The Mass Gap: The Missing Compact Objects Between Neutron Stars and Black Holes

A desert in the compact-object mass function

Stars end their lives as one of three cold, dead remnants: white dwarfs, neutron stars, or black holes. When astronomers tabulate the measured masses of the two densest kinds, they do not find a smooth continuum. Neutron stars cluster tightly around 1.1–1.6 M☉ and reach a hard ceiling near 2.2 M☉. Black holes measured in Galactic X-ray binaries begin near 5 M☉ and extend upward. The interval between — roughly 2.5 to 5 M☉ — is nearly empty. This is the lower mass gap, distinct from the separate upper mass gap near 50–120 M☉ carved by pair-instability supernovae.

The gap matters because it is a fingerprint of the physics we cannot watch directly: the moment a stellar core collapses and either bounces into a neutron star or keeps falling into a black hole. A clean, sharp gap implies the outcome is nearly bimodal. A filled-in gap would imply a smooth transition. Which one nature chose constrains the supernova explosion mechanism, the nuclear equation of state, and how compact-object binaries form and merge.

The supernova engine that carves the gap

The leading explanation ties the gap to how fast a core-collapse supernova explodes. When a massive star's iron core collapses, it bounces at nuclear density and launches a shock — but that shock stalls. It must be revived, primarily by neutrino heating aided by turbulent convection and the standing-accretion-shock instability, within a few hundred milliseconds before the whole core swallows itself into a black hole.

Belczynski, Fryer and collaborators (2012) showed that the timescale of that revival sets the remnant mass spectrum. In their rapid model, the explosion is launched fast (< 250 ms after bounce, driven by instabilities that grow in ~10–20 ms). It cleanly ejects the outer core and leaves either a light neutron star or, if too much falls back, a black hole above ~5 M☉ — producing a genuine gap. In their delayed model, the explosion is sluggish (> 500 ms), fallback accretion is graded, and remnants of every mass between 2 and 5 M☉ form, filling the gap. So the gap's very existence is a direct probe of the explosion timescale.

The numbers: TOV ceiling, black-hole floor, and the width

The gap is bracketed by two independent physics limits. The upper edge of neutron stars is the Tolman–Oppenheimer–Volkoff (TOV) limit — the maximum mass a cold, non-rotating neutron star can support before degeneracy pressure and the repulsive nuclear force lose to gravity. Depending on the dense-matter equation of state, the TOV mass is roughly 2.2–2.9 M☉; the binary neutron-star merger GW170817 tightened it empirically to about 2.01–2.17 M☉. The heaviest well-measured pulsar, PSR J0740+6620, sits near 2.08 M☉.

The lower edge of black holes comes from dynamics, not theory. Bailyn et al. (1998) found the black-hole mass function centered near 7 M☉ with a dearth below ~5 M☉; Özel et al. (2010) and Farr et al. (2011), with ~15–16 low-mass X-ray binaries, confirmed a floor around 5 M☉ and argued it was not a selection artifact. The rapid-explosion models reproduce this quantitatively: 75–95% of neutron stars form below 1.6 M☉, and very few remnants appear between 2 and 4 M☉. The gap width is therefore roughly Δ ≈ 2.5 M☉.

How the gap is observed: dynamics, microlensing, and gravitational waves

Three independent techniques probe the gap. First, dynamical mass measurements in X-ray binaries: during quiescence the companion star dominates the optical light, so classical spectroscopy of its radial-velocity curve and orbital period yields the mass function and, with inclination and mass ratio, the compact object's mass. This is how the ~5 M☉ black-hole floor was established.

Second, gravitational microlensing can weigh isolated remnants that emit no light. Sahu et al. (2022) used Hubble Space Telescope astrometry over six years to measure the relativistic image deflection of a background bulge star, yielding an isolated black hole of 7.1 ± 1.3 M☉ at 1.58 kpc — the first unambiguous isolated stellar-mass black-hole mass.

Third, and most decisively, gravitational waves: LIGO and Virgo measure the masses of merging compact objects directly from the inspiral chirp. GW190814 (O3) contained a 2.50–2.67 M☉ secondary sitting right at the gap's lower lip, and GW230529 (detected 29 May 2023 by LIGO Livingston) paired a ~1.3–2.1 M☉ neutron star with a 2.5–4.5 M☉ object squarely inside the gap.

Where it operates, and what it is not

The lower mass gap is a feature of the population of stellar-mass compact remnants formed by iron-core-collapse supernovae from stars of roughly 8–25 M☉ initial mass. It is emphatically not the same as the upper mass gap (~50–120 M☉), which is produced by pair-instability and pulsational pair-instability supernovae that leave no remnant at all. Nor is it the theoretical TOV limit itself — the TOV limit sets only the gap's lower boundary; the gap is the empty region above it.

Objects can land in the gap by routes other than direct collapse. A neutron star that accretes matter in a binary, or the remnant of two merged neutron stars (a plausible reading of GW190814's companion), can exceed the TOV mass and become a low-mass black hole. Hierarchical triple systems and dynamical assembly in dense clusters can also deposit merger products into the gap. So the gap is best understood as a scarcity in the single-star, direct-formation channel, not an absolute prohibition on 2.5–5 M☉ compact objects.

Open questions and why the gap matters

The central unresolved question is whether the gap is real or observational. X-ray binary samples are small and prone to selection effects — low-mass black holes may be harder to spot or misidentified as neutron stars. GW190814 and GW230529 show that objects do exist in the gap; the debate is now about how rare they are and whether a smooth distribution (favoring the delayed engine) or a depleted one (favoring the rapid engine) better fits the growing gravitational-wave catalog.

The stakes are high. Populating or emptying the gap discriminates between supernova explosion models, which in turn control neutron-star kick velocities, nucleosynthesis yields, and the birth rate of merging binaries that LIGO detects. The gap also probes the nuclear equation of state: pushing the TOV maximum toward 2.5 M☉ would shrink the gap from below. As the LIGO–Virgo–KAGRA network accumulates events and the Roman Space Telescope's microlensing survey weighs isolated remnants by the thousands, the coming decade should finally reveal whether nature truly leaves this ground empty.

Compact objects around the lower mass gap: characteristic masses, formation, and detection

Object / regime	Mass range	Origin / physics	How measured
Neutron star (typical)	1.1–1.6 M☉	Iron-core collapse, degeneracy + nuclear force support	Pulsar timing, X-ray binaries
Heaviest neutron stars	≈ 2.0–2.2 M☉	Near the TOV maximum-mass limit	PSR J0740+6620 (Shapiro delay), NICER
Lower mass gap	≈ 2.5–5 M☉	Predicted empty by rapid-explosion engine	GW190814, GW230529 objects fall here
Lightest X-ray binary BHs	≈ 5–8 M☉	Core collapse to black hole	Dynamical masses in quiescence (optical)
Isolated stellar BH (microlensing)	7.1 ± 1.3 M☉	Failed/successful supernova of massive star	HST astrometric microlensing (Sahu 2022)