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 mass
 Award ID(s):
 2006684
 NSFPAR ID:
 10350416
 Date Published:
 Journal Name:
 The Astrophysical Journal
 Volume:
 924
 Issue:
 1
 ISSN:
 0004637X
 Page Range / eLocation ID:
 34
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract M _{•}. We analyze two estimates for the peak fallback rate in a TDE, one being the “frozenin” 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 _{•}= 10^{6}M _{⊙}. The second estimate, which postulates that the star is completely destroyed when tides dominate the maximum stellar selfgravity, predicts thatt _{peak}is very weakly dependent on stellar type, with for 0.2 ≤ ${t}_{\mathrm{peak}}=\left(23.2\pm 4.0\phantom{\rule{0.25em}{0ex}}\mathrm{days}\right){\left({M}_{\u2022}/{10}^{6}{M}_{\odot}\right)}^{1/2}$M _{⋆}/M _{⊙}≤ 5, while for a Kroupa initial mass function truncated at 1.5 ${t}_{\mathrm{peak}}\phantom{\rule{0.25em}{0ex}}=\left(29.8\pm 3.6\phantom{\rule{0.25em}{0ex}}\mathrm{days}\right){\left({M}_{\u2022}/{10}^{6}{M}_{\odot}\right)}^{1/2}$M _{⊙}. This second estimate also agrees closely with hydrodynamical simulations, while the frozenin 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) massivestar TDEs power the largest accretion luminosities. Consequently, (a) decadeslong extragalactic outbursts cannot be powered by complete TDEs, including massivestar disruptions, and (b) the most highly superEddington 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 starforming host galaxies. 
Abstract We present a toy model for the thermal optical/UV/Xray 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 quasispherical pressuresupported 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 contractionR _{v} ∝t ^{−1}, its temperature risingT _{eff}∝t ^{1/2}while its total luminosity remains roughly constant; the optical luminosity decays as . Despite this similarity to the mass fallback rate $\nu {L}_{\nu}\propto \phantom{\rule{0.50em}{0ex}}{R}_{v}^{2}{T}_{\mathrm{eff}}\propto {t}^{3/2}$ , 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 latetime flattening of the optical/Xray 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 coolinginduced (rather than circularizationinduced) delay of up to several hundred days may account for the delayed onset of thermal Xrays, latetime radio flares, and highenergy neutrino generation, observed in some TDEs. We compare the model predictions to recent TDE lightcurve correlation studies, finding both agreement and points of tension. ${\stackrel{\u0307}{M}}_{\mathrm{fb}}\propto {t}^{5/3}$ 
Abstract The distribution of orbital energies imparted into stellar debris following the close encounter of a star with a supermassive black hole is the principal factor in determining the rate of return of debris to the black hole, and thus in determining the properties of the resulting lightcurves from such events. We present simulations of tidal disruption events for a range of β ≡ r t / r p where r p is the pericenter distance and r t the tidal radius. We perform these simulations at different spatial resolutions to determine the numerical convergence of our models. We compare simulations in which the heating due to shocks is included or excluded from the dynamics. For β ≲ 8, the simulation results are wellconverged at sufficiently moderatetohigh spatial resolution, while for β ≳ 8, the breadth of the energy distribution can be grossly exaggerated by insufficient spatial resolution. We find that shock heating plays a nonnegligible role only for β ≳ 4, and that typically the effect of shock heating is mild. We show that selfgravity can modify the energy distribution over time after the debris has receded to large distances for all β . Primarily, our results show that across a range of impact parameters, while the shape of the energy distribution varies with β , the width of the energy spread imparted to the bulk of the debris is closely matched to the canonical spread, Δ E = GM • R ⋆ / r t 2 , for the range of β we have simulated.more » « less

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 withβ than the previously predicted and ${\rho}_{\mathrm{max}}\propto {\beta}^{3}$ scalings. Below ${T}_{\mathrm{max}}\propto {\beta}^{2}$β ≃ 10, this shallower dependence occurs because the pressure gradient is dynamically significant before the pressure is comparable to the ram pressure of the freefalling gas, while aboveβ ≃ 10, we find that shocks prematurely halt the compression and yield the scalings and ${\rho}_{\mathrm{max}}\propto {\beta}^{1.62}$ . We find excellent agreement between our results and highresolution 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 nonpolytropic stars, and general relativistic effects, which become important when the pericenter of the star nears the direct capture radius, at ${T}_{\mathrm{max}}\propto {\beta}^{1.12}$β ∼ 12.5 (2.7) for a solarlike star disrupted by a 10^{6}M _{⊙}(10^{7}M _{⊙}) supermassive black hole. 
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.