A simple and accurate prescription for the tidal disruption radius of a star and the peak accretion rate in tidal disruption events

Abstract

A star destroyed by a supermassive black hole (SMBH) in a tidal disruption event (TDE) enables the study of SMBHs. We propose that the distance within which a star is completely destroyed by a SMBH, defined $r_{\mathrm{t},\mathrm{c}}$, is accurately estimated by equating the SMBH tidal field (including numerical factors) to the maximum gravitational field in the star. We demonstrate that this definition accurately reproduces the critical ${\beta }_{\mathrm{c}}=r_{\mathrm{t}}/r_{\mathrm{t},\mathrm{c}}$, where $r_{\mathrm{t}}=R_{\star }{\left(M_{\bullet }/M_{\star }\right)}^{1/3}$ is the standard tidal radius with $R_{\star }$ and $M_{\star }$ the stellar radius and mass and $M_{\bullet }$ the SMBH mass, for multiple stellar progenitors at various ages, and can be reasonably approximated by ${\beta }_{\mathrm{c}}\simeq {\left[{\rho }_{\mathrm{c}}/(4{\rho }_{\star })\right]}^{1/3}$, where ${\rho }_{\mathrm{c}}$ (${\rho }_{\star }$) is the central (average) stellar density. We also calculate the peak fallback rate and time at which the fallback rate peaks, finding excellent agreement with hydrodynamical simulations, and also suggest that the partial disruption radius -- the distance at which any mass is successfully liberated from the star -- is ${\beta }_{\mathrm{partial}}\simeq 4^{-1/3}\simeq 0.6$. For given stellar and SMBH populations, this model yields, e.g., the fraction of partial TDEs, the peak luminosity distribution of TDEs, and the number of directly captured stars.

5 pages, 3 figures, MNRASL Accepted

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Cited by in corpus (13)

• Dissonance in harmony: The UV/optical periodic outbursts of ASASSN-14ko exhibit repeated bumps and rebrightenings
• The dynamics of debris streams from tidal disruption events: exact solutions, critical stream density, and hydrogen recombination
• Detecting Population III Stars through Tidal Disruption Events in the Era of JWST and Roman
• Evolution of eccentric stellar disks around supermassive black holes: the complex disk disruption dynamics and the milliparsec stars
• Tidal disruption rate suppression by the event horizon of spinning black holes
• Gravitational Radiation-Driven Chaotic Tide in a White Dwarf-Massive Black Hole Binary as a Source of Repeating X-ray Transients
• The luminosity function of TDEs from fallback-powered emission: implications for the black hole mass function
• Stars Crushed by Black Holes. III. Mild Compression of Radiative Stars by Supermassive Black Holes
• Partial disruption of a planet around a white dwarf: the effect of perturbation from the remnant planet on the accretion
• Repeating X-ray bursts: Interaction between a neutron star and clumps partially disrupted from a planet
• Stellar Stripping and Disruption in Disks around Supermassive Black Hole Binaries: Repeating nuclear transients prior to LISA events
• Chaotic orbital dynamics of pulsating stars around black holes surrounded by dark matter halos
• Repeating Nuclear Transients from Repeating Partial Tidal Disruption Events