Mass-radius Relation Of Neutron Stars Research Articles

Building an Equation of State Density Ladder

The confluence of major theoretical, experimental, and observational advances are providing a unique perspective on the equation of state of dense neutron-rich matter—particularly its symmetry energy—and its imprint on the mass-radius relation for neutron stars. In this contribution, we organize these developments in an equation of the state density ladder. Of particular relevance to this discussion are the impact of the various rungs on the equation of state and the identification of possible discrepancies among the various methods. A preliminary analysis identifies possible tension between laboratory measurements and gravitational-wave detections that could indicate the emergence of a phase transition in the stellar core.

Studies of the equation-of-state of nuclear matter by heavy-ion collisions at intermediate energy in the multi-messenger era

The study of the nuclear matter equation-of-state (EoS) is a relevant topic of modern nuclear physics. It governs the behaviour of nuclear matter away from the normal conditions found in nuclei interiors and plays a major role in heavy-ion collisions, in determining neutron skin thicknesses of neutron rich nuclei and the mass-radius relation of neutron stars, and in modelizations of supernovae explosions. Its uncertain knowledge is related to difficulties in solving the many-body problem with realistic nuclear interactions. In the last decades several studies, from both theoretical and experimental sides, have allowed relevant progress in the description of the EoS, both for the isospin-symmetric matter and for the isospin-asymmetric one, the so-called symmetry energy, especially at densities below the saturation point. In this paper we review some of the studies on the high-density behavior of the EoS, obtained by studying heavy-ion collisions with incident energies between several hundred MeV up to about 2 GeV per nucleon, with a focus on those carried out at the GSI laboratory in Darmstadt (Germany) using the SIS18 accelerator beams. Constraints on the isospin-symmetric matter EoS, based on studies of kaon and pion production and collective flows, are reviewed. Regarding the symmetry energy, results based on charged pion ratios and neutron-to-charged particles elliptic flow ratios are discussed. A brief overview on the heavy-ion collisions studies sensitive to densities below the nuclear saturation density is presented, but the main emphasis of the review is on the density dependence of the symmetry energy above saturation density, which is also the region which is particularly important for astrophysics. Estimates of neutron star radii, as deduced by the results of heavy-ion collisions discussed in this review, are compared to astrophysics results, including the recent ones made possible by gravitational waves detection and X-ray satellite based observation. A multiple source analysis, using theoretical calculations, astrophysics and heavy-ion collision results, in constraining neutron star radii, is discussed as an illustrative example of the role played by heavy-ion collision results in the multi-messenger astronomy era. Finally, some future perspectives and experimental possibilities are outlined.

Characterizing the Breakdown of Quasi-universality in Postmerger Gravitational Waves from Binary Neutron Star Mergers

The postmerger gravitational wave (GW) emission from a binary neutron star merger is expected to provide exciting new constraints on the dense-matter equation of state (EoS). Such constraints rely, by and large, on the existence of quasi-universal relations, which relate the peak frequencies of the postmerger GW spectrum to properties of the neutron star structure in a model-independent way. In this work, we report on violations of existing quasi-universal relations between the peak spectral frequency, f 2, and the stellar radius, for EoS models with backwards-bending slopes in their mass–radius relations (such that the radius increases at high masses). The violations are extreme, with variations in f 2 of up to ∼600 Hz between EoSs that predict the same radius for a 1.4 M ⊙ neutron star but that have significantly different radii at higher masses. Quasi-universality can be restored by adding in a second parameter to the fitting formulae that depends on the slope of the mass–radius curve. We further find strong evidence that quasi-universality is better maintained for the radii of very massive stars (with masses 2 M ⊙). Both statements imply that f 2 is mainly sensitive to the high-density EoS. Combined with observations of the binary neutron star inspiral, these generalized quasi-universal relations can be used to simultaneously infer the characteristic radius and slope of the neutron star mass–radius relation.

