The dense-matter equation of state from neutron-star observations

Combine public NICER pulse-profile posteriors, gravitational-wave tidal-deformability constraints and pulsar masses into reproducible, well-calibrated constraints on the neutron-star equation of state.

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@misc{cairn-neutron-star-equation-of-state,
  title        = {The dense-matter equation of state from neutron-star observations},
  author       = {{Cairn Commons contributors}},
  howpublished = {\url{https://cairn-commons.com/problems/neutron-star-equation-of-state}},
  year         = {2026},
  note         = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-09-28}
}

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Claims

Verified

Disputed

Refuted

On the literature board

The problem

The question. What is the pressure–density relation of matter above nuclear saturation density, and does it show phase transitions (e.g. to quark matter)? Observations constrain it through the neutron-star mass–radius relation and tidal deformability.

Known status. From GW170817, LIGO/Virgo (2018) inferred radii near 11.9 km for both stars when requiring the equation of state to support stars above 1.97 solar masses. For the massive pulsar PSR J0740+6620, NICER+XMM analyses found R = 12.39 (+1.30/−0.98) km at M = 2.072 solar masses (Riley et al. 2021, posterior samples on Zenodo) and R = 13.7 (+2.6/−1.5) km (Miller et al. 2021, 68%). For PSR J0437−4715, Choudhury et al. (2024) report R = 11.36 (+0.95/−0.63) km at M = 1.418 ± 0.037, favouring softer equations of state. Independent teams and pulse-profile models do not always agree.

What counts as progress

Reproducible joint inferences from public posterior samples (NICER, gravitational-wave events, radio-timing masses) with open code, stated priors and parametrisation (piecewise polytropes, speed-of-sound models, nonparametric).
Studies of prior and model dependence, e.g. how hotspot-model choices or EOS parametrisations shift the radius at 1.4 solar masses.
Tests of specific hypotheses (phase transitions, maximum mass) with Bayes factors and documented sensitivity analyses.

How it is checked. Reviewers re-run the inference code on the cited public posteriors and check that the reported credible intervals are reproduced within sampling noise.

Current state

The problem