We develop a semi-supervised variational autoencoder (SSVAE) framework to reconstruct and generate neutron star (NS) equations of state (EOS). The SSVAE consists of an encoder network that maps high-dimensional EOS data into a lower-dimensional latent space and a decoder network that reconstructs the full EOS from the latent representation. The latent space includes supervised NS observables derived from the training EOS data, as well as variational latent variables that capture additional EOS features learned automatically. Using a SSVAE trained on a Skyrme EOS dataset, we find that a latent space consisting of two supervised observables, the maximum mass M_max and the canonical radius R_1.4, together with a single variational latent variable associated mainly with the EOS near the crust-core transition, is sufficient to reconstruct Skyrme EOSs with high fidelity. The decoder reconstructed EOSs reproduce M_max and R_1.4 with mean absolute percentage errors within 0.14%. Sampling the latent space generates new EOSs that are causal, thermodynamically stable, and consistent with imposed constraints on the supervised observables. The framework therefore provides a compact and physically interpretable parameterization of the NS EOS that is well suited for Bayesian inference with multimessenger observations, including pulsar mass-radius measurements and gravitational wave data.

We propose a new Bayesian framework to infer the neutron star equation of state (EOS) from mass and radius observations and neutron matter theory by defining priors that directly parameterize mass-radius space instead of pressure-energy density space. We use direct and accurate inversion approximations to map mass-radius relations to the underlying EOS. We systematically compare its EOS inferences with those inferred from traditional EOS parameterizations, taking care to quantify the systematic prior uncertainties of both. Our results show that prior uncertainties should be included in all Bayesian approaches. The more natural alternative framework provides broader coverage of the physically allowed mass-radius space, especially small radius configurations, and yields enhanced computational efficiency and substantially reduced dependence on prior choices. Our results demonstrate that direct parameterization in observed space offers a robust and efficient alternative to traditional methods.

Performing Bayesian inference on quarkyonic equation-of-state models for neutron star matter, we find they satisfy all current astrophysical observations, thus reinforcing the argument for the use of such neutron star matter equation-of-state models alongside traditional ones. To observationally differentiate between stars with and without a quarkyonic phase, we identify a novel observational signature- the slope of the mass-radius relation at some fixed mass in conjunction with the sound speed at the star's center. In this plane, we find quarkyonic stars in a region with high central sound speed and positive slope, that is distinct from purely nucleonic stars. High accuracy NS radii measurements facilitated by the next generation of detectors, coupled with ongoing studies of mapping astrophysical observables to microphysical properties like sound speed can be used for testing this signature. Our results indicate that a neutron star with these properties would be a strong evidence for existence of a quarkyonic phase or a similar crossover transition in its core.

We develop an analytic method of inverting the Tolman–Oppenheimer–Volkoff relations to high accuracy. In principle, a specified energy density–pressure relation gives a unique mass–radius ( M – R ) relation and vice versa. Our method is developed from the strong correlations that are shown to exist between the neutron star mass–radius curve and the equation of state (EOS) or pressure–energy density relation. Selecting points that have masses equal to fixed fractions of the maximum mass, we find a semi-universal power-law relation between the central energy densities, pressures, sound speeds, chemical potentials, and number densities of those stars, with the maximum mass and the radii of one or more fractional maximum mass points. Rms fitting accuracies, for EOSs without large first-order phase transitions, are typically 0.5% for all quantities at all mass points. The method also works well, although less accurately, in reconstructing the EOS of hybrid stars with first-order phase transitions. These results permit, in effect, an analytic method of inverting an arbitrary M – R curve to yield its underlying EOS. We discuss applications of this inversion technique to the inference of the dense matter EOS from measurements of neutron star masses and radii as a possible alternative to traditional Bayesian approaches.

We report Bayesian inference of the mass, radius and hot X-ray emitting region properties - using data from the Neutron Star Interior Composition ExploreR (NICER) - for the brightest rotation-powered millisecond X-ray pulsar PSR J0437x20134715. Our modeling is conditional on informative tight priors on mass, distance and binary inclination obtained from radio pulsar timing using the Parkes Pulsar Timing Array (PPTA) (Reardon et al. 2024), and we use NICER background models to constrain the non-source background, cross-checking with data from XMM-Newton. We assume two distinct hot emitting regions, and various parameterized hot region geometries that are defined in terms of overlapping circles; while simplified, these capture many of the possibilities suggested by detailed modeling of return current heating. For the preferred model identified by our analysis we infer a mass of M = 1.418 ± 0.037 M_⊙ (largely informed by the PPTA mass prior) and an equatorial radius of R = 11.36^+0.95_-0.63 km, each reported as the posterior credible interval bounded by the 16 favors softer dense matter equations of state and is highly consistent with constraints derived from gravitational wave measurements of neutron star binary mergers. The hot regions are inferred to be non-antipodal, and hence inconsistent with a pure centered dipole magnetic field.

