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Register a new userHydrodynamical Simulations to Determine the Feeding Rate of Black Holes by the Tidal Disruption of Stars: The Importance of the Impact Parameter and Stellar Structure
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James Guillochon
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The disruption of stars by supermassive black holes has been linked to more than a dozen flares in the cores of galaxies out to redshift $z sim 0.4$. Modeling these flares properly requires a prediction of the rate of mass return to the black hole after a disruption. Through hydrodynamical simulation, we show that aside from the full disruption of a solar mass star at the exact limit where the star is destroyed, the common assumptions used to estimate $dot{M}(t)$, the rate of mass return to the black hole, are largely invalid. While the analytical approximation to tidal disruption predicts that the least-centrally concentrated stars and the deepest encounters should have more quickly-peaked flares, we find that the most-centrally concentrated stars have the quickest-peaking flares, and the trend between the time of peak and the impact parameter for deeply-penetrating encounters reverses beyond the critical distance at which the star is completely destroyed. We also show that the most-centrally concentrated stars produced a characteristic drop in $dot{M}(t)$ shortly after peak when a star is only partially disrupted, with the power law index $n$ being as extreme as -4 in the months immediately following the peak of a flare. Additionally, we find that $n$ asymptotes to $simeq -2.2$ for both low- and high-mass stars for approximately half of all stellar disruptions. Both of these results are significantly steeper than the typically assumed $n = -5/3$. As these precipitous decay rates are only seen for events in which a stellar core survives the disruption, they can be used to determine if an observed tidal disruption flare produced a surviving remnant. These results should be taken into consideration when flares arising from tidal disruptions are modeled. [abridged]
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When a star approaches a black hole closely, it may be pulled apart by gravitational forces in a tidal disruption event (TDE). The flares produced by TDEs are unique tracers of otherwise quiescent supermassive black holes (SMBHs) located at the centre of most galaxies. In particular, the appearance of such flares and the subsequent decay of the light curve are both sensitive to whether the star is partially or totally destroyed by the tidal field. However, the physics of the disruption and the fall-back of the debris are still poorly understood. We are here modelling the hydrodynamical evolution of realistic stars as they approach a SMBH on parabolic orbits, using for the first time the moving-mesh code AREPO, which is particularly well adapted to the problem through its combination of quasi-Lagrangian behaviour, low advection errors, and high accuracy typical of mesh-based techniques. We examine a suite of simulations with different impact parameters, allowing us to determine the critical distance at which the star is totally disrupted, the energy distribution and the fallback rate of the debris, as well as the hydrodynamical evolution of the stellar remnant in the case of a partial disruption. Interestingly, we find that the internal evolution of the remnants core is strongly influenced by persistent vortices excited in the tidal interaction. These should be sites of strong magnetic field amplification, and the associated mixing may profoundly alter the subsequent evolution of the tidally pruned star.
We present the first simulations of the tidal disruption of stars with realistic structures and compositions by massive black holes (BHs). We build stars in the stellar evolution code MESA and simulate their disruption in the 3D adaptive-mesh hydrodynamics code FLASH, using an extended Helmholtz equation of state and tracking 49 elements. We study the disruption of a 1$M_odot$ star and 3$M_odot$ star at zero-age main sequence (ZAMS), middle-age, and terminal-age main sequence (TAMS). The maximum BH mass for tidal disruption increases by a factor of $sim$2 from stellar radius changes due to MS evolution; this is equivalent to varying BH spin from 0 to 0.75. The shape of the mass fallback rate curves is different from the results for polytropes of Guillochon & Ramirez-Ruiz (2013). The peak timescale $t_{rm peak}$ increases with stellar age, while the peak fallback rate $dot M_{rm peak}$ decreases with age, and these effects diminish with increasing impact parameter $beta$. For a $beta=1$ disruption of a 1$M_odot$ star by a $10^6 M_odot$ BH, from ZAMS to TAMS, $t_{rm peak}$ increases from 30 to 54 days, while $dot M_{rm peak}$ decreases from 0.66 to 0.14 $M_odot$/yr. Compositional anomalies in nitrogen, helium, and carbon can occur before the peak timescale for disruptions of MS stars, which is in contrast to predictions from the frozen-in model. More massive stars can show stronger anomalies at earlier times, meaning that compositional constraints can be key in determining the mass of the disrupted star. The abundance anomalies predicted by these simulations provide a natural explanation for the spectral features and varying line strengths observed in tidal disruption events.
