Effect of mass-loss due to stellar winds on the formation of supermassive black hole seeds in dense nuclear star clusters

ABSTRACT The observations of high-redshifts quasars at z ≳ 6 have revealed that supermassive black holes (SMBHs) of mass $\sim 10^9\, \mathrm{M_{\odot }}$ were already in place within the first ∼Gyr after the big bang. Supermassive stars (SMSs) with masses $10^{3-5}\, \mathrm{M_{\odot }}$ are potential seeds for these observed SMBHs. A possible formation channel of these SMSs is the interplay of gas accretion and runaway stellar collisions inside dense nuclear star clusters (NSCs). However, mass-loss due to stellar winds could be an important limitation for the formation of the SMSs and affect the final mass. In this paper, we study the effect of mass-loss driven by stellar winds on the formation and evolution of SMSs in dense NSCs using idealized N-body simulations. Considering different accretion scenarios, we have studied the effect of the mass-loss rates over a wide range of metallicities Z* = [.001–1]Z⊙ and Eddington factors $f_{\rm Edd}=L_\ast /L_{\mathrm{Edd}}=0.5,0.7,\, \,\mathrm{ and}\, 0.9$. For a high accretion rate of $10^{-4}\, \mathrm{M_{\odot }yr^{-1}}$, SMSs with masses $\gtrsim 10^3\, \mathrm{M_{\odot }yr^{-1}}$ could be formed even in a high metallicity environment. For a lower accretion rate of $10^{-5}\, \mathrm{M_{\odot }yr^{-1}}$, SMSs of masses $\sim 10^{3-4}\, \mathrm{M_{\odot }}$ can be formed for all adopted values of Z* and fEdd, except for Z* = Z⊙ and fEdd = 0.7 or 0.9. For Eddington accretion, SMSs of masses $\sim 10^3\, \mathrm{M_{\odot }}$ can be formed in low metallicity environments with Z* ≲ 0.01 Z⊙. The most massive SMSs of masses $\sim 10^5\, \mathrm{M_{\odot }}$ can be formed for Bondi–Hoyle accretion in environments with Z* ≲ 0.5 Z⊙. An intermediate regime is likely to exist where the mass-loss from the winds might no longer be relevant, while the kinetic energy deposition from the wind could still inhibit the formation of a very massive object.

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