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Abstract An accretion disk formed around a supermassive black hole after it disrupts a star is expected to be initially misaligned with respect to the equatorial plane of the black hole. This misalignment induces relativistic torques (the Lense–Thirring effect) on the disk, causing the disk to precess at early times, whereas at late times the disk aligns with the black hole and precession terminates^1,2. Here we report, using high-cadence X-ray monitoring observations of a tidal disruption event (TDE), the discovery of strong, quasi-periodic X-ray flux and temperature modulations. These X-ray modulations are separated by roughly 15 days and persist for about 130 days during the early phase of the TDE. Lense–Thirring precession of the accretion flow can produce this X-ray variability, but other physical mechanisms, such as the radiation-pressure instability^3,4, cannot be ruled out. Assuming typical TDE parameters, that is, a solar-like star with the resulting disk extending at most to the so-called circularization radius, and that the disk precesses as a rigid body, we constrain the disrupting dimensionless spin parameter of the black hole to be 0.05 ≲ ∣a∣ ≲ 0.5. 

Abstract Some massive stars likely fail to produce core-collapse supernovae, but these failed supernovae (FSNe) can generate an electromagnetic outburst prior to the disappearance of the star, as the mass lost to neutrinos during the stellar core collapse results in the formation and breakout of a second shock. We show that, when the mass lost to neutrinos is sufficiently small, there are two self-similar solutions that describe the propagation of a weak shock into a hydrodynamically expanding envelope that simultaneously yield accretion onto the black hole. The larger Mach number solution is unstable and yields the minimum Mach number that a shock must have to strengthen into the energy-conserving regime. Above a critical mass loss, there are no weak-shock solutions, implying that there are only strong explosions if the neutrino mass loss is above a critical value, and this value is a few percent of the mass of the star (and is physically achievable) for typical parameters. Our results imply that the fate of the explosion from an FSN—weak with little to no mass ejection or strong with the expulsion of the majority of the envelope—is a sensitive function of the stellar properties and the neutrino mass loss. We also show that there is a second type of self-similar solution for the shock that results in thesettlingof the gas near the compact object, which may be applicable to nonterminal stellar eruptions and the response of a gaseous disk to gravitational-wave induced mass loss from a binary black hole merger. 

Abstract Observations and theory suggest that core-collapse supernovae can span a range of explosion energies, and when sub-energetic the shockwave initiating the explosion can decelerate to speeds comparable to the escape speed of the progenitor. In these cases, gravity will complicate the explosion hydrodynamics and conceivably cause the shock to stall at large radii within the progenitor star. To understand these unique properties of weak explosions, we develop a perturbative approach for modeling the propagation of an initially strong shock into a time-steady, infalling medium in the gravitational field of a compact object. This method writes the shock position and the post-shock velocity, density, and pressure as series solutions in the (time-dependent) ratio of the freefall speed to the shock speed, and predicts that the shock stalls within the progenitor if the explosion energy is below a critical value. We show that our model agrees very well with hydrodynamic simulations, and accurately predicts (for example) the time-dependent shock position and velocity and the radius at which the shock stalls. Our results have implications for black hole formation and the newly detected class of fast X-ray transients (FXTs). In particular, we propose that a “phantom shock breakout”—where the outer edge of the star falls through a stalled shock—can yield a burst of X-rays without a subsequent optical/UV signature, similar to FXTs. This model predicts the rise time of the X-ray burst,t_d, and the mean photon energy,kT, are anticorrelated, approximately as $T\propto t_{\mathrm{d}}^{-5/8}$. 

ABSTRACT 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. 

Abstract 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. 

Abstract 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 massM_•. We analyze two estimates for the peak fallback rate in a TDE, one being the “frozen-in” 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_•= 10⁶M_⊙. The second estimate, which postulates that the star is completely destroyed when tides dominate the maximum stellar self-gravity, predicts thatt_peakis very weakly dependent on stellar type, with $t_{\mathrm{peak}}=\left(23.2\pm 4.0\mathrm{days}\right){\left(M_{•}/{10}^6{M}_{\odot }\right)}^{1/2}$for 0.2 ≤M_⋆/M_⊙≤ 5, while $t_{\mathrm{peak}}=\left(29.8\pm 3.6\mathrm{days}\right){\left(M_{•}/{10}^6{M}_{\odot }\right)}^{1/2}$for a Kroupa initial mass function truncated at 1.5M_⊙. This second estimate also agrees closely with hydrodynamical simulations, while the frozen-in 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) massive-star TDEs power the largest accretion luminosities. Consequently, (a) decades-long extra-galactic outbursts cannot be powered by complete TDEs, including massive-star disruptions, and (b) the most highly super-Eddington 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 star-forming host galaxies. 

Galactic nuclei showing recurrent phases of activity and quiescence have recently been discovered. Some have recurrence times as short as a few hours to a day and are known as quasi-periodic X-ray eruption (QPE) sources. Others have recurrence times as long as hundreds to a thousand days and are called repeating nuclear transients. Here we present a multiwavelength overview of Swift J023017.0+283603 (hereafter Swift J0230+28), a source from which repeating and quasi-periodic X-ray flares are emitted from the nucleus of a previously unremarkable galaxy at ∼165 Mpc. It has a recurrence time of approximately 22 days, an intermediary timescale between known repeating nuclear transients and QPE sources. The source also shows transient radio emission, likely associated with the X-ray emission. Such recurrent soft X-ray eruptions, with no accompanying ultraviolet or optical emission, are strikingly similar to QPE sources. However, in addition to having a recurrence time that is ∼25 times longer than the longest-known QPE source, Swift J0230+28’s eruptions exhibit somewhat distinct shapes and temperature evolution compared to the known QPE sources. Scenarios involving extreme mass ratio inspirals are favoured over disk instability models. The source reveals an unexplored timescale for repeating extragalactic transients and highlights the need for a wide-field, time-domain X-ray mission to explore the parameter space of recurring X-ray transients. 

ABSTRACT 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). 

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.