Dense Matter Equation Of State Research Articles

Bayesian inference of the dense matter equation of state built upon extended Skyrme interactions

Bayesian inference of the dense matter equation of state built upon extended Skyrme interactions

Constraining the Dense Matter Equation of State with New NICER Mass–Radius Measurements and New Chiral Effective Field Theory Inputs

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 (χEFT), 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 ⊙ 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 χEFT 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 ⊙ (2.0 M ⊙) 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 ⊙ and 2.08−0.16+0.28 M ⊙ for the PP and CS models, respectively. We explore the sensitivity of our results to different orders and different densities up to which χEFT 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 ⊙ and 1.4 M ⊙ neutron stars within our EOS inference.

A NICER View of the Nearest and Brightest Millisecond Pulsar: PSR J0437–4715

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 ⊙ (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.

Constraints on the dense matter equation of state from young and cold isolated neutron stars

Constraints on the dense matter equation of state from young and cold isolated neutron stars

Relativistic description of dense matter equation of state and neutron star observables constrained by recent astrophysical observations

In the present work, we investigate the bulk properties of nuclear matter and neutron stars with the newly proposed relativistic interaction NL-RS which provides an opportunity to readjust the coupling constants keeping in view the properties of finite nuclei, nuclear matter, PREX-II results for neutron skin thickness in 208Pb and astrophysical observations. The NL-RS model interaction has been proposed by fitting the ground state properties (binding energies and charge radii) of finite nuclei, bulk nuclear matter properties, and PREX-II results for neutron skin thickness of 208Pb. The relativistic interaction has been generated by including nonlinear self-interactions of σ and ω μ -mesons and mixed interactions of ω μ , and ρ μ -meson up to the quartic order. The proposed interaction harmonizes with the finite nuclei, bulk nuclear matter, and neutron star properties. A covariance analysis is performed to assess the statistical uncertainties on the model parameters and nuclear observables of interest along with correlations amongst them. The equation of state (EoS) composed of nucleons and leptons in β-equilibrium is computed with the proposed parameter set and used to study the neutron star structure. The maximum mass of the neutron star by employing the EoS computed with the NL-RS parameter set is 2.04 ± 0.03M ⊙ and the radius of a canonical mass neutron star (R 1.4) comes out to be equal to 13.06 ± 0.16 Km. The value of dimensionless tidal deformability, for canonical mass, is 602.23 ± 33.13 which satisfies the constraints of waveform models analysis of GW170817 within 90% confidence level.

Constraining the Onset Density for the QCD Phase Transition with the Neutrino Signal from Core-collapse Supernovae

The occurrence of a first-order hadron–quark matter phase transition at high baryon densities is investigated in astrophysical simulations of core-collapse supernovae, to decipher yet incompletely understood properties of the dense matter equation of state (EOS) using neutrinos from such cosmic events. It is found that the emission of a nonstandard second neutrino burst, dominated by electron antineutrinos, is not only a measurable signal for the appearance of deconfined quark matter but also reveals information about the state of matter at extreme conditions encountered at the supernova (SN) interior. To this end, a large set of spherically symmetric SN models is investigated, studying the dependence on the EOS and the stellar progenitor. General relativistic neutrino-radiation hydrodynamics is employed featuring three-flavor Boltzmann neutrino transport and a microscopic hadron-quark hybrid matter EOS class. Therefore, the DD2 relativistic mean-field hadronic model is employed, and several variations of it, and the string-flip model for the description of deconfined quark matter. The resulting hybrid model covers a representative range of onset densities for the phase transition and latent heats. This facilitates the direct connection between intrinsic signatures of the neutrino signal and properties of the EOS. In particular, a set of linear relations has been found empirically. These potentially provide a constraint for the onset density of a possible QCD phase transition from the future neutrino observation of the next galactic core-collapse SN, if a millisecond electron anti-neutrino burst is present around or less than 1 s.

