Stars that plunge into the centre of a galaxy are tidally perturbed by a supermassive black hole (SMBH), with closer encounters resulting in larger perturbations. Exciting these tides comes at the expense of the star’s orbital energy, which leads to the naive conclusion that a smaller pericentre (i.e. a closer encounter between the star and SMBH) always yields a more tightly bound star to the SMBH. However, once the pericentre distance is small enough that the star is partially disrupted, morphological asymmetries in the mass lost by the star can yield an increase in the orbital energy of the surviving core, resulting in its ejection – not capture – by the SMBH. Using smoothed particle hydrodynamics simulations, we show that the combination of these two effects – tidal excitation and asymmetric massloss – results in a maximum amount of energy lost through tides of $\sim 2.5{{\ \rm per\ cent}}$ of the binding energy of the star, which is significantly smaller than the theoretical maximum of the total stellar binding energy. This result implies that stars that are repeatedly partially disrupted by SMBHs many (≳10) times on shortperiod orbits (≲few years), as has been invoked to explain the periodic nuclearmore »
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ABSTRACT 
Abstract 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 distance
β satisfiesβ ≫ 1, the star is tidally compressed and heated. It was predicted that the maximum density and temperature attained during deep TDEs scale as ∝β ^{3}and ∝β ^{2}, respectively, and nuclear detonation is triggered byβ ≳ 5, but these predictions have been debated over the last four decades. We perform Newtonian smoothedparticle hydrodynamics simulations of deep TDEs between a Sunlike star and a 10^{6}M _{⊙}SMBH for 2 ≤β ≤ 10. We find that neither the maximum density nor temperature follow the ∝β ^{3}and ∝β ^{2}scalings or, for that matter, any powerlaw dependence, and that the maximumachieved 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 » 
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.

ABSTRACT A corecollapse supernova is generated by the passage of a shock wave through the envelope of a massive star, where the shock wave is initially launched from the ‘bounce’ of the neutron star formed during the collapse of the stellar core. Instead of successfully exploding the star, however, numerical investigations of corecollapse supernovae find that this shock tends to ‘stall’ at small radii (≲10 neutron star radii), with stellar material accreting on to the central object through the standing shock. Here, we present timesteady, adiabatic solutions for the density, pressure, and velocity of the shocked fluid that accretes on to the compact object through the stalled shock, and we include the effects of general relativity in the Schwarzschild metric. Similar to previous works that were carried out in the Newtonian limit, we find that the gas ‘settles’ interior to the stalled shock; in the relativistic regime analysed here, the velocity asymptotically approaches zero near the Schwarzschild radius. These solutions can represent accretion on to a material surface if the radius of the compact object is outside of its event horizon, such as a neutron star; we also discuss the possibility that these solutions can approximately represent the accretion ofmore »

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 Periodic nuclear transients have been detected with increasing frequency, with one such system—ASASSN14ko—exhibiting highly regular outbursts on a timescale of 114 ± 1 days. It has been postulated that the outbursts from this source are generated by the repeated partial disruption of a star, but how the star was placed onto such a tightly bound orbit about the supermassive black hole remains unclear. Here we use analytic arguments and threebody integrations to demonstrate that the Hills mechanism, where a binary system is destroyed by the tides of the black hole, can lead to the capture of a star on a ∼114 days orbit and with a pericenter distance that is comparable to the tidal radius of one of the stars within the binary. Thus, Hills capture can produce stars on tightly bound orbits that undergo repeated partial disruption, leading to a viable mechanism for generating not only the outbursts detected from ASASSN14ko but periodic nuclear transients in general. We also show that the rate of change of the period of the captured star due to gravitationalwave emission is likely too small to produce the observed value for ASASSN14ko, indicating that in this system there must be additional effects thatmore »Free, publiclyaccessible full text available April 1, 2023

Abstract Corecollapse supernovae can display evidence of interaction with preexisting, circumstellar shells of material by rebrightening and forming spectral lines, and can even change types as hydrogen appears in previously hydrogenpoor spectra. However, a recently observed corecollapse supernova—SN 2019tsf—was found to brighten after roughly 100 days after it was first observed, suggesting that the supernova ejecta was interacting with surrounding material, but it lacked any observable emission lines and thereby challenged the standard supernovainteraction picture. We show through linear perturbation theory that delayed rebrightenings without the formation of spectral lines are generated as a consequence of the finite soundcrossing time of the postshock gas left in the wake of a supernova explosion. In particular, we demonstrate that sound waves—generated in the postshock flow as a consequence of the interaction between a shock and a density enhancement—traverse the shocked ejecta and impinge upon the shock from behind in a finite time, generating sudden changes in the shock properties in the absence of ambient density enhancements. We also show that a blast wave dominated by gas pressure and propagating in a windfed medium is unstable from the standpoint that small perturbations lead to the formation of reverse shocks within the postshock flow,more »Free, publiclyaccessible full text available March 1, 2023

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 »Free, publiclyaccessible full text available March 1, 2023

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 ofmore » ${T}_{\mathrm{max}}\propto {\beta}^{1.12}$ 
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 »