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

Abstract

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 estimateṀ (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 inṀ (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 −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.

The X-Ray Through Optical Fluxes and Line Strengths of Tidal Disruption Events

“…The peak luminosity is high, 10 44 erg s −1 , and the spectral energy distribution (SED) peaks at soft X-ray energies 0.1 keV. After peak, the luminosity fades as a power law in time similar to L∝t −5/3 , a dependence predicted for the fallback of disrupted stellar debris (Rees 1988;Evans & Kochanek 1989;Phinney 1989;Lodato et al 2009;Guillochon & Ramirez-Ruiz 2013).…”

DISCOVERY OF AN OUTFLOW FROM RADIO OBSERVATIONS OF THE TIDAL DISRUPTION EVENT ASASSN-14li

“…Because the fallback of matter onto a black hole following a disruption only follows the canonical −5/3 law for half of disruptions, and only several months after the peak fallback rate (Guillochon & Ramirez-Ruiz 2013), the fitting of tidal disruption light curves using a Monte Carlo approach is a far more robust procedure for constraining important temporal milestones for a given flare, such as the time of disruption and when the accretion rate crosses various thresholds such as the Eddington limit. TDEFit utilizes a maximum-likelihood analysis to determine the most likely combination of disruption parameters, with one of the products being an ensemble of accretion rates onto the SMBH as functions of time.…”

Abundance anomalies in tidal disruption events

“…On the main sequence, typically the star will be completely disrupted (e.g. Evans & Kochanek 1989, Guillochon & Ramirez-Ruiz 2013. Evolved stars, however, are only likely to be stripped into the hydrogen burning zone because of the huge jump in density at its base.…”