The detection of gravitational waves originating from a neutron-star merger, GW170817, by the LIGO and Virgo Collaborations has recently provided new stringent limits on the tidal deformabilities of the stars involved in the collision. Combining this measurement with the existence of two-solar-mass stars, we generate a generic family of neutron-star-matter equations of state (EOSs) that interpolate between state-ofthe-art theoretical results at low and high baryon density. Comparing the results to ones obtained without the tidal-deformability constraint, we witness a dramatic reduction in the family of allowed EOSs. Based on our analysis, we conclude that the maximal radius of a 1.4-solar-mass neutron star is 13.6 km, and that the smallest allowed tidal deformability of a similar-mass star is Λð1.4 M ⊙ Þ ¼ 120.

The theory governing the strong nuclear force—quantum chromodynamics—predicts that at sufficiently high energy densities, hadronic nuclear matter undergoes a deconfinement transition to a new phase of quarks and gluons1. Although this has been observed in ultrarelativistic heavy-ion collisions2,3, it is currently an open question whether quark matter exists inside neutron stars4. By combining astrophysical observations and theoretical ab initio calculations in a model-independent way, we find that the inferred properties of matter in the cores of neutron stars with mass corresponding to 1.4 solar masses (M⊙) are compatible with nuclear model calculations. However, the matter in the interior of maximally massive stable neutron stars exhibits characteristics of the deconfined phase, which we interpret as evidence for the presence of quark-matter cores. For the heaviest reliably observed neutron stars5,6 with mass M ≈ 2M⊙, the presence of quark matter is found to be linked to the behaviour of the speed of sound cs in strongly interacting matter. If the conformal bound $${c}_{\rm{s}}^{2}\le 1/3$$ c s 2 ≤ 1 / 3 (ref. 7) is not strongly violated, massive neutron stars are predicted to have sizable quark-matter cores. This finding has important implications for the phenomenology of neutron stars and affects the dynamics of neutron star mergers with at least one sufficiently massive participant.

We perform an Oð 2 s Þ perturbative calculation of the equation of state of cold but dense QCD matter with two massless and one massive quark flavor, finding that perturbation theory converges reasonably well for quark chemical potentials above 1 GeV. Using a running coupling constant and strange quark mass, and allowing for further nonperturbative effects, our results point to a narrow range where absolutely stable strange quark matter may exist. Absent stable strange quark matter, our findings suggest that quark matter in (slowly rotating) compact star cores becomes confined to hadrons only slightly above the density of atomic nuclei. Finally, we show that equations of state including quark matter lead to hybrid star masses up to M $ 2M , in agreement with current observations. For strange stars, we find maximal masses of M $ 2:75M and conclude that confirmed observations of compact stars with M > 2M would strongly favor the existence of stable strange quark matter.