Dense-matter equation of state at zero & finite temperature

At high density, matter is expected to undergo a phase transition to deconfined quark matter. Although the density at which it happens and the strength of the transition are still largely unknown, we can model it to be in agreement with known experimental data and reliable theoretical results. We discuss how deconfinement in dense matter can be affected by both by temperature and by strong magnetic fields within the Chiral Mean Field (CMF) model. To explore different dependencies in our approach, we also explore how deconfinement can be affected by the assumption of different degrees of freedom, different vector coupling terms, and different deconfining potentials, all at zero temperature. Both zero-net-strangeness and isospin-symmetric heavy-ion collision matter and beta-equilibrated charge-neutral matter in neutron stars are discussed.

Timing of accreting neutron stars with future X-ray instruments: towards new constraints on dense matter equation of state

Timing of accreting neutron stars with future X-ray instruments: towards new constraints on dense matter equation of state

Realizing the potential of deep neural network for analyzing neutron star observables and dense matter equation of state

Realizing the potential of deep neural network for analyzing neutron star observables and dense matter equation of state

Exploration of extreme QCD matter with deep learning

To study hot and dense nuclear matter, relativistic nuclear collisions are carried out experimentally, while lattice field theory provides a first-principles investigation. Meanwhile, astronomical observations of neutron stars also provide constraints on cold and dense nuclear matter. In this talk, I present the potential of deep learning based strategies to aid the exploration of QCD matter under extreme conditions, ranging from identifying essential physics from nuclear collision experiments, to facilitating lattice QCD data analysis, to efficiently exploiting astronomical observations in extracting the dense matter equation of state.

Universal relations to measure neutron star properties from targeted r-mode searches

ABSTRACT R-mode oscillations of rotating neutron stars (NS) are promising candidates for continuous gravitational wave (GW) observations. In our recent work, we derived universal relations between the NS parameters compactness and dimensionless tidal deformability with the r-mode frequency. In this work, we investigate how these universal relations can be used to infer various NS intrinsic parameters following a successful detection of the r-modes. In particular, we show that for targeted r-mode searches, these universal relations along with the ‘I–Love–Q’ relation can be used to estimate both the moment of inertia and the distance of the NS, thus breaking the degeneracy of distance measurement for continuous gravitational wave (CGW) observations. We also discuss that, with a prior knowledge of the distance of the NS from electromagnetic observations, these universal relations can also be used to constrain the dense matter equation of state (EOS) inside the NS. We quantify the accuracy to which such measurements can be done using the Fisher information matrix for a broad range of possible, unknown parameters for both the a-LIGO and Einstein Telescope (ET) sensitivities.

Impact of O4 future detections on the determination of the dense matter equations of state

In view of the next LIGO-Virgo-KAGRA Observing period O4 (to start in Spring 2023), we address the question of the ability of the interferometers network to discriminate among different neutron stars equation of states better than what was possible with the observation of the binary neutron stars merger GW170817. We show that the observation of an event similar to GW170817 during O4 would allow us to resolve the dimensionless effective tidal deformability $\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}$ within an uncertainty 7 times better than the one obtained in O2. Thanks to the expected increase in sensitivities, we show that any GW170817-like single-event within a distance of 100 Mpc would imply significantly improved constraints of the neutron stars equations of state. We also illustrate the important impact of the noise in the analysis of the signal, showing how it can impact the effective tidal deformability probability density function for large signal-to-noise ratio.

