Neutron-star equation of state from joint NICER mass–radius and GW tidal-deformability inference
Several independent probes exist and the field is limited by systematics (NICER hotspot models disagree by 1–3 km on the same pulsar) and by the absence of new loud BNS events in O4, so mid-range difficulty. Application value 14 for nuclear-physics spin-off; leverage 52 because the EOS gates compact-object astrophysics, kilonova and r-process modelling.
The problem
Figure out what matter is like inside neutron stars by combining their sizes, masses and how they stretch in collisions.
- 1Neutron stars squeeze matter beyond lab limits
- 2Matter's stiffness sets star radius
- 3X-rays, gravitational waves, radio give clues
- 4Probes sometimes disagree
- 5Combine into one equation of state
The goal. Infer the pressure–density relation (the equation of state, EOS) of cold matter at 1 to 8 times nuclear saturation density (the density at the centre of a heavy nucleus). Given the EOS, the Tolman–Oppenheimer–Volkoff equations give the mass–radius curve of neutron stars, so measuring masses and radii constrains the EOS.
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Path to understanding
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- Relativistic two-body dynamics and waveform modelsTheory · host
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- Neutron-star equation of state from joint NICER mass–radius and GW tidal-deformability inferenceThe problem
State of the art
GW170817 gave Λ̃ ≲ 800 and radii around 11–13 km (arXiv:1805.11581), and Dietrich et al. combined multimessenger data with the Hubble constant (arXiv:2002.11355). Legred et al. (arXiv:2106.05313) combined the J0740+6620 radius with other data. NICER's J0437−4715 analysis (Choudhury et al., arXiv:2407.06789, July 2024) found R = 11.36 (+0.95/−0.63) km at M = 1.418 M☉, while a December 2025 reanalysis that includes a modulated nonthermal component finds 11.8–15.1 km at 68% for the same pulsar and shows the nonthermal component is strongly preferred by the Bayesian evidence (Miller et al., arXiv:2512.08790; ApJL 2026). That two analyses of the same data differ so much shows hotspot-model systematics have not converged. Other NICER targets add leverage but also complexity: PSR J0614−3329 gives R = 10.29 (+1.01/−0.86) km at 1.44 M☉ (Mauviard et al., arXiv:2506.14883), smaller than most other NICER radii, and PSR J1231−1411 gives 12.6–13.5 km at about 1.04 M☉ with results that depend on the prior and are only likely converged (Salmi et al., arXiv:2409.14923). On the gravitational-wave side, O4 ended on 18 November 2025 without a confirmed binary neutron-star merger: GWTC-4.0 (O4a) contains only two neutron-star–black-hole events and GWTC-5.0 (O4b, May 2026) reports no new sources with a neutron star (arXiv:2605.27225); O4c results are pending. GW170817 therefore remains the only tidal measurement with a counterpart. No EOS is accepted at the 3% radius level.
Realistic applications
The EOS fixes the neutron-star mass–radius relation and maximum mass, informs the quark-matter or hyperon content of dense matter, the kilonova and short-GRB engine, supernova remnant masses and the gravitational-wave signal for future detectors. No practical application.
What counts as solved
Resolved when independent NICER, GW and nuclear-theory constraints are consistent and the pressure at 2–6 times saturation density is known to within about 20%, with radius at 1.4 M☉ constrained to better than 3%.
How it gets verified
ObservationSettled by new measurements or observations.
Needs new NICER mass-radius and gravitational-wave tidal-deformability data, consistent with nuclear-theory constraints, so that the pressure at 2 to 6 times saturation density is known to about 20% and the radius at 1.4 solar masses to better than 3%.
Claims under verification
+ add a claimNo claimed results on the Verification board for this problem yet.
Where the work is
New observations (NICER, O4/O5 events, radio masses) and Bayesian modelling dominate, with nuclear-theory input.
Bottlenecks
ranked by votes- #1EmpiricalNICER pulse-profile systematics
Hotspot geometry and nonthermal components change radii by about 1–3 km, as the two J0437 analyses show.
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Connected problems
Progress
- Dec 9, 2025Reanalysis of J0437−4715source
A nonthermal component broadens the radius posterior to 11.8–15.1 km.
- Jun 17, 2025NICER PSR J0614−3329source
Radius 10.29 (+1.01/−0.86) km at 1.44 M☉, on the compact side of NICER results.
- Jul 9, 2024NICER J0437−4715source
First radius for the nearest millisecond pulsar.
- May 29, 2018GW170817 EOS constraintssource
Tidal deformability bound radii near 11–13 km.