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1. Cooling Envelope Model for Tidal Disruption Events

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

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

   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 themore »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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2. Stars Crushed by Black Holes. III. Mild Compression of Radiative Stars by Supermassive Black Holes

   https://doi.org/10.3847/1538-4357/ac9734  

   Kundu, Suman Kumar ; Coughlin, Eric R. ; Nixon, C. J. ( November 2022 , The Astrophysical Journal)

   A tidal disruption event (TDE) occurs when the gravitational field of a supermassive black hole (SMBH) destroys a star. For TDEs in which the star enters deep within the tidal radius, such that the ratio of the tidal radius to the pericenter distanceβsatisfiesβ≫ 1, the star is tidally compressed and heated. It was predicted that the maximum density and temperature attained during deep TDEs scale as ∝β³and ∝β², respectively, and nuclear detonation is triggered byβ≳ 5, but these predictions have been debated over the last four decades. We perform Newtonian smoothed-particle hydrodynamics simulations of deep TDEs between a Sun-like star and a 10⁶M_⊙SMBH for 2 ≤β≤ 10. We find that neither the maximum density nor temperature follow the ∝β³and ∝β²scalings or, for that matter, any power-law dependence, and that the maximum-achieved density and temperature are reduced by ∼1 order of magnitude compared to past predictions. We also perform simulations in the Schwarzschild metric and find that relativistic effects modestly increase the maximum density (by a factor of ≲1.5) and induce a time lag relative to the Newtonian simulations, which is induced by time dilation. We also confirm that the time the star spends at high density and temperature ismore »a very small fraction of its dynamical time. We therefore predict that the amount of nuclear burning achieved by radiative stars during deep TDEs is minimal.

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3. Evidence for the Preferential Disruption of Moderately Massive Stars by Supermassive Black Holes

   https://doi.org/10.3847/1538-4357/ac35d5  

   Mockler, Brenna ; Twum, Angela A. ; Auchettl, Katie ; Dodd, Sierra ; French, K. D. ; Law-Smith, Jamie A. P. ; Ramirez-Ruiz, Enrico ( January 2022 , The Astrophysical Journal)

   Tidal disruption events (TDEs) provide a unique opportunity to probe the stellar populations around supermassive black holes (SMBHs). By combining light-curve modeling with spectral line information and knowledge about the stellar populations in the host galaxies, we are able to constrain the properties of the disrupted star for three TDEs. The TDEs in our sample have UV spectra, and measurements of the UV Niiito Ciiiline ratios enabled estimates of the nitrogen-to-carbon abundance ratios for these events. We show that the measured nitrogen line widths are consistent with originating from the disrupted stellar material dispersed by the central SMBH. We find that these nitrogen-to-carbon abundance ratios necessitate the disruption of moderately massive stars (≳1–2M_⊙). We determine that these moderately massive disruptions are overrepresented by a factor of ≳10²when compared to the overall stellar population of the post-starburst galaxy hosts. This implies that SMBHs are preferentially disrupting higher mass stars, possibly due to ongoing top-heavy star formation in nuclear star clusters or to dynamical mechanisms that preferentially transport higher mass stars to their tidal radii.
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)

   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 ofmore »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. 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)

   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.