This paper compiles the model parameters and zero-temperature properties of an extensive collection of published theoretical nuclear interactions, including 255 non-relativistic (Skyrme-like) forces, 270 relativistic mean field (RMF) and point-coupling (RMF-PC) forces, and 13 Gogny-like forces. This forms the most exhaustive tabulation of model parameters to date. The properties of uniform symmetric matter and pure neutron matter at the saturation density are determined. Symmetry properties found from the second-order term of a Taylor expansion in neutron excess are compared to the energy difference of pure neutron and symmetric nuclear matter at the saturation density. Selected liquid-droplet model parameters, including the surface tension and surface symmetry energy, are determined for semi-infinite surfaces. Theoretical liquid droplet model neutron skin thicknesses of the neutron-rich closed-shell nuclei $^{48}$Ca and $^{208}$Pb are compared to published theoretical Hartree-Fock and experimental results. A similar comparison is made between theoretical liquid-droplet and experimental values of dipole polarizabilities. In addition, radii, binding energies, moments of inertia and tidal deformabilities of 1.2, 1.4 and 1.6 M$_\odot$ neutron stars are computed. An extensive correlation analysis of bulk matter, nuclear structure, and low-mass neutron star properties is performed and compared to nuclear experiments and astrophysical observations.

We report Bayesian inference of the mass, radius, and hot X-ray emitting region properties-using data from the Neutron Star Interior Composition ExploreR (NICER)-for the brightest rotation-powered millisecond X-ray pulsar, PSR J0437-4715. Our modeling is conditional on informative tight priors on mass, distance, and binary inclination obtained from radio pulsar timing using the Parkes Pulsar Timing Array (PPTA; Reardon et al.), and we use NICER background models to constrain the nonsource background, cross-checking with data from XMM-Newton. We assume two distinct hot emitting regions and various parameterized hot region geometries that are defined in terms of overlapping circles; while simplified, these capture many of the possibilities suggested by detailed modeling of return current heating. For the preferred model identified by our analysis, we infer a mass of M = 1.418 +/- 0.037 M circle dot (largely informed by the PPTA mass prior) and an equatorial radius of R=11.36-0.63+0.95 km, each reported as the posterior credible interval bounded by the 16% and 84% quantiles. This radius favors softer dense matter equations of state and is highly consistent with constraints derived from gravitational wave measurements of neutron star binary mergers. The hot regions are inferred to be nonantipodal and hence inconsistent with a pure centered dipole magnetic field.

Pulse profile modeling of X-ray data from the Neutron Star Interior Composition Explorer is now enabling precision inference of neutron star mass and radius. Combined with nuclear physics constraints from chiral effective field theory (chi EFT), and masses and tidal deformabilities inferred from gravitational-wave detections of binary neutron star mergers, this has led to a steady improvement in our understanding of the dense matter equation of state (EOS). Here, we consider the impact of several new results: the radius measurement for the 1.42 M circle dot pulsar PSR J0437-4715 presented by Choudhury et al., updates to the masses and radii of PSR J0740+6620 and PSR J0030+0451, and new chi EFT results for neutron star matter up to 1.5 times nuclear saturation density. Using two different high-density EOS extensions-a piecewise-polytropic (PP) model and a model based on the speed of sound in a neutron star (CS)-we find the radius of a 1.4 M circle dot (2.0 M circle dot) neutron star to be constrained to the 95% credible ranges 12.28-0.76+0.50 km ( 12.33-1.34+0.70 km) for the PP model and 12.01-0.75+0.56 km ( 11.55-1.09+0.94 km) for the CS model. The maximum neutron star mass is predicted to be 2.15-0.16+0.14 M circle dot and 2.08-0.16+0.28 M circle dot for the PP and CS models, respectively. We explore the sensitivity of our results to different orders and different densities up to which chi EFT is used, and show how the astrophysical observations provide constraints for the pressure at intermediate densities. Moreover, we investigate the difference R 2.0 - R 1.4 of the radius of 2 M circle dot and 1.4 M circle dot neutron stars within our EOS inference.

