Quasistars and the cosmic evolution of massive black holes

arXiv:1003.5220v2 [astro-ph.HE] 15 Jul 2010 Mon. Not. R. Astron. Soc. 000, 1–13 (2010) Printed 11 October 2021 (MN LATEX style file v2.2) Quasistars and the cosmic evolution of massive black holes Marta Volonteri1⋆and Mitchell C. Begelman2,3⋆ 1Department of Astronomy, University of Michigan, 500 Church Street, Ann Arbor, MI, USA 2JILA, 440 UCB, University of Colorado at Boulder, Boulder, CO 80309-0440, USA 3 Department of Astrophysical and Planetary Sciences, 391 UCB, University of Colorado, Boulder, CO 80309-0391, USA ABSTRACT We explore the cosmic evolution of massive black hole (MBH) seeds forming within ‘quasistars’ (QSs), accreting black holes embedded within massive hydrostatic gaseous envelopes. These structures could form if the infall of gas into the center of a halo exceeds about 1 M⊙yr−1. The collapsing gas traps its own radiation and forms a radiation pressure-supported supermassive star. When the core of the supermassive star collapses, the resulting system becomes a quasistar. We use a merger-tree approach to estimate the rate at which supermassive stars might form as a function of redshift, and the statistical properties of the resulting QS and seed black hole populations. We relate the triggering of runaway infall to major mergers of gas-rich galaxies, and to a threshold for global gravitational instability, which we link to the angular momentum of the host. This is the main parameter of our models. Once infall is triggered, its rate is determined by the halo potential; the properties of the resulting supermassive star, QS and seed black hole depend on this rate. After the epoch of QSs, we model the growth of MBHs within their hosts in a merger-driven accretion scenario. We compare MBH seeds grown inside quasistars to a seed model that derives from the remnants of the first metal-free stars, and also study the case in which both channels of MBH formation operate simultaneously. We find that a limited range of supermassive star/QS/MBH formation efficiencies exists that allows one to reproduce observational constraints. Our models match the density of z = 6 quasars, the cumulative mass density accreted onto MBHs (according to So ltan’s argument), and the current mass density of MBHs. The mass function of QSs peaks at MQS ≃106 M⊙, and we calculate the number counts for the JWST 2 −10 µm band. We find that JWST could detect up to several QSs per field at z ≃5 −10. Key words: black hole physics — infrared: stars — cosmology: theory — galaxies: formation — galaxies: nuclei — quasars: general 1 INTRODUCTION While there is ample evidence that supermassive black holes populate the nuclei of most large galaxies and that some black holes with masses exceeding 109 M⊙formed as early as z ≳6 (e.g., Fan 2001; Barth et al. 2003; Djorgovski et al. 2008; Willott et al. 2009; Jiang et al. 2009), there is little consensus as to the progenitors of these holes. Two schools of thought have persisted since Rees (1978) first devised a flow chart outlining possible routes of massive black hole (MBH1) formation. According to one line of argument, supermassive ⋆E-mail: martav@umich.edu (MV); mitch@jila.colorado.edu (MCB) 1 We refer here generically to MBHs when the hole mass is above the limit for black hole formation in today’s stars, ≃50 M⊙. This definition comprises both seed black holes and supermassive black holes in galaxies and quasars. black holes grew from the remnants of an early population of massive stars, the so-called Population III (Pop III), which is believed to have formed in pregalactic minihalos at z ≳ 20. According to the other, the precursors of supermassive black holes could have formed by the ‘direct collapse’ of large amounts of gas in much larger halos at later times. Each scenario has both positive and negative at- tributes. Although Pop III remnants were unlikely to have been more massive than a few hundred M⊙each, they would have formed relatively early and thus their growth process would have had a considerable head start. They could have congregated and merged in the cores of merging minihalos, while simultaneously growing by accretion. Models for the growth of supermassive black holes from stellar-mass seeds (Madau & Rees 2001; Volonteri et al. 2003; Rhook & Haehnelt 2006; Monaco et al. 2007; Somerville et al. 2008; Volonteri et al. 2008) are moderately successful in reproducing the current-day population of 2 Volonteri and Begelman supermassive black holes, but have rather more difficulty in producing enough 109 M⊙holes at z ≳6 to explain the earliest known quasars (Volonteri & Rees 2005; Shapiro 2005; Volonteri & Rees 2006). Additional worries about the Pop III scenario include the possibility that too many of the remnants would have been ejected from the cores of merging halos and that their accretion rates would be depressed by the shallow potential wells of the host mini-halos and heating of the ambient gas by stellar radiation and winds (Milosavljevi´c et al. 2009, and references therein). Se

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