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
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.
 Publication Date:
 NSFPAR ID:
 10371809
 Journal Name:
 Monthly Notices of the Royal Astronomical Society: Letters
 Volume:
 517
 Issue:
 1
 Page Range or eLocationID:
 p. L26L30
 ISSN:
 17453925
 Publisher:
 Oxford University Press
 Sponsoring Org:
 National Science Foundation
More Like this

Abstract 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 themore » ${\stackrel{\u0307}{M}}_{\mathrm{fb}}\propto {t}^{5/3}$ 
Abstract The tidal disruption of stars by supermassive black holes (SMBHs) probes relativistic gravity. In the coming decade, the number of observed tidal disruption events (TDEs) will grow by several orders of magnitude, allowing statistical inferences of the properties of the SMBH and stellar populations. Here we analyze the probability distribution functions of the pericenter distances of stars that encounter an SMBH in the Schwarzschild geometry, where the results are completely analytic, and the Kerr metric. From this analysis we calculate the number of observable TDEs, defined to be those that come within the tidal radius
r _{t}but outside the direct capture radius (which is, in general, larger than the horizon radius). We find that relativistic effects result in a steep decline in the number of stars that have pericenter distancesr _{p}≲ 10r _{g}, wherer _{g}=GM /c ^{2}, and that for maximally spinning SMBHs the distribution function ofr _{p}at such distances scales as , or in terms of ${f}_{{\mathrm{r}}_{\mathrm{p}}}\propto {r}_{\mathrm{p}}^{4/3}$β ≡r _{t}/r _{p}scales asf _{β}∝β ^{−10/3}. We find that spin has little effect on the TDE fraction until the veryhighmass end, where instead of being identically zero the rate is small (≲1% of the expected rate in the absence of relativistic effects). Effectively independent of spin, if the progenitorsmore » 
Abstract Tidal disruption events with tidal radius r t and pericenter distance r p are characterized by the quantity β = r t / r p , and “deep encounters” have β ≫ 1. It has been assumed that there is a critical β ≡ β c ∼ 1 that differentiates between partial and full disruption: for β < β c a fraction of the star survives the tidal interaction with the black hole, while for β > β c the star is completely destroyed, and hence all deep encounters should be full. Here we show that this assumption is incorrect by providing an example of a β = 16 encounter between a γ = 5/3, solarlike polytrope and a 10 6 M ⊙ black hole—for which previous investigations have found β c ≃ 0.9—that results in the reformation of a stellar core postdisruption that comprises approximately 25% of the original stellar mass. We propose that the core reforms under selfgravity, which remains important because of the compression of the gas both near pericenter, where the compression occurs out of the orbital plane, and substantially after pericenter, where compression is within the plane. We find that the core forms onmore »

Abstract Upon entering the tidal sphere of a supermassive black hole, a star is ripped apart by tides and transformed into a stream of debris. The ultimate fate of that debris, and the properties of the bright flare that is produced and observed, depends on a number of parameters, including the energy of the center of mass of the original star. Here we present the results of a set of smoothed particle hydrodynamics simulations in which a 1 M ⊙ , γ = 5/3 polytrope is disrupted by a 10 6 M ⊙ supermassive black hole. Each simulation has a pericenter distance of r p = r t (i.e., β ≡ r t / r p = 1 with r t the tidal radius), and we vary the eccentricity e of the stellar orbit from e = 0.8 up to e = 1.20 and study the nature of the fallback of debris onto the black hole and the longterm fate of the unbound material. For simulations with eccentricities e ≲ 0.98, the fallback curve has a distinct, threepeak structure that is induced by selfgravity. For simulations with eccentricities e ≳ 1.06, the core of the disrupted star reforms following itsmore »

Abstract We present longduration numerical simulations of the tidal disruption of stars modeled with accurate stellar structures and spanning a range of pericenter distances, corresponding to cases where the stars are partially and completely disrupted. We substantiate the prediction that the latetime powerlaw index of the fallback rate n ∞ ≃ −5/3 for full disruptions, while for partial disruptions—in which the central part of the star survives the tidal encounter intact—we show that n ∞ ≃ −9/4. For the subset of simulations where the pericenter distance is close to that which delineates full from partial disruption, we find that a stellar core can reform after the star has been completely destroyed; for these events the energy of the zombie core is slightly positive, which results in latetime evolution from n ≃ −9/4 to n ≃ −5/3. We find that selfgravity can generate an n ( t ) that deviates from n ∞ by a small but significant amount for several years postdisruption. In one specific case with the stellar pericenter near the critical value, we find that selfgravity also drives the recollapse of the central regions of the debris stream into a collection of several cores while the rest ofmore »