Unified nuclear matter equations of state constrained by the in-medium balance in density-dependent covariant density functionals

Considering the effects of charge screening, we propose a new numerical recipe within the framework of Thomas-Fermi approximation, where the properties of nuclear matter throughout a vast density range can be obtained self-consistently. Assuming spherical and cylindrical approximations for the Wigner-Seitz cell, typical nuclear matter structures (droplet, rod, slab, tube, bubble, and uniform) are observed. We then investigate the EOSs and microscopic structures of nuclear matter with both fixed proton fractions and $\beta$-equilibration, where two covariant density functionals DD-LZ1 and DD-ME2 are adopted. Despite the smaller slope $L$ of symmetry energy obtained with the functional DD-LZ1, the curvature parameter $K_\mathrm{sym}$ is much larger than that of DD-ME2, which is attributed to the peculiar density-dependent behavior of meson-nucleon couplings guided by the restoration of pseudo-spin symmetry around the Fermi levels in finite nuclei. Consequently, different mass-radius relations of neutron stars are predicted by the two functionals. Different microscopic structures of nonuniform nuclear matter are obtained as well, which are expected to affect various physical processes in neutron star properties and evolutions.

Equations of State for Hadronic Matter and Mass-Radius Relations of Neutron Stars with Strong Magnetic Fields

Neutron star is an important object for us to verify the equation of state of hadronic matter. For a specific choice of equations of state, mass and radius of a neutron star are determined, for which there are constraints from observations. According to some previous studies, since the strong magnetic field acts as a repulsive force, there is a possibility that neutron stars with strong magnetic fields may have relatively heavier masses than other non-magnetized neutron stars. In this paper, the structure of a neutron star with a strong internal magnetic field is investigated by changing its internal functional form to see how much the neutron star can be massive and also how radius of a neutron star can be within a certain range.

Quark-quark interaction and quark matter in neutron stars

Hyperon ($Y$) mixing in neutron-star matter brings about a remarkable softening of the equation of state (EoS) and the maximum mass is reduced to a value far less than $2M_{\odot}$. One idea to avoid this "hyperon puzzle in neutron stars" is to assume that the many-body repulsions work universally for every kind of baryons. The other is to take into account the quark deconfinement phase transitions from a hadronic EoS to a sufficiently stiff quark-matter EoS. In the present approach, both effects are handled in a common framework. As well as the hadronic matter, the quark matter with the two-body quark-quark interactions are treated within the Brueckner-Bethe-Goldstone theory beyond the mean field frameworks, where interaction parameters are based on the terrestrial data. The derived mass-radius relations of neutron stars show that maximum masses reach over $2M_{\odot}$ even in the cases of including hadron-quark phase transitions, being consistent with the recent observations for maximum masses and radii of neutron stars by the NICER measurements and the other multimessenger data.

Neutron stars and phase diagram from a double hard-wall

Description of nuclear matter in the core of neutron stars eludes the main tools of investigation of QCD, such as perturbation theory and the lattice formulation of the theory. Recently, the application of the holographic paradigm (both via top-down and bottom-up models) to this task has led to many encouraging results, both qualitatively and quantitatively. We present our approach to the description of neutron star cores, relying on a simple model of the (double) hard-wall type: we discuss results concerning the nature of homogeneous nuclear matter at high density emerging from the model including a quarkyonic phase, the mass-radius relation for neutron stars, as well as the rather stiff equation of state we have found. We show how, despite the very simple model employed, for an appropriate calibration we are able to obtain neutron stars that only slightly fall short of the observational bounds on radius and tidal deformability.

