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 (1206.2350v3)

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]

• The paper reveals that high-resolution simulations overturn conventional models by showing that more concentrated stars yield faster peak fallback rates.
• The paper quantifies critical impact parameters with βd values of 1.85 for γ = 4/3 and 0.9 for γ = 5/3 stars, determining full versus partial disruption.
• The paper introduces detailed parametric models for mass loss, peak accretion timing, and decline rates, refining predictions of tidal disruption events.

Hydrodynamical Simulations and Stellar Tidal Disruption: Impacts on Black Hole Feeding Rates

This paper by Guillochon and Ramirez-Ruiz investigates the intricate dynamics of stellar tidal disruption by supermassive black holes (SMBHs) through a series of hydrodynamical simulations. The paper critically evaluates the validity of conventional analytical models which predict the rate of mass fallback, emphasizing the significant role played by impact parameters and stellar structure. Tidal disruptions are events where stars wander too close to an SMBH and are torn apart, an astronomical phenomenon linked to flares observed in various galaxies.

Key Findings and Methodology

The authors employed high-resolution hydrodynamical simulations to explore how different impact parameters ($\beta$) and stellar structures (polytropic indices $\gamma$) affect the mass return rate ($M$) to the black hole. Two distinct families of stars were considered: those like our Sun, modeled with a polytropic index of $\gamma = 4/3$, and less centrally-concentrated stars, modeled with $\gamma = 5/3$.

1. Contradiction to Traditional Models: Contrary to the expectation from the widely-used energy-freezing models, which predict rapid flares for least centrally-concentrated stars, the paper found that the most centrally concentrated stars exhibited faster peak fallback rates. This suggests that tidal disruption physics may not always conform to such simplified models, which typically predict $M \propto t^{-5/3}$.
2. Star Survival and Mass Loss: The research identified specific thresholds, characterized by the impact parameter $\beta$, that dictate whether a star is completely disrupted or partially survives. Critical $\beta$ values for full disruption were found to be $\beta_{\rm d} = 1.85$ for $\gamma = 4/3$ and $\beta_{\rm d} = 0.9$ for $\gamma = 5/3$ stars. Beyond these thresholds, the star’s core can exert significant influence, steepening the post-peak decline of the accretion rate, with gradients as steep as $n = -4$.
3. Advanced Modeling of Fallback Rates: The simulations provided detailed parametric descriptions of four fundamental quantities—total mass loss, time of peak accretion, accretion rate at peak, and post-peak power-law decay index. These empirical formulations allow for more accurate modeling of accretion events.

Implications and Future Prospects

The numerical results suggest a reevaluation of how SMBHs consume mass from their stellar counterparts, challenging conventional approximations. This has critical implications for interpreting observed flare signatures potentially linked to tidal disruptions, allowing astronomers to discern star structure and the disruption mechanics more accurately.

• Observational Signatures: The work elucidates the energetics of tidal disruption events (TDEs), offering enhanced tools to interpret the observed flares. By comparing observed light curves against the derived simulations, astronomers can infer details of star-black hole encounters, potentially identifying stars that survive their disruptive confluence.
• Population Dynamics and SMBH Feeding: The findings impact our understanding of SMBH growth and behavior in galaxies. With more refined predictions for mass accretion rates, assessments of SMBH feeding cycles and dynamics become more nuanced.
• Model Limitations and Expansion: While the focus here was on polytropic main sequence stars, post-main sequence stars might significantly contribute to TDE observations. Future studies could expand on these results by exploring diverse stellar evolutionary stages and considering relativistic effects near SMBHs.

By offering fresh insights into the hydrodynamics of tidal disruptions, Guillochon and Ramirez-Ruiz's research underscores the need for sophisticated models that can incorporate star-specific and encounter-specific characteristics. This work lays the groundwork for more comprehensive approaches to understanding the life cycle of stars within the zone of gravitational influence of SMBHs and the consequential feeding processes at galactic cores.