Angular Momentum and the Formation of Stars and Black Holes

The formation of compact objects like stars and black holes is strongly constrained by the requirement that nearly all of the initial angular momentum of the diffuse material from which they form must be removed or redistributed during the formation process. The mechanisms that may be involved and their implications are discussed for (1) low-mass stars, most of which probably form in binary or multiple systems; (2) massive stars, which typically form in clusters; and (3) supermassive black holes that form in galactic nuclei. It is suggested that in all cases, gravitational interactions with other stars or mass concentrations in a forming system play an important role in redistributing angular momentum and thereby enabling the formation of a compact object. If this is true, the formation of stars and black holes must be a more complex, dynamic, and chaotic process than in standard models. The gravitational interactions that redistribute angular momentum tend to couple the mass of a forming object to the mass of the system, and this may have important implications for mass ratios in binaries, the upper stellar IMF in clusters, and the masses of supermassive black holes in galaxies.

💡 Research Summary

The paper addresses the fundamental “angular momentum problem” that arises during the formation of compact objects such as stars and supermassive black holes (SMBHs). The author argues that the initial diffuse material from which these objects form possesses orders of magnitude more specific angular momentum than can be accommodated by a single star or black hole, even when rotating at break‑up speed. Consequently, nearly all of this angular momentum must be removed or redistributed during the formation process.

The discussion is organized into three astrophysical regimes: low‑mass stars, massive stars, and SMBHs in galactic nuclei. For low‑mass stars, observational evidence shows that the majority form in binary or higher‑order multiple systems. In this context, the angular momentum budget is split between orbital motion of the companions and the spin of the individual protostars. Early in the collapse, magnetic braking and magnetic torques dominate because the ionization fraction is high enough for the gas to be well coupled to the magnetic field. This stage can shed roughly one to two orders of magnitude of the original angular momentum, as supported by measurements of slowly rotating prestellar cores. As the density rises, ambipolar diffusion weakens magnetic coupling and gravity takes over. Non‑axisymmetric structures such as trailing spiral arms, bars, and clumps develop in simulations, producing gravitational torques that transport angular momentum outward. The residual spin angular momentum of each protostar is further transferred to surrounding gas and to the orbital motions of companions via tidal torques, dynamical friction, and gravitational drag. Disk‑mediated processes (viscous transport, magnetocentrifugal winds, jets) are also present but, according to the author, cannot by themselves account for the required angular momentum loss because realistic disks are too small, short‑lived, and limited by the α‑viscosity parameter.

In the case of massive stars, formation occurs within dense stellar clusters where the surrounding mass reservoir is much larger. Here, the dominant angular momentum sinks are dynamical interactions among many stars: three‑body encounters, binary hardening, and cluster‑scale gravitational potential fluctuations. Massive stars tend to migrate toward the cluster centre, where they can accrete gas and capture orbital angular momentum from nearby lower‑mass stars. This process naturally explains the observed correlation between the mass of the most massive star and the total mass of its host cluster (the “mass‑maximum star” relation). The author emphasizes that the same gravitational torques that redistribute angular momentum also set the upper end of the stellar initial mass function (IMF) in clusters.

For SMBHs, the problem is amplified because the black hole’s physical size is minuscule compared to the galactic scale over which the gas acquires its angular momentum. The paper proposes that large‑scale gas disks in galactic nuclei become gravitationally unstable, forming bars, spirals, and clumps that generate strong torques. These torques drive gas inward while ejecting angular momentum outward, often into the surrounding stellar bulge or into outflows. Interactions with a dense nuclear star cluster or with other massive black holes further absorb angular momentum. The net effect is a coupling between the SMBH mass and the host galaxy’s bulge mass or velocity dispersion (the M‑σ relation). The author suggests that the same angular‑momentum‑redistribution physics that operates in star formation also underlies the scaling relations observed for SMBHs.

Overall, the paper argues that magnetic processes dominate the early, low‑density phases, but once gravity takes over, gravitational torques—whether from spiral density waves, tidal interactions, or cluster dynamics—become the primary agents of angular momentum transport. This leads to a formation picture that is far more chaotic, dynamic, and environment‑dependent than the classic isolated‑collapse models. The redistribution of angular momentum not only solves the angular momentum budget but also links the final mass of the compact object to the mass of its surrounding system, offering a unified framework for understanding binary mass ratios, the high‑mass end of the IMF, and the SMBH‑galaxy scaling relations.