TY - JOUR

T1 - A simple and accurate prescription for the tidal disruption radius of a star and the peak accretion rate in tidal disruption events

AU - Coughlin, Eric R.

AU - Nixon, C. J.

N1 - Publisher Copyright:
© 2022 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society.

PY - 2022/11/1

Y1 - 2022/11/1

N2 - 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 an SMBH, defined rt,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 βc = rt/rt,c, where rt = R∗(M•/M∗)1/3 is the standard tidal radius with R∗ and M∗ the stellar radius and mass, and M• the SMBH mass, for multiple stellar progenitors at various ages, and can be reasonably approximated by βc ≲ [ρc/(4ρ∗)]1/3, where ρc (ρ∗) 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 βpartial ≲ 4-1/3 ≲ 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.

AB - 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 an SMBH, defined rt,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 βc = rt/rt,c, where rt = R∗(M•/M∗)1/3 is the standard tidal radius with R∗ and M∗ the stellar radius and mass, and M• the SMBH mass, for multiple stellar progenitors at various ages, and can be reasonably approximated by βc ≲ [ρc/(4ρ∗)]1/3, where ρc (ρ∗) 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 βpartial ≲ 4-1/3 ≲ 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.

KW - black hole physics

KW - methods: analytical

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U2 - 10.1093/mnrasl/slac106

DO - 10.1093/mnrasl/slac106

M3 - Article

AN - SCOPUS:85142048711

SN - 1745-3925

VL - 517

SP - L26-L30

JO - Monthly Notices of the Royal Astronomical Society: Letters

JF - Monthly Notices of the Royal Astronomical Society: Letters

IS - 1

ER -