2.6 M⊙ compact object and neutron stars in Eddington-inspired Born-Infeld theory of gravity

In the context of whether a massive compact object recently observed in the GW190814 event is a neutron star (NS) or not, we have studied the role of the parameters $\kappa$ and $\Lambda_c$ of the Eddington-inspired Born-Infeld (EiBI) gravity theory on the NS mass-radius relation, moment of inertia, and tidal deformability. The results are compared to recent observation constraints extracted from the analysis of NS observation data. The NS core equation of state (EoS) is calculated using the relativistic mean-field model with the G3 parameter set. In the hyperon sector, the SU(3) and hyperon potential depths are used to determine the hyperon coupling constants. For the inner and outer crusts, we use the crust EoS from Miyatsu et al. (2013). We also maintain the sound speed to not exceed $c$/$\sqrt{3}$ at high densities. We have found that, in general, the NS mass significantly depends on the value of $\kappa$, and the radius $R$ is sensitive to the value of $\Lambda_c$. Moreover, as $\Lambda_c$ is equal to zero or less than the accepted bound of the cosmological constant, the NS within the EiBI theory is compatible with observation constraints, including $2.0 M_\odot$ mass, canonical radius $R_{1.4 M_{\odot}}$, moment of inertia, and tidal deformation. Our investigation also reveals that the $2.6 M_\odot$ mass compact object and current observational constraint of canonical radius $R_{1.4 M_{\odot}}$ can simultaneously be satisfied only when the $\Lambda_c$ value is unphysically too large and negative. Therefore, within the spesific EoS employed in this work, we conclude that the secondary object with $2.6 M_\odot$ observed in the GW190814 event is not likely a static (or a slow-rotating) NS within the EiBI gravity theory.

Constraining the Neutron Star Mass–Radius Relation and Dense Matter Equation of State with NICER. III. Model Description and Verification of Parameter Estimation Codes

Abstract We describe the X-ray pulse profile models we use and how we use them to analyze Neutron Star Interior Composition Explorer (NICER) observations of rotation-powered millisecond pulsars to obtain information about the mass–radius relation of neutron stars and the equation of state of the dense matter in their cores. Here we detail our modeling of the observed profile of PSR J0030+0451 that we analyzed in Miller et al. and Riley et al. and describe a cross-verification of computations of the pulse profiles of a star with R/M 3, in case stars this compact need to be considered in future analyses. We also present our early cross-verification efforts of the parameter estimation procedures used by Miller et al. and Riley et al. by analyzing two distinct synthetic data sets. Both codes yielded credible regions in the mass–radius plane that are statistically consistent with one another, and both gave posterior distributions for model parameter values consistent with the values that were used to generate the data. We also summarize the additional tests of the parameter estimation procedure of Miller et al. that used synthetic pulse profiles and the NICER pulse profile of PSR J0030+0451. We then illustrate how the precision of mass and radius estimates depends on the pulsar’s spin rate and the size of its hot spot by analyzing four different synthetic pulse profiles. Finally, we assess possible sources of systematic error in the estimates made using this technique, some of which may warrant further investigation.

Mixed phase transition from hypernuclear matter to deconfined quark matter fulfilling mass-radius constraints of neutron stars

A recent solution of the hyperon puzzle by a first order phase transition to color superconducting quark matter is revisited in order to replace the Maxwell construction by an interpolation method which describes a mixed phase. To do this, we apply for the first time the finite-range polynomial interpolation method for constructing a transition between hadronic and quark matter phases to the situation that is characterized in the literature as the reconfinement problem. For the description of the hadronic phase the lowest order constrained variational method is used while for the quark phase the nonlocal Nambu–Jona–Lasinio model with constant and with density-dependent parameters is employed. Applying the replacement interpolation method to both quark matter models results in a hybrid equation of state that allows a coexistence of nuclear matter, hypernuclear matter and quark matter in a mixed phase between the pure hadronic and quark phases which can also be realized in the structure of the corresponding hybrid star sequences. The predicted hybrid stars fulfill the constraints on the mass-radius relation for neutron stars obtained from recent observations.

A Study of Low-Temperature Neutron Star Atmospheres

We present a study of how a low-temperature accreted atmosphere influences the emitted X-ray spectrum of a neutron star. The atmosphere models and spectra were computed with Zcode, a multigroup radiation transfer code developed at the Los Alamos National Laboratory. Though the underlying hot neutron star behaves as a blackbody, the atmosphere shifts the peak of spectrum away from a blackbody and toward higher energies, producing an emitted spectrum similar to a dilute blackbody. Quantifying the effects of this atmosphere will remove a source of uncertainty in X-ray observations and better constrain the mass-radius relation for neutron stars and thus the equation of state of dense matter. We present a suite of these atmospheres with varying compositions and temperatures as well as the resulting spectra.