Nuclear mass measurements and neutron matter theory tightly constrain the nuclear symmetry energy parameters J, L, K_sym and Q_sym. Corroboration of these constraints on J and L can be found from measurements of the neutron skin thicknesses and dipole polarizabilities of neutron-rich nuclei. The experimental constraints on these parameters are compared with those obtained from consideration of astrophysical measurements of the neutron star radius, which we show is highly correlated with L. Attention is aimed at the recent PREX and CREX neutron skin measurements from Jefferson Lab, NICER neutron star radius measurements, and a new interpretation of the GW170817 tidal deformability measurement. We find joint satisfaction of PREX and CREX gives J=32.2±1.7 MeV and L=52.9±13.2 MeV, in excellent agreement with neutron matter predictions of J=32.0±1.1 MeV and L=51.9±7.9 MeV.

A review is made of constraints on the nuclear symmetry energy parameters arising from nuclear binding energy measurements, theoretical chiral effective field predictions of neutron matter properties, the unitary gas conjecture, and measurements of neutron skin thicknesses and dipole polarizabilities. While most studies have been confined to the parameters SV and L, the important roles played by, and constraints on Ksym, or, equivalently, the neutron matter incompressibility KN, are discussed. Strong correlations among SV,L, and KN are found from both nuclear binding energies and neutron matter theory. However, these correlations somewhat differ in the two cases, and those from neutron matter theory have smaller uncertainties. To 68% confidence, it is found from neutron matter theory that SV=32.0±1.1 MeV, L=51.9±7.9 MeV and KN=152.2±38.1 MeV. Theoretical predictions for neutron skin thickness and dipole polarizability measurements of the neutron-rich nuclei 48Ca, 120Sn, and 208Pb are compared to recent experimental measurements, most notably the CREX and PREX neutron skin experiments from Jefferson Laboratory. By themselves, PREX I+II measurements of 208Pb and CREX measurement of 48Ca suggest L=121±47 MeV and L=−5±40 MeV, respectively, to 68% confidence. However, we show that nuclear interactions optimally satisfying both measurements imply L=53±13 MeV, nearly the range suggested by either nuclear mass measurements or neutron matter theory, and is also consistent with nuclear dipole polarizability measurements. This small parameter range implies R1.4=11.6±1.0 km and Λ1.4=228−90+148, which are consistent with NICER X-ray and LIGO/Virgo gravitational wave observations of neutron stars.

Our limited understanding of the physical properties of matter at ultra-high density, high proton/neutron number asymmetry, and low temperature is presently one of the major outstanding problems in physics. As matter in this extreme state is known to only exist stably in the cores of neutron stars (NSs), complementary measurements from electromagnetic and gravitational wave astrophysical observations of NSs, combined with terrestrial laboratory constraints and further theoretical investigations, hold the promise to provide important insight into the properties of matter in a region of the quantum chromodynamics phase space that is otherwise inaccessible. This multidisciplinary endeavor imposes the following requirements for facilities and resources in the upcoming decade and beyond: * A next generation of gravitational wave detectors to uncover more double NS and neutron star-black hole mergers; * Sensitive radio telescopes to find the most massive and fastest spinning NSs; * Large-area, high-time-resolution and/or high angular resolution X-ray telescopes to constrain the NS mass-radius relation; * Suitable laboratory facilities for nuclear physics experiments to constrain the dense matter equation of state; * Funding resources for theoretical studies of matter in this regime; * The availability of modern large-scale high performance computing infrastructure. The same facilities and resources would also enable significant advances in other high-profile fields of inquiry in modern physics such as the nature of dark matter, alternative theories of gravity, nucleon superfluidity and superconductivity, as well as an array of astrophysics, including but not limited to stellar evolution, nucleosynthesis, and primordial black holes.

Posterior sample files associated with "A NICER View of PSR J0030+0451: Millisecond Pulsar Parameter Estimation" by Riley et al. (2019; DOI: 10.3847/2041-8213/ab481c). Also included are model modules and scripts in the Python language using the X-PSI framework. Please refer to the README for detailed information.

