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DOE OSTI2025

Assessing the impact of uniform rotation on the structure of neutron stars

Driven by recent laboratory experiments and astronomical observations, significant advances have deepened our understanding of neutron-star physics. NICER's Pulse Profile Modeling has refined our knowledge of neutron star masses and radii, while gravitational-wave detections have revealed key insights into the structure of neutron stars. Particularly relevant is the extraction of the tidal deformability by the LIGO-Virgo collaboration and the most recent determination of stellar radii by NICER, both suggesting a relatively soft equation of state (EOS) at intermediate densities. Additionally, measurements from the PREX collaboration and from pulsar timing suggest instead that the EOS is stiff in the vicinity of saturation density and at the highest densities accessible to date. But how stiff can the EOS be at these very high densities? Recent events featuring compact objects near the “lower mass gap” have raised questions about the existence of very massive neutron stars. Motivated by this finding and in light of new refinements to theoretical models, we explore the possibility that these massive objects may indeed be rapidly rotating neutron stars. Here, we explore how rotation affects both the maximum neutron star mass and their associated radii, and discuss the implications they may have on the equation of state.

Equations of state of nuclear matter↗

NASA NTRS2006

Theory of Radiation Transfer in Neutron Star Atmospheres

The possibility for direct investigation of thermal emission from isolated neutron stars opened about a quarter of century ago with the launch of the first X-ray observatories Einstein and EXOSAT stimulated developing models of the neutron star surface radiation which began at the end of 80's. Confronting observational data with theoretical models of thermal emission allows one to infer the surface temperatures, magnetic fields, chemical composition, and neutron star masses and radii. This information, supplemented with the model equations of state and neutron star cooling models, provides an opportunity to understand the fundamental properties of the superdense matter in the stars' interiors. Almost all available models are based on the assumption that thermal radiation emitted by a neutron star is formed in the superficial star's layers--atmosphere. The neutron star atmospheres are very different from those of usual stars due to the immense gravity and huge magnetic fields. In this presentation we review the current status of the neutron star atmosphere modeling, present most important results, discuss problems and possible future developments.

Zavlin, Vyacheslav↗

NASA NTRS1987

On the theory of type I X-ray bursts - The energetics of bursts and the nuclear fuel reservoir in the envelope

A comparison is made between the observed properties of type I X-ray bursts from 4U/MXB 1636-53 and those of models of thermonuclear flashes on accreting neutron stars. Possible explanations of variations in the burst recurrence properties without an apparent correlation with accretion rate are discussed. The strongest bursts with photospheric expansion are described well by current spherically symmetric models. The observed weak bursts suggest a mechanism that can promote the inward propagation and heating of accreted fuel so as to give rise to thermonuclear runaways much earlier than expected from spherical models. A sufficient amount of fuel to feed the weak bursts can be stored in the outer layers for neutron stars with radii greater than 8 km. The proposed mechanism and fuel storage can resolve the longstanding problem of bursts in rapid succession with intervals shorter than about 10 minutes. The proposed model explains the variation of burst peak fluxes observed from 4U/MSB 1636-53.

Fujimoto, Masayuki Y.↗

DOE OSTI2020

Bayesian Inference of the Symmetry Energy of Superdense Neutron-rich Matter from Future Radius Measurements of Massive Neutron Stars

In this work, using as references the posterior probability distribution functions of the equation of state (EOS) parameters inferred from the radii of canonical neutron stars (NSs) reported by the LIGO/VIRGO and NICER Collaborations based on their observations of GW170817 and PSR J0030+0451, we investigate how future radius measurements of more massive NSs will improve our current knowledge about the EOS of superdense neutron-rich nuclear matter, especially its symmetry energy term. Within the Bayesian statistical approach using an explicitly isospin-dependent parametric EOS for the core of NSs, we infer the EOS parameters of superdense neutron-rich nuclear matter from three sets of imagined mass–radius correlation data representing typical predictions by various nuclear many-body theories, that is, the radius stays the same, decreases, or increases with increasing NS mass within ±15% between 1.4 and 2.0 M$_\odot$. The corresponding NS average density increases quickly or slowly or slightly decreases as the NS mass increases from 1.4 to 2.0 M$_\odot$. While the EOSs of symmetric nuclear matter (SNM) inferred from the three data sets are approximately the same, the corresponding symmetry energies above about twice the saturation density of nuclear matter are very different, indicating that the radii of massive NSs carry important information about the high-density behavior of nuclear symmetry energy with little influence from the remaining uncertainties of the SNM EOS at suprasaturation densities.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Neutron Star Mass and Radius Measurements

