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A star destroyed by a supermassive black hole (SMBH) in a tidal disruption event (TDE) is transformed into a filamentary structure known as a tidally disrupted stellar debris stream. We show that when ideal gas pressure dominates the thermodynamics of the stream, there is an exact solution to the hydrodynamics equations that describes the stream evolution and accounts for self-gravity, pressure, the dynamical expansion of the gas, and the transverse structure of the stream. We analyse the stability of this solution to cylindrically symmetric perturbations, and show that there is a critical stream density below which the stream is unstable and is not self-gravitating; this critical density is a factor of at least 40–50 smaller than the stream density in a TDE. Above this critical density the stream is overstable, self-gravity confines the stream, the oscillation period is exponentially long, and the growth rate of the overstability scales as t1/6. The power-law growth and small power-law index of the overstability implies that the stream is effectively stable to cylindrically symmetric perturbations. We also use this solution to analyse the effects of hydrogen recombination, and suggest that even though recombination substantially increases the gas entropy, it is likely incapable of completely destroying the influence of self-gravity. We also show that the transient produced by recombination is far less luminous than previous estimates.

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 mass-loss – 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 short-period orbits (≲few years), as has been invoked to explain the periodic nuclear transient ASASSN-14ko and quasi-periodic eruptions, must be bound to the SMBH through a mechanism other than tidal capture, such as a dynamical exchange (i.e. Hills capture).

Stars that interact with supermassive black holes (SMBHs) can be either completely or partially destroyed by tides. In a partial tidal disruption event (TDE), the high-density core of the star remains intact, and the low-density outer envelope of the star is stripped and feeds a luminous accretion episode. The TDE AT 2018fyk, with an inferred black hole mass of 10^7.7±0.4M_⊙, experienced an extreme dimming event at X-ray (factor of >6000) and UV (factor of ∼15) wavelengths ∼500–600 days after discovery. Here we report on the reemergence of these emission components roughly 1200 days after discovery. We find that the source properties are similar to those of the predimming accretion state, suggesting that the accretion flow was rejuvenated to a similar state. We propose that a repeated partial TDE, where the partially disrupted star is on an ∼1200 day orbit about the SMBH and periodically stripped of mass during each pericenter passage, powers its unique light curve. This scenario provides a plausible explanation for AT 2018fyk’s overall properties, including the rapid dimming event and the rebrightening at late times. We also provide testable predictions for the behavior of the accretion flow in the future; if the second encounter was also a partial disruption, then we predict another strong dimming event around day 1800 (2023 August) and a subsequent rebrightening around day 2400 (2025 March). This source provides strong evidence of the partial disruption of a star by an SMBH.

Tidal disruption events (TDEs), in which a star is destroyed by the gravitational field of a supermassive black hole (SMBH), are being observed at a high rate owing to the advanced state of survey science. One of the properties of TDEs that is measured with increasing statistical reliability is the TDE luminosity function,$d{\dot{N}}_{\mathrm{TDE}}/\mathit{dL}$, which is the TDE rate per luminosity (i.e., how many TDEs are within a given luminosity range). Here we show that if the luminous emission from a TDE is directly coupled to the rate of return of tidally destroyed debris to the SMBH, then the TDE luminosity function is in good agreement with observations and scales as ∝L^−2.5for high luminosities, provided that the SMBH mass function${\mathit{dN}}_{•}/{\mathit{dM}}_{•}$—the number of SMBHs (N_•) per SMBH mass (M_•)—is approximately flat in the mass range over which we observe TDEs. We also show that there is a cutoff in the luminosity function at low luminosities that is a result of direct captures, and this cutoff has been tentatively observed. If${\mathit{dN}}_{•}/{\mathit{dM}}_{•}$is flat, which is in agreement with some observational campaigns, these results suggest that the fallback rate feeds the accretion rate in TDEs. Contrarily, if${\mathit{dN}}_{•}/d\log M_{•}$is flat, which has been found theoretically and is suggested by other observational investigations, then the emission from TDEs is likely powered by another mechanism. Future observations and more TDE statistics, provided by the Rubin Observatory/LSST, will provide additional evidence as to the reality of this tension.

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.

We present simulated optical light curves of super-Eddington tidal disruption events (TDEs) using the ZEro-BeRnoulli Accretion (ZEBRA) flow model, which proposes that during the super-Eddington phase, the disc is quasi-spherical, radiation-pressure dominated, and accompanied by the production of strong jets. We construct light curves for both on- and off-axis (with respect to the jet) observers to account for the anisotropic nature of the jetted emission. We find that at optical wavelengths, emission from the accretion flow is orders of magnitude brighter than that produced by the jet, even with boosting from synchrotron self-Compton. Comparing to the observed jetted TDE Swift J2058.4+0516, we find that the ZEBRA model accurately captures the time-scale for which accretion remains super-Eddington and reproduces the luminosity of the transient. However, we find the shape of the light curves deviate at early times and the radius and temperature of our modelled ZEBRA are ∼2.7–4.1 times smaller and ∼1.4–2.3 times larger, respectively, than observed. We suggest that this indicates the ZEBRA inflates more, and more rapidly, than currently predicted by the model, and we discuss possible extensions to the model to account for this. Such refinements, coupled with valuable new data from upcoming large-scale surveys, could help to resolve the nature of super-Eddington TDEs and how they are powered.

A core-collapse 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 core-collapse 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 time-steady, 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 of gas on to a newly formed black hole following a core-collapse event. Our findings and solutions are particularly relevant in weak and failed supernovae, where the shock is pushed to small radii and relativistic effects are large.

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 is 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.

Periodic nuclear transients have been detected with increasing frequency, with one such system—ASASSN-14ko—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 three-body 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 ASASSN-14ko but periodic nuclear transients in general. We also show that the rate of change of the period of the captured star due to gravitational-wave emission is likely too small to produce the observed value for ASASSN-14ko, indicating that in this system there must be additional effects that contribute to the decay of the orbit. In general, however, gravitational-wave emission can be important for limiting the lifetimes of these systems and could produce observable period decay rates in future events.

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 progenitors 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_⊙.