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

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 similar to 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 solarmass star at the exact limit where the star is destroyed, the common assumptions used to estimate (M) over dot(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 (M) over dot(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 similar or equal to-2.2 for both low-a nd 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.