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1. 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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2. The Eccentric Nature of Eccentric Tidal Disruption Events

   https://doi.org/10.3847/1538-4357/ac32be  

   Cufari, M. ; Coughlin, Eric R. ; Nixon, C. J. ( January 2022 , The Astrophysical Journal)

   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 long-term fate of the unbound material. For simulations with eccentricities e ≲ 0.98, the fallback curve has a distinct, three-peak structure that is induced by self-gravity. For simulations with eccentricities e ≳ 1.06, the core of the disrupted star reforms following itsmore »initial disruption. Our results have implications for, e.g., tidal disruption events produced by supermassive black hole binaries.« less
3. Stars Crushed by Black Holes. I. On the Energy Distribution of Stellar Debris in Tidal Disruption Events

   https://doi.org/10.3847/1538-4357/ac2ee8  

   Norman, S. M. ; Nixon, C. J. ; Coughlin, Eric R. ( December 2021 , The Astrophysical Journal)

   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 well-converged at sufficiently moderate-to-high 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 non-negligible role only for β ≳ 4, and that typically the effect of shock heating is mild. We show that self-gravity can modify the energy distribution over time after the debris has receded to large distances for all β . Primarily, our results show thatmore »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.« less
4. On the Impact of Relativistic Gravity on the Rate of Tidal Disruption Events

   https://doi.org/10.3847/1538-4357/ac85b3  

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

   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 radiusr_tbut 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/c², and that for maximally spinning SMBHs the distribution function ofr_pat such distances scales as$f_{{\mathrm{r}}_{\mathrm{p}}}\propto r_{\mathrm{p}}^{4/3}$, or in terms ofβ≡r_t/r_pscales asf_β∝β^−10/3. We find that spin has little effect on the TDE fraction until the very-high-mass 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 »of TDEs reflect the predominantly low-mass stellar population and thus have masses ≲1M_⊙, we expect a substantial reduction in the rate of TDEs above 10⁷M_⊙.

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5. Hydrodynamics of Collisions and Close Encounters between Stellar Black Holes and Main-sequence Stars

   https://doi.org/10.3847/1538-4357/ac714f  

   Kremer, Kyle ; Lombardi, James C. ; Lu, Wenbin ; Piro, Anthony L. ; Rasio, Frederic A. ( July 2022 , The Astrophysical Journal)

   Abstract Recent analyses have shown that close encounters between stars and stellar black holes occur frequently in dense star clusters. Depending upon the distance at closest approach, these interactions can lead to dissipating encounters such as tidal captures and disruptions, or direct physical collisions, all of which may be accompanied by bright electromagnetic transients. In this study, we perform a wide range of hydrodynamic simulations of close encounters between black holes and main-sequence stars that collectively cover the parameter space of interest, and we identify and classify the various possible outcomes. In the case of nearly head-on collisions, the star is completely disrupted with roughly half of the stellar material becoming bound to the black hole. For more distant encounters near the classical tidal-disruption radius, the star is only partially disrupted on the first pericenter passage. Depending upon the interaction details, the partially disrupted stellar remnant may be tidally captured by the black hole or become unbound (in some cases, receiving a sufficiently large impulsive kick from asymmetric mass loss to be ejected from its host cluster). In the former case, the star will undergo additional pericenter passages before ultimately being disrupted fully. Based on the properties of the materialmore »bound to the black hole at the end of our simulations (in particular, the total bound mass and angular momentum), we comment upon the expected accretion process and associated electromagnetic signatures that are likely to result.« less