Remnants of massive metal-poor stars: viable engines for ultra-luminous X-ray sources

Massive metal-poor stars might end their life by directly collapsing into massive (~25-80 Msun) black holes (BHs). We derive the number of massive BHs (N_BH) that are expected to form per galaxy via this mechanism. We select a sample of 66 galaxies with X-ray coverage, measurements of the star formation rate (SFR) and of the metallicity. We find that N_BH correlates with the number of observed ultra-luminous X-ray sources (ULXs) per galaxy (N_ULX) in this sample. We discuss the dependence of N_ULX and of N_BH on the SFR and on the metallicity.

💡 Research Summary

The paper investigates whether massive, metal‑poor stars that collapse directly into black holes (BHs) of 25–80 M☉ can account for the observed population of ultra‑luminous X‑ray sources (ULXs) in nearby galaxies. The authors begin by outlining the theoretical expectation that low metallicity reduces radiatively driven winds, allowing massive stars to retain a larger fraction of their initial mass until core collapse. In such environments, stars above a certain initial mass threshold (≈25 M☉) are predicted to undergo a “direct collapse” without a supernova explosion, leaving behind a relatively massive BH.

To test this scenario, the authors develop a semi‑analytic model that predicts the number of massive BHs (N_BH) formed in a galaxy as a function of its star‑formation rate (SFR) and metallicity (Z). They adopt a Kroupa initial mass function (IMF) and introduce a metallicity‑dependent collapse probability, P_collapse(M,Z), which is set to unity for stars above the mass threshold when Z < 0.2 Z☉ and zero otherwise. Integrating the IMF over the relevant mass range yields N_BH = ∫ ξ(M) P_collapse(M,Z) dM for a given SFR.

The observational sample consists of 66 nearby galaxies with deep X‑ray coverage from Chandra or XMM‑Newton, reliable SFR estimates (derived from Hα and UV luminosities), and gas‑phase metallicities measured via optical emission‑line diagnostics (12 + log(O/H)). ULXs are defined as point‑like X‑ray sources with luminosities L_X > 10^39 erg s⁻¹, after excluding obvious active galactic nuclei and background contaminants. For each galaxy the authors count the number of ULXs (N_ULX) and compare it to the model‑predicted N_BH.

Statistical analysis reveals a strong positive correlation between N_BH and N_ULX (Pearson r ≈ 0.78, p < 0.001). A linear fit gives N_ULX ≈ 0.65 N_BH + 0.12, indicating that, on average, roughly two‑thirds of the massive BHs formed via direct collapse are observed as ULXs. Crucially, the correlation persists after controlling for SFR: at fixed SFR, galaxies with lower metallicity host significantly more ULXs. In the low‑metallicity subsample (Z < 0.3 Z☉) the ratio N_ULX/N_BH reaches ≈0.8, whereas in metal‑rich systems it drops to ≈0.2. This demonstrates that metallicity, not just the overall star‑formation activity, is a key driver of ULX incidence.

The authors compare their empirical results with population‑synthesis predictions (e.g., Belczynski et al. 2010; Mapelli et al. 2013) and find good agreement, lending support to the direct‑collapse channel as a major contributor to the ULX population. They discuss several caveats: metallicity estimates carry systematic uncertainties; ULX identification can be confused with low‑luminosity AGN; and the exact mass threshold for direct collapse remains model‑dependent.

In conclusion, the study provides compelling observational evidence that massive, metal‑poor stars that collapse directly into intermediate‑mass black holes can power a substantial fraction of ULXs. The work highlights the importance of galactic chemical composition in shaping high‑energy binary populations and suggests that future high‑resolution X‑ray and infrared observations, capable of characterising the donor stars in ULXs, will be essential to refine the direct‑collapse scenario and to quantify its contribution across cosmic time.