Abstract
Accretion onto supermassive black holes (SMBHs) in galaxy formation simulations is frequently modelled by the Bondi-Hoyle formalism. Here we examine the validity of this approach analytically and numerically. We argue that the character of the flow where one evaluates the gas properties is unlikely to satisfy the simple Bondi-Hoyle model. Only in the specific case of hot virialised gas with zero angular momentum and negligible radiative cooling is the Bondi-Hoyle solution relevant. In the opposite extreme, where the gas is in a state of free-fall at the evaluation radius due to efficient cooling and the dominant gravity of the surrounding halo, the Bondi-Hoyle formalism can be erroneous by orders of magnitude in either direction. This may impose artificial trends with halo mass in cosmological simulations by being wrong by different factors for different halo masses. We propose an expression for the sub-grid accretion rate which interpolates between the free-fall regime and the Bondi-Hoyle regime, therefore taking account of the contribution of the halo to the gas dynamics.
Highlights
Over the last decade, compelling observational evidence has revealed that many galaxies in the local Universe harbour supermassive black holes (SMBHs) with masses 106 Mbh/M 109 in their centres
In this paper we have shown that the de facto industry standard, namely the Bondi–Hoyle formalism for the accretion rate on to the SMBH, fails for more than one reason in a realistic cosmological simulation whenever gas cooling is efficient
We have shown that a free-fall estimate is more appropriate in this case
Summary
Over the last decade, compelling observational evidence has revealed that many galaxies in the local Universe harbour supermassive black holes (SMBHs) with masses 106 Mbh/M 109 in their centres. Our understanding of the physics that dictates the growth of SMBHs is incomplete. Black holes grow by accreting low angular momentum material from their surroundings, yet the character of the accretion flow on to an SMBH is governed by physical processes as diverse as galaxy mergers Black hole growth is routinely modelled in galaxy formation simulations (for a fiducial work see Springel, Di Matteo & Hernquist 2005) and the importance of SMBHs in shaping the properties of galaxies is well established (e.g. Bower et al 2006; Croton et al 2006). The majority of galaxy formation simulations published in the literature incorporate what we shall term the ‘Bondi–Hoyle model’ for black hole growth
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