Constraints on neutron star masses and radii now come from a variety of sources: theoretical and experimental nuclear physics, astrophysical observations including pulsar timing, thermal and bursting X-ray sources, and gravitational waves, and the assumptions inherent to general relativity and causality of the equation of state. These measurements and assumptions also result in restrictions on the dense matter equation of state. The two most important structural parameters of neutron stars are their typical radii, which impacts intermediate densities in the range of one to two times the nuclear saturation density, and the maximum mass, which impacts the densities beyond about three times the saturation density. Especially intriguing has been the multi-messenger event GW170817, the first observed binary neutron star merger, which provided direct estimates of both stellar masses and radii as well as an upper bound to the maximum mass.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Pulse profile modelling of thermonuclear burst oscillations − I. The effect of neglecting variability

ABSTRACT We study the effects of the time-variable properties of thermonuclear X-ray bursts on modelling their millisecond-period burst oscillations. We apply the pulse profile modelling technique that is being used in the analysis of rotation-powered millisecond pulsars by the Neutron Star Interior Composition Explorer to infer masses, radii, and geometric parameters of neutron stars. By simulating and analysing a large set of models, we show that overlooking burst time-scale variability in temperatures and sizes of the hot emitting regions can result in substantial bias in the inferred mass and radius. To adequately infer neutron star properties, it is essential to develop a model for the time-variable properties or invest a substantial amount of computational time in segmenting the data into non-varying pieces. We discuss prospects for constraints from proposed future X-ray telescopes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Simultaneous fitting of neutron star structure and cooling data

Using a model for the equation of state and composition of dense matter and the magnitude of singlet proton superconductivity and triplet neutron superfluidity, we perform the first simultaneous fit of neutron star masses and radii determined from observations of quiescent low-mass X-ray binaries and luminosities and ages determined from observations of isolated neutron stars. We find that the Vela pulsar strongly determines the values inferred for the superfluid/superconducting gaps and the neutron star radius. Here, we find, regardless of whether or not the Vela pulsar is included in the analysis, that the threshold density for the direct Urca process lies between the central density of 1.7 and 2 solar mass neutron stars. We also find that 2 solar mass stars are unlikely to cool principally by the direct Urca process because of the suppression by neutron triplet superfluidity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Correlations between the Neutron Star Mass–Radius Relation and the Equation of State of Dense Matter

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.

Bayesian statistics↗

NASA NTRS1982

Observable properties of neutron stars

This paper reviews the information on neutron stars that has been obtained from observations of pulsars and pulsing X-ray stars, with emphasis on results from timing studies. Included are summaries of the most recent theoretical work on neutron star structure and the current evidence concerning neutron star masses and radii. Also included are discussions of large frequency jumps and small-scale timing irregularities, the description of the latter phenomenon in terms of random noise processes, and the use of both as probes of the internal structure and dynamical properties of neutron stars. Finally, some of the most promising directions for future work are briefly noted.

Lamb, F. K.↗

NASA NTRS1984

Probing the interiors of neutron stars

Lamb, F. K.↗

NASA NTRS2004

Quiescent Emission from Transient Type-I X-ray Bursters

The purpose of the funded activity was to analyze and interpret data obtained with the European Space Agency X-ray Multiple Mission (XMM) observatory, of two transiently accreting type-I X-ray bursters observed in the field, Cen X-4 and Aql X-1. Both observations were accepted as class-A for AO-1. The main goal of the analysis is to measure the X-ray spectrum of the neutron stars in these systems, and interpret them as H atmosphere neutron stars, and measure their radii. Secondarily, the behavior of the systems were expected to adhere to the predicted properties of a quiescent neutron star system - specifically, to have a constant intensity.