Lee-Yang–inspired energy-density functional including contributions from p -wave scattering

The ELYO functional proposed in [M. Grasso, D. Lacroix, and C. J. Yang, Phys. Rev. C \textbf{95}, 054327 (2017)] belongs to the family of energy-density functionals (EDFs) inspired by effective-field theories (EFTs) and constrained by \textit{ab--initio} pseudo-data. We present here an extension of this EDF which also accounts for the first $p$-wave term appearing in the low-density expansion from which it derives. It is shown that this enrichment of the ansatz on which the functional is based leads to a significant improvement of the description of neutronic systems, especially in regimes besides the pseudo--data set employed to adjust the parameters. As an illustrative application, the mass-radius relation of neutron stars is considered. In contrast to its initial version, the new functional predicts values which are qualitatively consistent with recent observations.

Spin-polarized Neutron Matter, the Maximum Mass of Neutron Stars, and GW170817

We investigate how a phase transition from neutron-star matter to spin-polarized neutron matter affects the equation of state and mass-radius relation of neutron stars. While general extension schemes for the equation of state allow for high pressures inside neutron stars, we find that a phase transition to spin-polarized neutron matter excludes extreme regimes. Hence, such a transition limits the maximum mass of neutron stars to lie below 2.6$-$$2.9 \, M_{\odot}$, depending on the microscopic nuclear forces used, while significantly larger masses could be reached without these constraints. These limits are in good agreement with recent constraints extracted from the neutron-star merger GW170817 and its electromagnetic counterpart. Assuming the description in terms of spin-polarized neutron matter to be valid in the center of neutron stars, we find that stars with a large spin-polarized domain in their core are ruled out by GW170817.

A neutron star with a strange quark star-like mass-radius relation

We study the structure of spherically symmetric and static objects in the presence of a nonminimally coupled scalar field having a potential of the form $V(\phi)=-\mu^2\phi^2/2+\lambda\phi^4/4$. We numerically solve equations of the system using two different realistic equations of state for neutron matter and give the mass-radius relations as well as the radial profiles of the scalar field, densities and the mass function for a sample configuration. We show that a specific solution type encountered in such systems causes characteristic neutron star mass-radius relations to turn into the ones belonging to strange quark stars.

Gravitational antiscreening in stellar interiors

A new class of relativistic stellar structure equations which include the effects of an energy-dependent Newton coupling is presented. Significant modifications in the mass-radius relation for neutron stars are possible only if the running of the Newton coupling due to quantum gravity occurs at low energies. A new Buchdahl limit is derived and its physical implications are discussed. In particular, sub-Planckian self-gravitating objects with arbitrarily small radii are possible.

Constraining the Neutron Star Mass–Radius Relation and Dense Matter Equation of State with NICER. I. The Millisecond Pulsar X-Ray Data Set

Abstract We present the set of deep Neutron Star Interior Composition Explorer (NICER) X-ray timing observations of the nearby rotation-powered millisecond pulsars PSRs J0437−4715, J0030+0451, J1231−1411, and J2124−3358, selected as targets for constraining the mass–radius relation of neutron stars and the dense matter equation of state (EoS) via modeling of their pulsed thermal X-ray emission. We describe the instrument, observations, and data processing/reduction procedures, as well as the series of investigations conducted to ensure that the properties of the data sets are suitable for parameter estimation analyses to produce reliable constraints on the neutron star mass–radius relation and the dense matter EoS. We find that the long-term timing and flux behavior and the Fourier-domain properties of the event data do not exhibit any anomalies that could adversely affect the intended measurements. From phase-selected spectroscopy, we find that emission from the individual pulse peaks is well described by a single-temperature hydrogen atmosphere spectrum, with the exception of PSR J0437−4715, for which multiple temperatures are required.

