The cosmic merger rate density of black hole binaries (BHBs) can give us an essential clue to constraining the formation channels of BHBs, in light of current and forthcoming gravitational wave detections. Following a Monte Carlo approach, we couple new population-synthesis models of BHBs with the Illustris cosmological simulation, to study the cosmic history of BHB mergers. We explore six population-synthesis models, varying the prescriptions for supernovae, common envelope, and natal kicks. In most considered models, the cosmic BHB merger rate follows the same trend as the cosmic star formation rate. The normalization of the cosmic BHB merger rate strongly depends on the treatment of common envelope and on the distribution of natal kicks. We find that most BHBs merging within LIGO's instrumental horizon come from relatively metal-poor progenitors (< 0.2 Z ). The total masses of merging BHBs span a large range of values, from ∼ 6 to ∼ 82 M . In our fiducial model, merging BHBs consistent with GW150914, GW151226 and GW170104 represent ∼ 6, 3, and 12 per cent of all BHBs merging within the LIGO horizon, respectively. The heavy systems, like GW150914, come from metal-poor progenitors (< 0.15 Z ). Most GW150914-like systems merging in the local Universe appear to have formed at high redshift, with a long delay time. In contrast, GW151226-like systems form and merge all the way through the cosmic history, from progenitors with a broad range of metallicities. Future detections will be crucial to put constraints on common envelope, on natal kicks, and on the BHB mass function.

Massive metal-poor stars might form massive stellar black holes (BHs), with mass 25<=mBH/Msun<=80, via direct collapse. We derive the number of massive BHs (NBH) that are expected to form per galaxy through this mechanism. Such massive BHs might power most of the observed ultra-luminous X-ray sources (ULXs). We select a sample of 64 galaxies with X-ray coverage, measurements of the star formation rate (SFR) and of the metallicity. We find that NBH correlates with the number of observed ULXs per galaxy (NULX) in this sample. We discuss the dependence of our model on the SFR and on the metallicity. The SFR is found to be crucial, consistently with previous studies. The metallicity plays a role in our model, since a lower metallicity enhances the formation of massive BHs. Consistently with our model, the data indicate that there might be an anticorrelation between NULX, normalized to the SFR, and the metallicity. A larger and more homogeneous sample of metallicity measurements is required, in order to confirm our results.Comment: 21 pages, 8 figures, accepted for publication in MNRA

The mechanisms which could lead to chemo-thermal instabilities and fragmentation during the formation of primordial protostars are investigated analytically. We introduce new analytic approximations for H 2 cooling rates bridging the optically thin and thick regimes. These allow us to discuss chemo-thermal instabilities up to densities when protostars become optically thick to continuum radiation (n ≡ ρ/m H < ∼ 10 16−17 cm −3 ). During the proto-stellar collapse instabilities are active in two different density regimes. In the well known "low density" regime (n ∼ 10 8 − 10 10 cm −3 ), instability is due to 3-body reactions quickly converting atomic hydrogen into H 2 . In the "high density" regime (n > ∼ 10 14 cm −3 ), another instability is triggered by the strong increase in the cooling rate due to H 2 Collisional Induced Emission (CIE). In agreement with the three dimensional simulations, we find that the "low density" instabilities cannot lead to fragmentation, both because fluctuations are too small to survive turbulent mixing, and because their growth times are too slow. The situation for the newly found "high density" instability is analytically similar. This continuum cooling instability is as weak as "low density" instability, with similar ratios of growth and dynamical time scales, as well as allowing for the necessary fragmentation condition t cool < ∼ t dyn . Because the instability growth timescale is always longer than the free fall timescale, it seems unlikely that fragmentation could occur in this high density regime. Consequently, one expects the first stars to be very massive, not to form binaries nor harbour planets. Nevertheless, full three dimensional simulations are required to be certain. Such 3D calculations could become possible using simplified approaches to approximate the effects of radiative transfer, which we show to work very well in 1D calculations, giving virtually indistinguishable results from calculations employing full line transfer. This indicates that the effects of radiative transfer during the initial stages of formation of primordial proto-stars are local corrections to cooling rather than influencing the energetics of distant regions of the flow.

We study the effects of weakly interacting massive particles (WIMPs) dark matter (DM) on the collapse and evolution of the first stars in the Universe. Using a stellar evolution code, we follow the pre-main-sequence (pre-MS) phase of a grid of metal-free stars with masses in the range 5 <= M* <= 600Msolar forming in the centre of a 106Msolar halo at z = 20. DM particles of the parent halo are accreted in the protostellar interior by adiabatic contraction and scattering/capture processes, reaching central densities of O(1012 GeVcm-3) at radii of the order of 10au. Energy release from annihilation reactions can effectively counteract the gravitational collapse, in agreement with results from other groups. We find this stalling phase (known as a dark star) is transient and lasts from 2.1 × 103yr (M* = 600Msolar) to 1.8 × 104yr (M* = 9Msolar). Later in the evolution, DM scattering/capture rate becomes high enough that energy deposition from annihilations significantly alters the pre-MS evolution of the star in a way that depends on DM (i) velocity dispersion, , (ii) density, ρ, (iii) elastic scattering cross-section with baryons, σ0. For our fiducial set of parameters we find that the evolution of stars of mass M* < 40Msolar `freezes' on the HR diagram before reaching the zero-age main sequence (ZAMS). Stars with M* >= 40Msolar manage to ignite nuclear reactions; however, DM `burning' prolongs their lifetimes by a factor of 2 (5) for a 600Msolar (40Msolar) star. For ρ >~ 1012GeVcm-3, and same values of the other parameters, we find that all our models are entirely supported by DM annihilation and `freeze' on the HR diagram before igniting nuclear reactions

The evolution of radiation emitted during the dynamical collapse of metal-free protostellar clouds is investigated within a spherically symmetric hydrodynamical scheme that includes the transfer of radiation and the chemistry of the primordial gas. The cloud centre collapses on a time scale of about 10^5-10^6 years, thanks to line cooling from molecular hydrogen (H2). For most of the collapse time, when the evolution proceeds self-similarly, the luminosity slowly rises up to about 10^36 erg/s and is essentially due to H2 IR line emission. Later, continuum IR radiation provides an additional contribution, which is mostly due to the accretion of an infalling envelope upon a small hydrostatic protostellar core which develops in the centre. We follow the beginning of the accretion phase, when the enormous accretion rate (~ 0.1 Msun/yr) produces a very high continuum luminosity of about 10^36 erg/s. Despite the high luminosities, the radiation field is unable to affect the gas dynamics during the collapse and the first phases of accretion, because the opacity of the infalling gas is too small; this is quite different from present-day star formation. We also find that the protostellar evolution is similar among clouds with different initial configurations, including those resulting from 3D cosmological simulations of primordial objects; in particular, the shape of the molecular spectra is quite universal. Finally, we briefly discuss the detectability of this pristine cosmic star formation activity.Comment: 39 pages, 12 figures; revised version with major changes (including title) to appear in MNRA