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

TL;DR

This study uses hydrodynamical simulations to improve understanding of the mass return rate after stellar tidal disruptions by black holes, revealing that common assumptions are often invalid and that the decay of the flare can be steeper than previously thought.

Contribution

It provides new insights into the impact parameter and stellar structure effects on tidal disruption flare profiles, challenging existing analytical models.

Findings

Most-centrally concentrated stars produce quicker-peaking flares.

Decay rate n can be as steep as -4 after partial disruption.

Decay rate n asymptotes to approximately -2.2 for many disruptions.

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 $z \sim 0.4$. 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]