Inferring the neutron star equation of state with nuclear-physics informed semiparametric models

Over the past decade, an abundance of information from neutron-star observations, nuclear experiments and theory has transformed our efforts to elucidate the properties of dense matter. However, at high densities relevant to the cores of neutron stars (NSs), substantial uncertainty about the dense matter equation of state (EoS) remains. In this work, we present a semiparametric EoS framework aimed at better integrating knowledge across these domains in astrophysical inference. We use a meta-model and realistic crust at low densities, and Gaussian process (GP) extensions at high densities. Comparisons between our semiparametric framework to fully nonparametric EoS representations show that imposing nuclear theoretical and experimental constraints through the meta-model up to nuclear saturation density results in constraints on the pressure up to twice nuclear saturation density. We also show that our GP trained on EoS models with nucleonic, hyperonic, and quark compositions extends the range of EoS explored at high density compared to a piecewise polytropic extension schema, under the requirements of causality of matter and of supporting the existence of heavy pulsars (PSRs). We find that maximum Tolman–Oppenheimer–Volkoff masses above 3.2 M⊙ can be supported by causal EoS compatible with nuclear constraints at low densities. We then combine information from existing observations of heavy PSR masses, gravitational waves emitted from binary NS mergers, and x-ray pulse profile modeling of millisecond PSRs within a Bayesian inference scheme using our semiparametric EoS prior. With information from all public NS Interior Composition ExploRer PSRs (including PSR J0030+0451, PSR J0740+6620, PSR J0437–4715, and PSR J0614–3329), we find an astrophysically favored pressure at two times nuclear saturation density of P(2ρ_(nuc)) = 1.98^(+2.13)_(-1.08) x 10³⁴ dyn cm⁻², a radius of a  1.4 M⊙ NS value of R_(1.4) = 11.4^(+0.98)_(-0.60) km, and M_(max) = 2.31^(+0.35)_(-0.23) M⊙ at the 90% credible level (C.L).

The authors thank Valerie Poynor, the developers of CUTER, Anthea Fantina and Francesca Gulminelli for useful discussions. S N, L T, and J R acknowledges support by NSF Grants PHY-2409736, PHY-2110441, and the Nicholas and Lee Begovich Center for Gravitational-Wave Physics and Astronomy. J R acknowledges support from Perimeter Institute. I L acknowledges support from the DOE under Award No. DE-SC0023101. L S acknowledges the financial support of the National Science Foundation Grant No. PHY 21-16686. The authors are grateful for computational resources provided by the LIGO Laboratory and supported by National Science Foundation Grants PHY-0757058 and PHY-0823459. This material is based upon work supported by NSF’s LIGO Laboratory which is a major facility fully funded by the National Science Foundation. This research has made use of data or software obtained from the Gravitational Wave Open Science Center (gwosc.org), a service of the LIGO Scientific Collaboration, the Virgo Collaboration, and KAGRA. This material is based upon work supported by NSF’s LIGO Laboratory which is a major facility fully funded by the National Science Foundation, as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. Virgo is funded, through the European Gravitational Observatory (EGO), by the French Centre National de Recherche Scientifique (CNRS), the Italian Istituto Nazionale di Fisica Nucleare (INFN) and the Dutch Nikhef, with contributions by institutions from Belgium, Germany, Greece, Hungary, Ireland, Japan, Monaco, Poland, Portugal, Spain. KAGRA is supported by Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan Society for the Promotion of Science (JSPS) in Japan; National Research Foundation (NRF) and Ministry of Science and ICT (MSIT) in Korea; Academia Sinica (AS) and National Science and Technology Council (NSTC) in Taiwan.