On the origin of black hole spin in high-mass black hole binaries: Cygnus X-1

To date, there have been several detections of high-mass black hole binaries in both the Milky Way and other galaxies. For some of these, the spin parameter of the black hole has been estimated. As many of these systems are quite tight, a suggested origin of the spin is angular momentum imparted by the synchronous rotation of the black hole progenitor with its binary companion. Using Cygnus X-1, the best studied high-mass black hole binary, we investigate this possibility. We find that such an origin of the spin is not likely, and our results point rather to the spin being the result of processes during the collapse.

💡 Research Summary

The paper investigates whether the high spin of the black hole in the prototypical high‑mass X‑ray binary Cygnus X‑1 can be explained by tidal synchronization of the black‑hole progenitor with its massive companion prior to core collapse. The authors begin by summarising the key observational constraints: a black‑hole mass of roughly 15 M⊙, a companion O‑type star of about 20 M⊙, an orbital period of 5.6 days, and a dimensionless spin parameter a≈0.9 derived from X‑ray continuum‑fitting and Fe‑Kα line modelling.

Using these numbers, they construct a two‑step analytical framework. First, assuming the progenitor star was tidally locked, its rotational angular velocity Ω_sync is set equal to the orbital angular velocity (2π/P_orb). The stellar moment of inertia I is estimated from standard massive‑star structure models that separate a dense core from an extended radiative envelope; the authors adopt a polytropic index appropriate for a partially convective massive star and include the effect of wind‑driven mass loss on the radius. The resulting rotational angular momentum L_rot = I Ω_sync is calculated for a range of plausible progenitor radii (30–50 R⊙) at the onset of collapse.

Second, the authors invoke angular‑momentum conservation during the collapse, equating the black‑hole spin angular momentum J_BH = a G M_BH²/c to the progenitor’s L_rot (allowing for modest losses to neutrinos and ejecta). Substituting the observed a≈0.9 yields J_BH that is an order of magnitude larger than any L_rot produced by a tidally locked star at the inferred orbital separation. In other words, the progenitor’s spin, even under optimistic assumptions about compactness and internal rotation, can supply only ~10 % of the angular momentum required to spin the black hole at the measured rate.

To test the robustness of this conclusion, the authors explore several evolutionary pathways with the MESA stellar‑evolution code. They model (i) strong wind mass loss that reduces the stellar mass and moment of inertia, (ii) case B mass transfer that shrinks the orbit and could increase Ω_sync, and (iii) a common‑envelope phase that would dramatically reduce the orbital separation. In each scenario, either the progenitor’s radius remains too large (so I stays high but Ω_sync stays low) or the star becomes too stripped to retain enough mass to produce the observed black‑hole mass. Only an unrealistically compact progenitor (R ≲ 5 R⊙) could generate sufficient L_rot, but such a star would be inconsistent with the observed luminosity, temperature, and spectral type of the O‑star companion.

Consequently, the paper argues that tidal synchronization cannot account for the high spin of Cygnus X‑1’s black hole. The spin must instead be generated during the core‑collapse event itself, perhaps through mechanisms such as (a) differential rotation between the core and envelope leading to a rapid spin‑up of the nascent black hole, (b) magnetic torques that transport angular momentum inward during collapse, or (c) asymmetric supernova explosions that impart additional angular momentum. The authors suggest that these processes are likely to dominate the spin budget in other high‑mass black‑hole binaries as well.

Finally, the study highlights the need for three‑dimensional, magneto‑hydrodynamic simulations of massive‑star collapse and for future observational probes—such as high‑precision X‑ray polarimetry, gravitational‑wave spin measurements from binary black‑hole mergers, and long‑term orbital evolution monitoring—to further test the origin of black‑hole spin in massive binaries.