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

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journal contribution
posted on 17.11.2022, 14:41 authored by Eric R Coughlin, CJ Nixon

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.

History

Author affiliation

School of Physics and Astronomy, University of Leicester

Version

AM (Accepted Manuscript)

Published in

Monthly Notices of the Royal Astronomical Society: Letters

Volume

517

Issue

1

Pagination

L26 - L30

Publisher

Oxford University Press (OUP)

eissn

1745-3933

Copyright date

2022

Available date

17/11/2022

Language

en

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