The Angular Momenta of Neutron Stars and Black Holes as a Window on Supernovae

It is now clear that a subset of supernovae display evidence for jets and are observed as gamma-ray bursts. The angular momentum distribution of massive stellar endpoints provides a rare means of constraining the nature of the central engine in core-collapse explosions. Unlike supermassive black holes, the spin of stellar-mass black holes in X-ray binary systems is little affected by accretion, and accurately reflects the spin set at birth. A modest number of stellar-mass black hole angular momenta have now been measured using two independent X-ray spectroscopic techniques. In contrast, rotation-powered pulsars spin-down over time, via magnetic braking, but a modest number of natal spin periods have now been estimated. For both canonical and extreme neutron star parameters, statistical tests strongly suggest that the angular momentum distributions of black holes and neutron stars are markedly different. Within the context of prevalent models for core-collapse supernovae, the angular momentum distributions are consistent with black holes typically being produced in GRB-like supernovae with jets, and with neutron stars typically being produced in supernovae with too little angular momentum to produce jets via magnetohydrodynamic processes. It is possible that neutron stars are imbued with high spin initially, and rapidly spun-down shortly after the supernova event, but the available mechanisms may be inconsistent with some observed pulsar properties.

💡 Research Summary

The paper investigates whether the angular‑momentum (spin) distributions of stellar‑mass black holes (BHs) and rotation‑powered neutron stars (NSs) can reveal distinct core‑collapse supernova (SN) mechanisms. The authors compile two independent BH spin measurements—disk‑reflection spectroscopy and thermal‑continuum fitting—from 12 X‑ray binary systems, requiring statistically robust spectral fits and reliable system parameters (mass, distance, inclination). Disk‑reflection fits use relativistically broadened Fe Kα lines to infer the innermost stable circular orbit (ISCO) radius, while continuum fits model the multicolor black‑body emission assuming the disk extends to the ISCO. Both methods yield dimensionless spin parameters a = cJ/GM² that are high: the reflection sample has a mean ≈ 0.66 (Gaussian fit centroid 0.71 ± 0.26) and the continuum sample a mean ≈ 0.72 (centroid 0.81 ± 0.06).

For NSs, the authors adopt nine natal spin periods for isolated pulsars from Faucher‑Giguère & Kaspi (2006). Because the neutron‑star moment of inertia I is uncertain, they approximate I = (2/5) MR² for a uniform‑density sphere and explore two extreme radius assumptions: R = 10 km and R = 15 km, both with M = 1.4 M⊙. The resulting dimensionless spins are very low, with means of a ≈ 0.018 (R = 10 km) and a ≈ 0.029 (R = 15 km). Gaussian fits give centroids of 9.5 × 10⁻³ and 2.1 × 10⁻² respectively.

Kolmogorov–Smirnov (KS) tests compare the BH and NS distributions. Even under the most generous NS assumptions (R = 15 km), the KS p‑values are ≤ 3.6 × 10⁻⁴, strongly rejecting the hypothesis that both samples are drawn from the same parent distribution. Thus BHs are statistically shown to be born with substantially higher dimensionless angular momentum than NSs.

The authors discuss systematic uncertainties. BH spin estimates can be biased low if the accretion disk does not reach the ISCO (especially in hard states) or if spectral models assume constant disk density. Conversely, limited spectral resolution may underestimate the breadth of the Fe line, also lowering a. For NSs, the unknown equation of state introduces uncertainty in I, but the adopted uniform‑density approximation is deliberately neutral. Recent observations of a ≈ 2 M⊙ neutron star have already ruled out many soft equations of state, supporting the plausibility of the chosen I values.

Interpreting the results, the authors argue that high‑spin BHs are consistent with the “collapsar” model of long‑duration gamma‑ray bursts (GRBs). In this scenario, a massive progenitor (≈ 35 M⊙) retains enough pre‑collapse angular momentum to form a centrifugally supported disk around the nascent BH, rapidly spinning it up to a ≈ 0.9 and launching relativistic jets via magnetohydrodynamic (MHD) processes. The observed BH spin distribution (a ≈ 0.7–0.9) aligns with these predictions. In contrast, typical core‑collapse SNe that produce NSs apparently lack sufficient angular momentum to form such disks; consequently the resulting NSs inherit low spins.

The paper also examines whether NSs could be born with high spin and then be braked quickly. Magnetic dipole braking, gravitational‑wave emission, or interaction with fallback material are considered, but the required braking efficiencies appear inconsistent with observed pulsar properties. Therefore a low‑spin birth scenario is favored.

In conclusion, the distinct spin distributions provide empirical evidence that BHs and NSs originate from different angular‑momentum regimes in core‑collapse events. High‑spin BHs likely trace jet‑producing, GRB‑like explosions, while low‑spin NSs trace ordinary supernovae without jets. The study highlights the need for larger, higher‑quality BH spin samples and more precise NS moment‑of‑inertia estimates to refine these conclusions.