Among the various oscillation modes of neutron stars, f- and g- modes are the most likely to be ultimately observed in binary neutron star mergers. The f-mode is known to correlate in normal neutron stars with their tidal deformability, moment of inertia and quadrupole moment. Using a piecewise polytropic parameterization scheme to model the uncertain hadronic high-density EOS and a constant sound-speed scheme to model pure quark matter, we refine this correlation and show that these universal relations also apply to both self-bound stars and hybrid stars containing phase transitions. We identify a novel 1-node branch of the f-mode that occurs in low-mass hybrid stars in a narrow mass range just beyond the critical mass necessary for a phase transition to appear. This 1-node branch shows the largest, but still small, deviations from the universal correlation we have found. The g-mode frequency only exists in matter with a non-barotropic equation of state involving temperature, chemical potential or composition, or a phase transition in barotropic matter. The g-mode therefore could serve as a probe for studying phase transitions in hybrid stars. In contrast with the f-mode, discontinuity g-mode frequencies depend strongly on properties of the transition (the density and the magnitude of the discontinuity) at the transition. Imposing causality and maximum mass constraints, the g-mode frequency in hybrid stars is found to have an upper bound of about 1.25 kHz. However, if the sound speed c_s in the inner core at densities above the phase transition density is restricted to c_s^2 < c^2/3, the g-mode frequencies can only reach about 0.8 kHz, which are significantly lower than f-mode frequencies, 1.3-2.8 kHz. Also, g-mode gravitational wave damping times are extremely long, >10^4 s (10^2 s) in the inner core with c_s^2< c^{2/3} (c^2), in comparison with the f-mode damping time, 0.1-1 s.

Since the release of the 2015 Long Range Plan in Nuclear Physics, major events have occurred that reshaped our understanding of quantum chromodynamics (QCD) and nuclear matter at large densities, in and out of equilibrium. The US nuclear community has an opportunity to capitalize on advances in astrophysical observations and nuclear experiments and engage in an interdisciplinary effort in the theory of dense baryonic matter that connects low- and high-energy nuclear physics, astrophysics, gravitational waves physics, and data science

PSR J0740$+$6620 has a gravitational mass of $2.08\pm 0.07~M_\odot$, which is the highest reliably determined mass of any neutron star. As a result, a measurement of its radius will provide unique insight into the properties of neutron star core matter at high densities. Here we report a radius measurement based on fits of rotating hot spot patterns to Neutron Star Interior Composition Explorer (NICER) and X-ray Multi-Mirror (XMM-Newton) X-ray observations. We find that the equatorial circumferential radius of PSR J0740$+$6620 is $13.7^{+2.6}_{-1.5}$ km (68%). We apply our measurement, combined with the previous NICER mass and radius measurement of PSR J0030$+$0451, the masses of two other $\sim 2~M_\odot$ pulsars, and the tidal deformability constraints from two gravitational wave events, to three different frameworks for equation of state modeling, and find consistent results at $\sim 1.5-3$ times nuclear saturation density. For a given framework, when all measurements are included the radius of a $1.4~M_\odot$ neutron star is known to $\pm 4$% (68% credibility) and the radius of a $2.08~M_\odot$ neutron star is known to $\pm 5$%. The full radius range that spans the $\pm 1\sigma$ credible intervals of all the radius estimates in the three frameworks is $12.45\pm 0.65$ km for a $1.4~M_\odot$ neutron star and $12.35\pm 0.75$ km for a $2.08~M_\odot$ neutron star.

In recent years our understanding of the dense matter equation of state (EOS) of neutron stars has significantly improved by analyzing multimessenger data from radio/X-ray pulsars, gravitational wave events, and from nuclear physics constraints. Here we study the additional impact on the EOS from the jointly estimated mass and radius of PSR J0740+6620, presented in Riley et al. (2021) by analyzing a combined dataset from X-ray telescopes NICER and XMM-Newton. We employ two different high-density EOS parameterizations: a piecewise-polytropic (PP) model and a model based on the speed of sound in a neutron star (CS). At nuclear densities these are connected to microscopic calculations of neutron matter based on chiral effective field theory interactions. In addition to the new NICER data for this heavy neutron star, we separately study constraints from the radio timing mass measurement of PSR J0740+6620, the gravitational wave events of binary neutron stars GW190425 and GW170817, and for the latter the associated kilonova AT2017gfo. By combining all these, and the NICER mass-radius estimate of PSR J0030+0451 we find the radius of a 1.4 solar mass neutron star to be constrained to the 95% credible ranges 12.33^{+0.76}_{-0.81} km (PP model) and 12.18^{+0.56}_{-0.79} km (CS model). In addition, we explore different chiral effective field theory calculations and show that the new NICER results provide tight constraints for the pressure of neutron star matter at around twice saturation density, which shows the power of these observations to constrain dense matter interactions at intermediate densities.