NICER X-Ray Observations of Seven Nearby Rotation-powered Millisecond Pulsars

Abstract The Neutron star Interior Composition Explorer observed several rotation-powered millisecond pulsars (MSPs) to search for or confirm the presence of X-ray pulsations. When broad and sine-like, these pulsations may indicate thermal emission from hot polar caps at the magnetic poles on the neutron star surface. We report confident detections (≥4.7σ after background filtering) of X-ray pulsations for five of the seven pulsars in our target sample: PSR J0614−3329, PSR J0636+5129, PSR J0751+1807, PSR J1012+5307, and PSR J2241−5236, while PSR J1552+5437 and PSR J1744−1134 remain undetected. Of those, only PSR J0751+1807 and PSR J1012+5307 had pulsations previously detected at the 1.7σ and almost 3σ confidence levels, respectively, in XMM-Newton data. All detected sources exhibit broad sine-like pulses, which are indicative of surface thermal radiation. As such, these MSPs are promising targets for future X-ray observations aimed at constraining the neutron star mass–radius relation and the dense matter equation of state using detailed pulse profile modeling. Furthermore, we find that three of the detected MSPs exhibit a significant phase offset between their X-ray and radio pulses.

Constraining the Neutron Star Mass–Radius Relation and Dense Matter Equation of State with NICER. II. Emission from Hot Spots on a Rapidly Rotating Neutron Star

Abstract We describe the model of surface emission from a rapidly rotating neutron star that is applied to Neutron Star Interior Composition Explorer X-ray data of millisecond pulsars in order to statistically constrain the neutron star mass–radius relation and dense matter equation of state. To ensure that the associated calculations are both accurate and precise, we conduct an extensive suite of verification tests between our numerical codes for both the Schwarzschild + Doppler and Oblate Schwarzschild approximations, and compare both approximations against exact numerical calculations. We find superb agreement between the code outputs, as well as in comparisons against a set of analytical and semi-analytical calculations, which, combined with their speed, demonstrates that the codes are well suited for large-scale statistical sampling applications. A set of verified, high-precision reference synthetic pulse profiles is provided to the community to facilitate testing of other independently developed codes.

More than the sum of its parts: Combining parametrized tests of extreme gravity

We connect two formalisms that describe deformations away from general relativity, one valid in the strong-field regime of neutrons stars and another valid in the radiative regime of gravitational waves: the post-Tolman-Oppenheimer-Volkoff and the parametrized-post-Einsteinian formalisms respectively. We find that post-Tolman-Oppenheimer-Volkoff deformations of the exterior metric of an isolated neutron star induce deformations in the orbital binding energy of a neutron star binary. Such a modification to the binding energy then percolates into the gravitational waves emitted by such a binary, with the leading-order post-Tolman-Oppenheimer-Volkoff modifications introducing a second post-Newtonian order correction to the gravitational wave phase. The lack of support in gravitational wave data for general relativity deformations at this post-Newtonian order can then be used to place constraints post-Tolman-Oppenheimer-Volkoff parameters. As an application, we use the binary neutron star merger event GW170817 to place the constraint $-2.4 \leq \chi \leq 44$ (at 90% credibility) on a combination of post-Tolman-Oppenheimer-Volkoff parameters. We also explore the implications of this result to the possible deformations of the mass-radius relation of neutron stars allowed within this formalism. This work opens the path towards theory-independent tests of gravity, combining astronomical observations of neutron stars and gravitational wave observations.

Impact of the Nuclear Equation of State on the Stability of Hybrid Neutron Stars

We construct a set of equations of state (EoS) of dense and hot matter with a 1st order phase transition from a hadronic system to a deconfined quark matter state. In this two-phase approach, hadrons are described using the relativistic mean field theory with different parametrisations and the deconfined quark phase is modeled using vBag, a bag–type model extended to include vector interactions as well as a simultaneous onset of chiral symmetry restoration and deconfinement. This feature results in a non–trivial connection between the hadron and quark EoS, modifying the quark phase beyond its onset density. We find that this unique property has an impact on the predicted hybrid (quark core) neutron star mass–radius relations.