Probing strong field f(R) gravity and ultradense matter with the structure and thermal evolution of neutron stars

Thermal evolution of neutron stars is studied in the $f(R)=R+\ensuremath{\alpha}{R}^{2}$ theory of gravity. We first review the equations of stellar structure and evolution for a spherically symmetric spacetime plus a perfect fluid at rest. We then present numerical results for the structure of neutron stars using four nucleonic dense matter equations of state and a series of gravity theories for $\ensuremath{\alpha}$ ranging from zero, i.e., general relativity, up to $\ensuremath{\alpha}\ensuremath{\approx}{10}^{16}\text{ }\text{ }{\mathrm{cm}}^{2}$. We emphasize properties of these neutron star models that are of relevance for their thermal evolution as the threshold masses for enhanced neutrino emission by the direct Urca process, the proper volume of the stellar cores where this neutrino emission is allowed, the crust thickness, and the surface gravitational acceleration that directly impact the observable effective temperature. Finally, we numerically solve the equations of thermal evolution and explicitly analyze the effects of altering gravity. We find that uncertainties in the dense matter microphysics, such as the core chemical composition and superfluidity/superconductivity properties, as well as the astrophysical uncertainties on the chemical composition of the surface layers, have a much stronger impact than possible modifications of gravity within the studied family of $f(R)$ theories. We conclude that within this family of gravity theories, conclusions from previous studies of neutron star thermal evolution are not significantly altered by modification of gravity theory. Conversely, this implies that neutron star cooling modeling may not be a useful tool to constrain deviations of gravity from Einstein theory unless these are much more radical than in the $f(R)=R+\ensuremath{\alpha}{R}^{2}$ framework.

Degeneracy in the Inference of Phase Transitions in the Neutron Star Equation of State from Gravitational Wave Data.

Gravitational wave (GW) detections of binary neutron star inspirals will be crucial for constraining the dense matter equation of state (EOS). We demonstrate a new degeneracy in the mapping from tidal deformability data to the EOS, which occurs for models with strong phase transitions. We find that there exists a new family of EOS with phase transitions that set in at different densities and that predict neutron star radii that differ by up to ∼500 m but that produce nearly identical tidal deformabilities for all neutron star masses. Next-generation GW detectors and advances in nuclear theory may be needed to resolve this degeneracy.

Reconstructing the neutron star equation of state from observational data via automatic differentiation

Neutron star observables like masses, radii, and tidal deformability are direct probes to the dense matter equation of state (EoS). A novel deep learning method that optimizes an EoS in the automatic differentiation framework of solving inverse problems is presented. The trained neural network EoS yields narrow bands for the relationship between the pressure and speed of sound as a function of the mass density. The results are consistent with those obtained from conventional approaches and the observational bound on the tidal deformability inferred from the gravitational wave event, GW170817.

Bayesian inference of the dense matter equation of state built upon covariant density functionals

A modified version of the density dependent covariant density functional model proposed in [T. Malik, M. Ferreira, B. K. Agrawal and C. Provid\^encia, ApJ 930, 17 (2022)] is employed in a Bayesian analysis to determine the equation of state (EOS) of dense matter with nucleonic degrees of freedom. Various constraints from nuclear physics and microscopic calculations of pure neutron matter (PNM) along with a lower bound on the maximum mass of neutron stars (NSs) are imposed on the EOS models to investigate the effectiveness of progressive incorporation of the constraints, their compatibility as well as correlations among parameters of nuclear matter and properties of NSs. Our results include the different roles played by pressure and energy per particle of PNM in constraining the isovector behavior of nuclear matter; tension with the values of Dirac effective mass extracted from spin-orbit splitting; correlations between the radius of the canonical mass NS and second and third order coefficients in the Taylor expansion of energy per particle as a function of density; correlation between the central pressure of the maximum mass configuration and Dirac effective mass of the nucleon at saturation. For some of our models the tail of the NS maximum mass reaches $2.7~\mathrm{M}_{\odot}$, which means that the secondary object in GW190814 could have been a NS.

