X-ray emission from helium star–black hole binaries as probes of tidally induced spin-up of second-born black holes

Context. Tidally induced spin-up of stripped helium stars in short-period (< 1 d) binaries with black holes (BHs) has been presented as a possible mechanism for reproducing the high-spin tail of the BH spin distribution derived from gravitational wave (GW) merger observations. With such short periods, a fraction of the strong stellar wind from the stripped helium stars could be accreted by the BHs, and its gravitational potential energy could be released as observable radiation in the X-ray regime. Aims. We estimated the X-ray luminosity and its observability from the population of BHs in orbit with stripped helium stars that evolve into BH–BH or BH–neutron star binaries and merge within a Hubble time. Methods. We post-processed recent advancements in estimating X-ray luminosities (via wind accretion onto stellar-mass BHs) into the rapid population synthesis codes <ns0:monospace>BSE</ns0:monospace> and <ns0:monospace>StarTrack</ns0:monospace>. We derived lower limits on the X-ray luminosity distribution from the population of stripped helium star–BH binaries at four metallicities (0.01, 0.1, 0.5, and 1 Z⊙) and two mass transfer stability criteria. Results. We find that a large fraction (0.1–0.5) of stripped helium stars in the above population transfer enough wind matter onto the BH to produce X-ray luminosities above 1035 erg s−1, up to ∼1039 erg s−1. Such binaries should be observable as X-ray-bright systems at 0.1 Z⊙, 0.5 Z⊙, and Z⊙, that is, in Sextans A, the Large Magellanic Cloud (LMC), and the solar neighbourhood, respectively. We show that most of these X-ray-bright systems also have the shortest orbital periods, and tides can spin up the stripped helium star component. The formation efficiency of these systems increases with decreasing metallicity. However, accounting for the local star formation rates, our population synthesis predicts that ∼2 and ∼1 such X-ray-bright helium star–BH binaries in the Milky Way and LMC, respectively, will produce a binary compact object merger within a Hubble time. Conclusions. Ongoing high-sensitivity X-ray surveys and high-resolution optical surveys of low-metallicity environments such as Sextans A are important stepping stones towards identifying the population of short-period helium star–BH binaries and possibly constraining the contribution of isolated binary evolution to the high spin tail of the BH spin distribution in GW mergers.