Tidal disruption events (TDEs) are among the brightest transients in the optical, ultraviolet, and X-ray sky. These flares are set into motion when a star is torn apart by the tidal field of a massive black hole, triggering a chain of events which is -- so far -- incompletely understood. However, the disruption process has been studied extensively for almost half a century, and unlike the later stages of a TDE, our understanding of the disruption itself is reasonably well converged. In this Chapter, we review both analytical and numerical models for stellar tidal disruption. Starting with relatively simple, order-of-magnitude physics, we review models of increasing sophistication, the semi-analytic ``affine formalism, hydrodynamic simulations of the disruption of polytropic stars, and the most recent hydrodynamic results concerning the disruption of realistic stellar models. Our review surveys the immediate aftermath of disruption in both typical and more unusual TDEs, exploring how the fate of the tidal debris changes if one considers non-main sequence stars, deeply penetrating tidal encounters, binary star systems, and sub-parabolic orbits. The stellar tidal disruption process provides the initial conditions needed to model the formation of accretion flows around quiescent massive black holes, and in some cases may also lead to directly observable emission, for example via shock breakout, gravitational waves or runaway nuclear fusion in deeply plunging TDEs.
We report an observational estimate of the rate of stellar tidal disruption flares (TDFs) in inactive galaxies, based on a successful search for these events among transients in galaxies using archival SDSS multi-epoch imaging data (Stripe 82). This search yielded 186 nuclear flares in galaxies, of which two are excellent TDF candidates. Because of the systematic nature of the search, the very large number of galaxies, the long time of observation, and the fact that non-TDFs were excluded without resorting to assumptions about TDF characteristics, this study provides an unparalleled opportunity to measure the TDF rate. To compute the rate of optical stellar tidal disruption events, we simulate our entire pipeline to obtain the efficiency of detection. The rate depends on the light curves of TDFs, which are presently still poorly constrained. Using only the observed part of the SDSS light curves gives a model-independent upper limit to the optical TDF rate: < 2 10^-4 per year per galaxy (90% CL). We develop three empirical models of the light curves, based on the two SDSS light curves and two more recent and better-sampled Pan-STARRS TDF light curves, leading to our best-estimate of the rate: (1.5 - 2.0)_{-1.3}^{+2.7} 10^-5 per year per galaxy. We explore the modeling uncertainties by considering two theoretically motivated light curve models, as well as two different relationships between black hole mass and galaxy luminosity, and two different treatments of the cutoff in the visibility of TDFs at large black hole mass. From this we conclude that these sources of uncertainty are not significantly larger than the statistical ones. Our results are applicable for galaxies hosting black holes with mass in the range of few million to 10^8 solar masses, and translates to a volumetric TDF rate of (4 - 8) 10^-8 per year per cubic Mpc.
We analyze the early growth stage of direct-collapse black holes (DCBHs) with $sim 10^{5} rm M_odot$, which are formed by collapse of supermassive stars in atomic-cooling halos at $z gtrsim 10$. A nuclear accretion disk around a newborn DCBH is gravitationally unstable and fragments into clumps with a few $10 rm M_odot$ at $sim 0.01-0.1 rm pc$ from the center. Such clumps evolve into massive population III stars with a few $10-100 rm M_odot$ via successive gas accretion and a nuclear star cluster is formed. Radiative and mechanical feedback from an inner slim disk and the star cluster will significantly reduce the gas accretion rate onto the DCBH within $sim 10^6 rm yr$. Some of the nuclear stars can be scattered onto the loss cone orbits also within $lesssim 10^6 rm yr$ and tidally disrupted by the central DCBH. The jet luminosity powered by such tidal disruption events can be $L_{rm j} gtrsim 10^{50} rm erg s^{-1}$. The prompt emission will be observed in X-ray bands with a peak duration of $delta t_{rm obs} sim 10^{5-6} (1+z) rm s$ followed by a tail $propto t_{rm obs}^{-5/3}$, which can be detectable by Swift BAT and eROSITA even from $z sim 20$. Follow-up observations of the radio afterglows with, e.g., eVLA and the host halos with JWST could probe the earliest AGN feedback from DCBHs.
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