A physics-based neural network reconstruction of the dense matter equation of state from neutron star observables

We introduce a novel technique that utilizes a physics-driven deep learning method to reconstruct the dense matter equation of state from neutron star observables, particularly the masses and radii. The proposed framework involves two neural networks: one to optimize the EoS using Automatic Differentiation in the unsupervised learning scheme; and a pre-trained network to solve the Tolman–Oppenheimer–Volkoff (TOV) equations. The gradient-based optimization process incorporates a Bayesian picture into the proposed framework. The reconstructed EoS is proven to be consistent with the results from conventional methods. Furthermore, the resulting tidal deformation is in agreement with the limits obtained from the gravitational wave event, GW170817.

Tension between implications from PREX-2 data and gravitational tidal response on dense matter equation of state

Recently an improved value of neutron skin thickness of 208Pb was reported in Lead Radius EXperiment-2 (PREX-2) to be Rskin = Rn Rp = (0.283 0.071) fm which corresponds to high estimations of nuclear symmetry energy (Esym) and its slope (Lsym). The updated values of Esym and Lsym commensurating to the neutron star observable estimations lie exterior to the astrophysical observed range. The higher values of Lsym at n0 deduced from recent PREX-2 data correlates to matter being easily deformable (yielding higher radius values) around intermediate matter densities leading to higher values of Λ̃ creating a tension between the terrestrial and astrophysical observations. In this study, we exploit this tension to constrain the Δ-scalar meson coupling parameter space.

Do we need dense matter equation of state in curved spacetime for neutron stars?

Neutron stars are regarded as natural laboratories for the study of dense strong interaction matter. The equation of state (EoS) of dense matter computed in flat spacetime is used to predict the structure of neutron stars by solving the Tolman-Oppenheimer-Volkoff (TOV) equation. Recently, it has been reported that the curved spacetime effect or specifically gravitational time dilation effect on the EoS of dense matter leads to a significant increase of the maximum mass limit of neutron stars [Phys. Rev. D \textbf{104}, 123005 (2021) and J. Cosmol. Astropart. Phys. 02 (2021) 026]. However, in this work, we show that to study the hydrostatic equilibrium of dense matter within the framework of general relativity and relativistic fluid dynamics, the grand canonical EoS of dense matter, $p(T,\mu)$, should be the same as that computed in flat spacetime, otherwise it is not consistent with local thermodynamic relations and energy-momentum conservation of the fluid. The gravitation influences the pressure $p$ only through enhancing the temperature $T$ and the chemical potential $\mu$, known as Tolman's law and Klein's law. We rewrite the TOV equation as an alternative version so that the grand canonical EoS computed by using field theoretical methods can be used as a direct input. This may provide a tool to study the grand canonical EoS of dense matter via deep learning.

Population properties and multimessenger prospects of neutron star–black hole mergers following GWTC-3

ABSTRACT Neutron star–black hole (NSBH) mergers detected in gravitational waves have the potential to shed light on supernova physics, the dense matter equation of state, and the astrophysical processes that power their potential electromagnetic counterparts. We use the population of four candidate NSBH events detected in gravitational waves so far with a false alarm rate ≤1 yr−1 to constrain the mass and spin distributions and multimessenger prospects of these systems. We find that the black holes in NSBHs are both less massive and have smaller dimensionless spins than those in black hole binaries. We also find evidence for a mass gap between the most massive neutron stars and least massive black holes in NSBHs at 98.6-per cent credibility. Using an approach driven by gravitational-wave data rather than binary simulations, we find that fewer than 14 per cent of NSBH mergers detectable in gravitational waves will have an electromagnetic counterpart. While the inferred presence of a mass gap and fraction of sources with a counterpart depend on the event selection and prior knowledge of source classification, the conclusion that the black holes in NSBHs have lower masses and smaller spin parameters than those in black hole binaries is robust. Finally, we propose a method for the multimessenger analysis of NSBH mergers based on the non-detection of an electromagnetic counterpart and conclude that, even in the most optimistic case, the constraints on the neutron star equation of state that can be obtained with multimessenger NSBH detections are not competitive with those from gravitational-wave measurements of tides in binary neutron star mergers and radio and X-ray pulsar observations.