We combine the equation of state of dense matter up to twice nuclear saturation density n(sat) obtained using chiral effective field theory (chi EFT) and recent observations of neutron stars to gain insights about the high-density matter encountered in their cores. A key element in our study is the recent Bayesian analysis of correlated EFT truncation errors based on order-by-order calculations up to next-to-next-to-next-to-leading order in the chi EFT expansion. We refine the bounds on the maximum mass imposed by causality at high densities and provide stringent limits on the maximum and minimum radii of similar to 1.4 M-circle dot and similar to 2.0 M-circle dot stars. Including chi EFT predictions from n(sat) to 2 n(sat) reduces the permitted ranges of the radius of a 1.4 M-circle dot star, R-1.4, by similar to 3.5 km. If observations indicate R-1.4 < 11.2km, then our study implies that either the squared speed of sound c(s)(2) > 1/2 for densities above 2 n(sat) or that x EFT breaks down below 2 n(sat). We also comment on the nature of the secondary compact object in GW190814 with mass similar or equal to 2.6 M-circle dot and discuss the implications of massive neutron stars >2.1 M-circle dot (2.6 M-circle dot) in future radio and gravitational-wave searches. Some form of strongly interacting matter with c(s)(2) > 0.35 (0.55) must be realized in the cores of such massive neutron stars. In the absence of phase transitions below 2 n(sat), the small tidal deformability inferred from GW170817 lends support for the relatively small pressure predicted by chi EFT for the baryon density n(B) in the range 1-2 n(sat). Together they imply that the rapid stiffening required to support a high maximum mass should occur only when n(B) greater than or similar to 1.5-1.8 n(sat).

We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740+6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint North American Nanohertz Observatory for Gravitational Waves and Canadian Hydrogen Intensity Mapping Experiment/Pulsar wideband radio timing measurements of Fonseca et al. We use XMM-Newton European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740+6620 to be 12.39−0.98+1.30 km and 2.072−0.066+0.067 M ⊙ respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, conditional on surface hot regions that are non-overlapping spherical caps of fully ionized hydrogen atmosphere with uniform effective temperature; a posteriori, the temperature is log10(T[K])=5.99−0.06+0.05 for each hot region. All software for the X-ray modeling framework is open-source and all data, model, and sample information is publicly available, including analysis notebooks and model modules in the Python language. Our marginal likelihood function of mass and equatorial radius is proportional to the marginal joint posterior density of those parameters (within the prior support) and can thus be computed from the posterior samples.

The possible detection of a compact object in the remnant of SN 1987A presents an unprecedented opportunity to follow its early evolution. The suspected detection stems from an excess of infrared emission from a dust blob near the compact object’s predicted position. The infrared excess could be due to the decay of isotopes like 44Ti, accretion luminosity from a neutron star or black hole, magnetospheric emission or a wind originating from the spin down of a pulsar, or to thermal emission from an embedded, cooling neutron star (NS 1987A). It is shown that the last possibility is the most plausible as the other explanations are disfavored by other observations and/or require fine-tuning of parameters. Not only are there indications that the dust blob overlaps the predicted location of a kicked compact remnant, but its excess luminosity also matches the expected thermal power of a 30 yr old neutron star. Furthermore, models of cooling neutron stars within the minimal cooling paradigm readily fit both NS 1987A and Cas A, the next-youngest known neutron star. If correct, a long heat transport timescale in the crust and a large effective stellar temperature are favored, implying relatively limited crustal n-1S0 superfluidity and an envelope with a thick layer of light elements, respectively. If the locations do not overlap, then pulsar spin down or accretion might be more likely, but the pulsar’s period and magnetic field or the accretion rate must be rather finely tuned. In this case, NS 1987A may have enhanced cooling and/or a heavy-element envelope.