HYDRODYNAMICAL SIMULATIONS TO DETERMINE THE FEEDING RATE OF BLACK HOLES BY THE TIDAL DISRUPTION OF STARS: THE IMPORTANCE OF THE IMPACT PARAMETER AND STELLAR STRUCTURE

By J. Guillochon, E. Ramirez-Ruiz. 2012

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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 ∼ 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 , 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 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 ≃ − 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. We provide fitting formulae for four fundamental quantities of tidal disruption as functions of the star's distance to the black hole at pericenter and its stellar structure: the total mass lost, the time of peak, the accretion rate at peak, and the power-law index shortly after peak. These results should be taken into consideration when flares arising from tidal disruptions are modeled.

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Citations in the corpus

Disc formation from tidal disruptions of stars on eccentric orbits by Schwarzschild black holes (2015, background): “…(1982), Rees (1988), Evans & Kochanek (1989) and Phinney (1989) is a t−5/3 decrease of the rate at which the stellar debris fall back towards the black hole.1 The same 1 This rate was later shown to be dependent on the stellar structure (Lodato, King & Pringle 2009; Guillochon & Ramirez-Ruiz 2013).”
The fast, luminous ultraviolet transient AT2018cow: extreme supernova, or disruption of a star by an intermediate-mass black hole? (2018, methodology): “The MOSFiT TDE model uses hydrodynamic simulations of tidal disruption events from (Guillochon & Ramirez-Ruiz 2013) to calculate the fallback rate of stellar debris to the black hole.”
A bright year for tidal disruptions (2015, background): “The poorly understood process by which matter dissipates its orbital energy is an area of active research (Kochanek 1994; Guillochon & Ramirez-Ruiz 2013; Hayasaki et al. 2015; Shiokawa et al. 2015).”
MOCCA code for star cluster simulations – IV. A new scenario for intermediate mass black hole formation in globular clusters (2015, background): “…radiation heating the gas, etc. - all of them not included in simulations presented in this paper) and recent simulations suggest that less than 50% of the incoming star mass can be directly accreted onto the BH (see e.g. Guillochon & Ramirez-Ruiz 2013; Kyutoku et al. 2015; Shiokawa et al. 2015).”
A Unified Model for Tidal Disruption Events (2018, background): “The rate that debris falls back to the black hole is expected to increase in ∼ 1 month, and then declines with time as t−5/3 in ∼ 1 year (Phinney 1989; Evans & Kochanek 1989; Lodato et al. 2009; Guillochon & Ramirez-Ruiz 2013).”
Swift J1112.2−8238: a candidate relativistic tidal disruption flare (2015, background): “…−5/3 (Rees 1988; Phinney 1989), although recent numerical simulations suggest that accounting for stellar structure and closeness of approach, -2.2 is expected in half of all disruptions (Guillochon & Ramirez-Ruiz 2013)) and the X-ray spectrum was somewhat harder (photon index ∼1.6, c.f. ∼2).”
GENERAL RELATIVISTIC HYDRODYNAMIC SIMULATION OF ACCRETION FLOW FROM A STELLAR TIDAL DISRUPTION (2015, background): “One (Lodato et al. 2009; Guillochon & Ramirez-Ruiz 2013b) is that realistic stellar structures lead to an energy distribution that isn’t exactly flat, so that the t−5/3 variation of the mass-return rate becomes valid only at a late stage or possibly not at all during the event.”
PS1-10jh: THE DISRUPTION OF A MAIN-SEQUENCE STAR OF NEAR-SOLAR COMPOSITION (2013, background): “It is clear that Ṁ does not asymptotically approach n = −5/3 for the most-likely model, as is expected given that the asymptotic n ranges from −1.4 to −2.2 for MS disruptions (Guillochon & Ramirez-Ruiz 2013).”
THE ULTRAVIOLET-BRIGHT, SLOWLY DECLINING TRANSIENT PS1-11af AS A PARTIAL TIDAL DISRUPTION EVENT (2013, methodology): “…& Ramirez-Ruiz 2013), which parameterize the ratio of the tidal radius to the pericenter distance where the (partial) disruption occurs as β. Guillochon & Ramirez-Ruiz (2013) give scaling relations for their families of curves in terms of several observables, but two of the parameters, the…”
Weighing Black Holes Using Tidal Disruption Events (2018, methodology): “The fallback rate and the peak timescale of TDEs are dependent on the mass of the disrupting black hole, the mass of the star, and the stellar structure of the star (Lodato et al. 2009; Guillochon & Ramirez-Ruiz 2013).”
New Physical Insights about Tidal Disruption Events from a Comprehensive Observational Inventory at X-Ray Wavelengths (2016, methodology): “However, Lodato et al. (2009) showed analytically, while Guillochon & Ramirez-Ruiz (2013) determined using hydrodynamical simulations, that the powerlaw index for decay depends heavily on the stellar structure (i.e., 30 For NGC3599 which Esquej et al. (2008) and Saxton et al. (2015) suggest could…”
Stellar Dynamics and Stellar Phenomena Near a Massive Black Hole (2017, background): “19It was recently realized that ∆ hardly depends on the penetration depth b = rp/rt, since once the star crosses rt, its self-gravity is negligible and the tidal field no longer performs work against it (Sari, Kobayashi & Rossi 2010; Stone, Sari & Loeb 2013; Guillochon & Ramirez-Ruiz 2013).”
Now You See It, Now You Don't: The Disappearing Central Engine of the Quasar J1011+5442 (2015, background): “The most recent simulations for feeding black holes with tidal disruption of stars show that the light curve of a TDE has a very narrow peak Guillochon & Ramirez-Ruiz (2013).”
Massive black hole binaries from runaway collisions: the impact of metallicity (2016, background): “Moreover, if the two colliding objects are a star and a BH, less than 50% of the incoming star mass might be directly accreted onto the BH (see e.g. Ramirez-Ruiz & Rosswog 2009; Guillochon & Ramirez-Ruiz 2013).”