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1. The Luminosity Function of Tidal Disruption Events from Fallback-powered Emission: Implications for the Black Hole Mass Function

   https://doi.org/10.3847/2041-8213/acd0b2  

   Coughlin, Eric R.; Nicholl, Matt (May 2023, The Astrophysical Journal Letters)

   Abstract Tidal disruption events (TDEs), in which a star is destroyed by the gravitational field of a supermassive black hole (SMBH), are being observed at a high rate owing to the advanced state of survey science. One of the properties of TDEs that is measured with increasing statistical reliability is the TDE luminosity function, $d{\dot{N}}_{\mathrm{TDE}}/\mathit{dL}$, which is the TDE rate per luminosity (i.e., how many TDEs are within a given luminosity range). Here we show that if the luminous emission from a TDE is directly coupled to the rate of return of tidally destroyed debris to the SMBH, then the TDE luminosity function is in good agreement with observations and scales as ∝L^−2.5for high luminosities, provided that the SMBH mass function ${\mathit{dN}}_{•}/{\mathit{dM}}_{•}$—the number of SMBHs (N_•) per SMBH mass (M_•)—is approximately flat in the mass range over which we observe TDEs. We also show that there is a cutoff in the luminosity function at low luminosities that is a result of direct captures, and this cutoff has been tentatively observed. If ${\mathit{dN}}_{•}/{\mathit{dM}}_{•}$is flat, which is in agreement with some observational campaigns, these results suggest that the fallback rate feeds the accretion rate in TDEs. Contrarily, if ${\mathit{dN}}_{•}/d\log M_{•}$is flat, which has been found theoretically and is suggested by other observational investigations, then the emission from TDEs is likely powered by another mechanism. Future observations and more TDE statistics, provided by the Rubin Observatory/LSST, will provide additional evidence as to the reality of this tension. 

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2. Repeating Nuclear Transients from Repeating Partial Tidal Disruption Events: Reproducing ASASSN-14ko and AT2020vdq

   https://doi.org/10.3847/1538-4357/ad6a5a  

   Bandopadhyay, Ananya; Coughlin, Eric_R; Nixon, C_J; Pasham, Dheeraj_R (October 2024, The Astrophysical Journal)

   Abstract Some electromagnetic outbursts from the nuclei of distant galaxies have been found to repeat on months-to-years timescales, and each of these sources can putatively arise from the accretion flares generated through the repeated tidal stripping of a star on a bound orbit about a supermassive black hole (SMBH), i.e., a repeating partial tidal disruption event (rpTDE). Here, we test the rpTDE model through analytical estimates and hydrodynamical simulations of the interaction between a range of stars, which differ from one another in mass and age, and an SMBH. We show that higher-mass (≳1M_⊙), evolved stars can survive many (≳10−100) encounters with an SMBH while simultaneously losingfew× 0.01M_⊙, resulting in accretion flares that are approximately evenly spaced in time with nearly the same amplitude, quantitatively reproducing ASASSN-14ko. We also show that the energy imparted to the star via tides can lead to a change in its orbital period that is comparable to the observed decay in the recurrence time of ASASSN-14ko’s flares, $\dot{P}\simeq -0.0026$. Contrarily, lower-mass and less-evolved stars lose progressively more mass and produce brighter accretion flares on subsequent encounters for the same pericenter distances, leading to the rapid destruction of the star and cessation of flares. Such systems cannot reproduce ASASSN-14ko-like transients, but are promising candidates for recreating events such as AT2020vdq, which displayed a second and much brighter outburst compared to the first. Our results imply that the lightcurves of repeating transients are tightly coupled with stellar type. 

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3. 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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4. Stars Crushed by Black Holes. II. A Physical Model of Adiabatic Compression and Shock Formation in Tidal Disruption Events

   https://doi.org/10.3847/1538-4357/ac3fb9  

   Coughlin, Eric R.; Nixon, C. J. (February 2022, The Astrophysical Journal)

   Abstract We develop a Newtonian model of a deep tidal disruption event (TDE), for which the pericenter distance of the star,r_p, is well within the tidal radius of the black hole,r_t, i.e., whenβ≡r_t/r_p≫ 1. We find that shocks form forβ≳ 3, but they are weak (with Mach numbers ∼1) for allβ, and that they reach the center of the star prior to the time of maximum adiabatic compression forβ≳ 10. The maximum density and temperature reached during the TDE follow much shallower relations withβthan the previously predicted ${\rho }_{\max }\propto {\beta }^3$and $T_{\max }\propto {\beta }^2$scalings. Belowβ≃ 10, this shallower dependence occurs because the pressure gradient is dynamically significant before the pressure is comparable to the ram pressure of the free-falling gas, while aboveβ≃ 10, we find that shocks prematurely halt the compression and yield the scalings ${\rho }_{\max }\propto {\beta }^{1.62}$and $T_{\max }\propto {\beta }^{1.12}$. We find excellent agreement between our results and high-resolution simulations. Our results demonstrate that, in the Newtonian limit, the compression experienced by the star is completely independent of the mass of the black hole. We discuss our results in the context of existing (affine) models, polytropic versus non-polytropic stars, and general relativistic effects, which become important when the pericenter of the star nears the direct capture radius, atβ∼ 12.5 (2.7) for a solar-like star disrupted by a 10⁶M_⊙(10⁷M_⊙) supermassive black hole. 

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5. 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 radiusR_v∼ 10¹⁴cm (photosphere radius ∼10¹⁵cm) surrounding the supermassive black hole (SMBH). As the envelope cools radiatively, it undergoes Kelvin–Helmholtz contractionR_v∝t⁻¹, its temperature risingT_eff∝t^1/2while its total luminosity remains roughly constant; the optical luminosity decays as $\nu L_{\nu }\propto R_v^2{T}_{\mathrm{eff}}\propto t^{-3/2}$. Despite this similarity to the mass fallback rate ${\dot{M}}_{\mathrm{fb}}\propto t^{-5/3}$, 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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