooling Envelope Model for Tidal Disruption Events

   https://doi.org/10.3847/2041-8213/ac90ba  

   Metzger, Brian D. (September 2022, The Astrophysical Journal Letters)

   Abstract We present a toy model for the thermal optical/UV/X-ray emission from tidal disruption events (TDEs). Motivated by recent hydrodynamical simulations, we assume that the debris streams promptly and rapidly circularize (on the orbital period of the most tightly bound debris), generating a hot quasi-spherical pressure-supported envelope of radius R v ∼ 10 14 cm (photosphere radius ∼10 15 cm) surrounding the supermassive black hole (SMBH). As the envelope cools radiatively, it undergoes Kelvin–Helmholtz contraction R v ∝ t −1 , its temperature rising T eff ∝ t 1/2 while its total luminosity remains roughly constant; the optical luminosity decays as ν L ν ∝ R v 2 T eff ∝ t − 3 / 2 . Despite this similarity to the mass fallback rate M ̇ fb ∝ t − 5 / 3 , envelope heating from fallback accretion is subdominant compared to the envelope cooling luminosity except near optical peak (where they are comparable). Envelope contraction can be delayed by energy injection from accretion from the inner envelope onto the SMBH in a regulated manner, leading to a late-time flattening of the optical/X-ray light curves, similar to those observed in some TDEs. Eventually, as the envelope contracts to near the circularization radius, the SMBH accretion rate rises to its maximum, in tandem with the decreasing optical luminosity. This cooling-induced (rather than circularization-induced) delay of up to several hundred days may account for the delayed onset of thermal X-rays, late-time radio flares, and high-energy neutrino generation, observed in some TDEs. We compare the model predictions to recent TDE light-curve correlation studies, finding both agreement and points of tension. 

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4. On the relative importance of shocks and self-gravity in modifying tidal disruption event debris streams

   https://doi.org/10.1093/mnras/stad2858  

   Fancher, Julia; Coughlin, Eric R; Nixon, C J (September 2023, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT In a tidal disruption event (TDE), a star is destroyed by the gravitational field of a supermassive black hole (SMBH) to produce a stream of debris, some of which accretes onto the SMBH and creates a luminous flare. The distribution of mass along the stream has a direct impact on the accretion rate, and thus modelling the time-dependent evolution of this distribution provides insight into the relevant physical processes that drive the observable properties of TDEs. Analytic models that only account for the ballistic evolution of the debris do not capture salient and time-dependent features of the mass distribution, suggesting that fluid dynamical effects significantly modify the debris dynamics. Previous investigations have claimed that shocks are primarily responsible for these modifications, but here we show – with high-resolution hydrodynamical simulations – that self-gravity is the dominant physical mechanism responsible for the anomalous (i.e. not predicted by ballistic models) debris stream features and its time dependence. These high-resolution simulations also show that there is a specific length-scale on which self-gravity modifies the debris mass distribution, and as such there is enhanced power in specific Fourier modes. Our results have implications for the stability of the debris stream under the influence of self-gravity, particularly at late times and the corresponding observational signatures of TDEs. 

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5. Counting the Unseen. II. Tidal Disruption Event Rates in Nearby Galaxies with REPTiDE

   https://doi.org/10.3847/1538-4357/addd1b  

   Hannah, Christian H; Stone, Nicholas C; Seth, Anil C; van_Velzen, Sjoert (July 2025, The Astrophysical Journal)

   Abstract Tidal disruption events (TDEs) are a class of transients that occur when a star is destroyed by the tides of a massive black hole (MBH). Their rates encode valuable MBH demographic information, but this can only be extracted if accurate TDE rate predictions are available for comparisons with observed rates. In this work, we present a new, observer-friendly Python package called REPTiDE, which implements a standard loss-cone model for computing TDE rates given a stellar density distribution and an MBH mass. We apply this software to a representative sample of 91 nearby galaxies over a wide range of stellar masses with high-resolution nuclear density measurements from C. H. Hannah et al. We measure per-galaxy TDE rates ranging between 10^−7.7and 10^−2.9yr^–1and find that the sample-averaged rates agree well with observations. We find a turnover in the TDE rate as a function of both galaxy stellar mass and black hole mass, with the peak rates being observed in galaxies at a galaxy mass of 10^9.5M_⊙and a black hole mass of 10^6.5M_⊙. Despite the lower TDE rates inferred for intermediate-mass black holes, we find that they have gained a higher fraction of their mass through TDEs when compared to higher-mass black holes. This growth of lower-mass black holes through TDEs can enable us to place interesting constraints on their spins; we find maximum spins ofa_• ≈ 0.9 for black holes with masses below ∼10^5.5M_⊙. 

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