Ultra-luminous X-ray sources and neutron-star-black-hole mergers from very massive close binaries at low metallicity

The detection of gravitational waves from the binary black hole (BH) merger GW150914 may enlighten our understanding of ultra-luminous X-ray sources (ULXs), as BHs of masses >30 M-circle dot can reach luminosities >4 x 10(39) erg s(-1) without exceeding their Eddington luminosities. It is then important to study variations of evolutionary channels for merging BHs, which might instead form accreting BHs and become ULXs. It was recently shown that very massive binaries with mass ratios close to unity and tight orbits can undergo efficient rotational mixing and evolve chemically homogeneously, resulting in a compact BH binary. We study similar systems by computing similar to 120 000 detailed binary models with the ME SA code covering a wide range of masses, orbital periods, mass ratios, and metallicities. For initial mass ratios q equivalent to M-2/M-1 similar or equal to 0.1-0.4, primaries with masses above 40 M-circle dot can evolve chemically homogeneously, remaining compact and forming a BH without experiencing Roche-lobe overflow. The secondary then expands and transfers mass to the BH, initiating a ULX phase. At a given metallicity this channel is expected to produce the most massive accreting stellar BHs and the brightest ULXs. We predict that similar to 1 out of 10(4) massive stars evolves this way, and that in the local universe 0.13 ULXs per M-circle dot yr(-1) of star formation rate are observable, with a strong preference for low metallicities. An additional channel is still required to explain the less luminous ULXs and the full population of high-mass X-ray binaries. At metallicities log Z > -3, BH masses in ULXs are limited to 60 M-circle dot, due to the occurrence of pair-instability supernovae which leave no remnant, resulting in an X-ray luminosity cut-off for accreting BHs. At lower metallicities, very massive stars can avoid exploding as pair-instability supernovae and instead form BHs with masses above 130 M-circle dot, producing a gap in the ULX luminosity distribution. After the ULX phase, neutron star BH binaries that merge in less than a Hubble time are produced with a low formation rate <0.2 Gpc(-3) yr(-1). We expect that upcoming X-ray observatories will test these predictions, which together with additional gravitational wave detections will provide strict constraints on the origin of the most massive BHs that can be produced by stars.