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 black holes (BHs) formed by the direct collapse of metal‑poor massive stars can account for the observed population of ultra‑luminous X‑ray sources (ULXs). Theory predicts that stars with final masses ≥ 40 M⊙, which can only be achieved in low‑metallicity environments (Z ≲ 0.4 Z⊙) because stellar winds are weak, will collapse directly into BHs with masses of 25–80 M⊙. Such massive BHs could power ULXs without invoking super‑Eddington accretion or strong beaming.

To test this scenario the authors compile a sample of 66 galaxies that have (i) X‑ray coverage sufficient to identify ULXs, (ii) measured star‑formation rates (SFRs), and (iii) metallicity estimates. Sixty‑four galaxies are taken from a previous study (Mapelli et al. 2010, “M10”), and two extremely metal‑deficient (XMD) dwarf galaxies— I Zw 18 and SBS 0335‑052—are added because they have Z < 0.03 Z⊙ and known ULX populations. For each galaxy the SFR is taken as the average of available measurements, metallicity is homogenized using the Pilyugin & Thuan (2005) calibration (or the value at 0.7 Holmberg radii when gradients exist), and the number of ULXs (N_ULX) is obtained after correcting for background contamination.

The observational analysis yields three key correlations:

1. N_ULX vs. SFR – A strong, nearly linear relationship (power‑law index ≈ 0.86–1.00) is found, confirming earlier work that ULX numbers scale with the current star‑formation activity.

2. N_ULX vs. metallicity – No direct correlation appears, but when ULX numbers are normalized by SFR (N_ULX/SFR), a modest anti‑correlation with metallicity emerges (index ≈ ‑0.55). This suggests that low‑Z environments are more efficient at producing ULXs per unit star formation.

3. N_BH vs. N_ULX – Using the theoretical model of Belczynski et al. (2010) for direct‑collapse BH formation, the expected number of massive BHs per galaxy (N_BH) is computed as a function of SFR and Z. N_BH scales linearly with SFR and shows a weak dependence on Z. When compared with the observed N_ULX, a statistically significant positive correlation (index ≈ 0.82, Pearson r ≈ 0.92) is found, indicating that the population of massive BHs predicted by the model can plausibly account for the observed ULXs.

The theoretical framework assumes a Kroupa initial mass function (IMF) with slope α≈1.3 for massive stars, a maximum stellar mass of 120 M⊙, and a minimum mass for direct‑collapse progenitors m_prog(Z) that decreases with metallicity. The normalization constant A(SFR) incorporates the current SFR and a characteristic companion lifetime t_co≈10⁷ yr (the lifetime of a ~15 M⊙ star), reflecting that only BHs with a massive donor can become observable ULXs.

The authors compare their results with an alternative model by Linden et al. (2010), which attributes the ULX–metallicity link to enhanced formation and longer lifetimes of high‑mass X‑ray binaries (HMXBs) at low Z, but still requires super‑Eddington accretion because direct‑collapse BHs would receive no natal kicks and thus could not undergo Roche‑lobe overflow. The present work argues that massive BHs formed by direct collapse can power ULXs without super‑Eddington rates, though it acknowledges uncertainties such as possible kicks from asymmetric neutrino emission or three‑body encounters, and the need to incorporate binary evolution effects on mass loss.

In conclusion, the study provides observational support for the hypothesis that massive, metal‑poor, directly‑collapsed BHs are viable engines of ULXs. While the correlation between ULX numbers and SFR is dominant, metallicity plays a secondary but measurable role, especially when normalizing by SFR. The inclusion of the two XMD galaxies, which host relatively many ULXs for their modest SFRs, strengthens the case. The authors stress that larger samples with accurate metallicity measurements, as well as refined binary evolution models that include direct‑collapse physics, are essential to solidify the connection and to understand the detailed accretion mechanisms in ULX systems.