Browsing by Author "Ferrara, Andrea"

We study the initial mass function (IMF) and hosting halo properties of intermediate-mass black holes (IMBHs, 10(4-6)M(circle dot)) formed inside metal-free, UV-illuminated atomic-cooling haloes (virial temperature T-vir >= 104 K) either via the direct collapse of the gas or via an intermediate supermassive star (SMS) stage. These IMBHs have been recently advocated as the seeds of the supermassive black holes observed at z approximate to 6. We achieve this goal in three steps: (a) we derive the gas accretion rate for a proto-SMS to undergo General Relativity instability and produce a direct collapse black hole (DCBH) or to enter the zero-age main sequence and later collapse into an IMBH; (b) we use merger-tree simulations to select atomic-cooling haloes in which either a DCBH or SMS can form and grow, accounting for metal enrichment and major mergers that halt the growth of the proto-SMS by gas fragmentation. We derive the properties of the hosting haloes and the mass distribution of black holes at this stage, and dub it the 'birth mass function'; (c) we follow the further growth of the DCBH by accreting the leftover gas in the parent halo and compute the final IMBH mass. We consider two extreme cases in which minihaloes (T-vir < 10(4) K) can (fertile) or cannot (sterile) form stars and pollute their gas leading to a different IMBH IMF. In the (fiducial) fertile case, the IMF is bimodal extending over a broad range of masses, M approximate to (0.5-20) x 10(5) M-circle dot, and the DCBH accretion phase lasts from 10 to 100 Myr. If minihaloes are sterile, the IMF spans the narrower mass range M approximate to (1-2.8) x 10(6) M-circle dot, and the DCBH accretion phase is more extended (70-120 Myr). We conclude that a good seeding prescription is to populate haloes (a) of mass 7.5 < log(M-h/M-circle dot) < 8, (b) in the redshift range 8 < z < 17, (c) with IMBH in the mass range 4.75 < (logM(center dot)/M-circle dot) < 6.25.

Context. Supermassive stars and quasi-stars (massive stars with a central black hole) are both considered as potential progenitors for the formation of supermassive black holes. They are expected to form from rapidly accreting protostars in massive primordial halos. Aims. We explore how long rapidly accreting protostars remain on the Hayashi track, implying large protostellar radii and weak accretion luminosity feedback. We assess the potential role of energy production in the nuclear core, and determine what regulates the evolution of such protostars into quasi-stars or supermassive stars. Methods. We followed the contraction of characteristic mass shells in rapidly accreting protostars, and inferred the timescales for them to reach nuclear densities. We compared the characteristic timescales for nuclear burning with those for which the extended protostellar envelope can be maintained. Results. We find that the extended envelope can be maintained up to protostellar masses of 3.6 x 10(8) m(3) M-circle dot, where m. denotes the accretion rate in solar masses per year. We expect the nuclear core to exhaust its hydrogen content in 7 x 106 yr. If accretion rates m >> 0.14 can still be maintained at this point, a black hole may form within the accreting envelope, leading to a quasi-star. Alternatively, the accreting object will gravitationally contract to become a main-sequence supermassive star. Conclusions. Due to the limited gas reservoir in typical 10(7) M-circle dot dark matter halos, the accretion rate onto the central object may drop at late times, implying the formation of supermassive stars as the typical outcome of direct collapse. However, if high accretion rates are maintained, a quasi-star with an interior black hole may form.