Rutledge, Robert E.↗

NASA NTRS2001

Models for X-Ray Emission from Isolated Pulsars

A model is proposed for the observed combination of power-law and thermal X-rays from rotationally powered pulsars. For gamma-ray pulsars with accelerators very many stellar radii above the neutron star surface, 100 MeV curvature gamma-rays from e(-) or e(+) flowing starward out of such accelerators are converted to e1 pairs on closed field lines all around the star. These pairs strongly affect X-ray emission from near the star in two ways. (1) The pairs are a source of synchrotron emission immediately following their creation in regions where B approx. 10(exp 10) G. This emission, in the photon energy range 0.1 keV less than E(sub X) less than 5 MeV, has a power-law spectrum with energy index 0.5 and X-ray luminosity that depends on the back-flow current, and is typically approx. 10(exp 33) ergs/ s. (2) The pairs ultimately a cyclotron resonance "blanket" surrounding the star except for two holes along the open field line bundles which pass through it. In such a blanket the gravitational pull on e(+,-) pairs toward the star is balanced by the hugely amplified push of outflowing surface emitted X-rays wherever cyclotron resonance occurs. Because of it the neutron star is surrounded by a leaky "hohlraum" of hot blackbody radiation with two small holes, which prevents direct X-ray observation of a heated polar cap of a gamma-ray pulsar. Weakly spin modulated radiation from the blanket together with more strongly spin-modulated radiation from the holes through it would then dominate observed low energy (0.1-10 keV) emission. For non-y-ray pulsars, in which no such accelerators with their accompanying extreme relativistic back-flow toward the star are expected, optically thick e1 resonance blankets should not form (except in special cases very close to the open field line bundle). From such pulsars blackbody radiation from both the warm stellar surface and the heated polar caps should be directly observable. In these pulsars, details of the surface magnetic field evolution, especially of polar cap areas, become relevant to observations. The models are compared to X-ray data from Geminga, PSR 1055-52, PSR 0656+14, PSR 1929+10, and PSR 0950+08.

Wang, F. Y.-H.↗

DOE OSTI2026

Bayesian Inference of Hybrid Star Properties from Future High-precision Measurements of Their Radii

Future high-precision X-ray and gravitational-wave observations of neutron stars (NSs) are expected to constrain NS radii with uncertainties as small as σ ≃ 0.1 km. Such unprecedented precision offers a unique opportunity to extract new information about the nature and equation of state (EOS) of supradense matter in NS cores. Using mock radius data with uncertainties ranging from σ = 1.0 to 0.1 km, together with a flexible meta-model NS EOS that allows for a first-order hadron–quark phase transition, we perform a Bayesian statistical analysis to assess the impact of radius measurements on EOS constraints. We find that high-precision radius measurements, particularly for massive NSs, significantly tighten constraints on the hadron–quark transition density ρ t , the quark matter mass fraction in NS cores, and several parameters characterizing the EOS of supranuclear hadronic matter, although the degree of improvement depends on the assumed prior range of ρ t . In contrast, even with the highest precision considered, NS radii—including those of massive stars—remain largely insensitive to the stiffness of quark matter, independent of the measurement accuracy or the prior range adopted for ρ t .

Neutron stars↗

DOE OSTI2025

Neutron stars and the dense matter equation of state

The past two decades have witnessed tremendous progress in understanding the properties of neutron stars, their maximum mass and radii, and the properties of the dense matter in their cores, made possible by electromagnetic observations of neutron stars and the detection of gravitational waves from their mergers. These observations have provided novel constraints on neutron-star structure that are intimately related to the properties of dense neutron-rich matter described by the nuclear equation of state. Nevertheless, constraining the equation of state over the wide range of densities probed by astrophysical observations is still challenging, as the physics involved is broad and the system spans many orders of magnitude in density. Here, theoretical approaches to calculate and model the neutron-star equation of state in various regimes of densities are reviewed, and the related consequent properties of neutron stars are discussed. How the equation of state at low densities can be calculated from nuclear interactions that are constrained and benchmarked by nuclear experiments is described. Neutron-star observations, with a particular emphasis on information provided by gravitational-wave signals and electromagnetic observations, are reviewed. Finally, future challenges and opportunities in the field are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1979

Possible observational constraints on the mass-radius relation of neutron stars

The effect of gravitational redshift on the blackbody radii, as deduced from the tails of X-ray bursts, is considered. Observed values of blackbody radii put an upper limit to the mass and constrain the mass-radius relations of neutron stars. Possible consequences for the equation of state of high-density matter are briefly discussed.

Van Paradijs, J.↗

DOE OSTI2021

Progress in Constraining Nuclear Symmetry Energy Using Neutron Star Observables Since GW170817

The density dependence of nuclear symmetry energy is among the most uncertain parts of the Equation of State (EOS) of dense neutron-rich nuclear matter. It is currently poorly known especially at suprasaturation densities partially because of our poor knowledge about isovector nuclear interactions at short distances. Because of its broad impacts on many interesting issues, pinning down the density dependence of nuclear symmetry energy has been a longstanding and shared goal of both astrophysics and nuclear physics. New observational data of neutron stars including their masses, radii, and tidal deformations since GW170817 have helped improve our knowledge about nuclear symmetry energy, especially at high densities. Based on various model analyses of these new data by many people in the nuclear astrophysics community, while our brief review might be incomplete and biased unintentionally, we learned in particular the following: (1) The slope parameter L of nuclear symmetry energy at saturation density ρ0 of nuclear matter from 24 new analyses of neutron star observables was about L≈57.7±19 MeV at a 68% confidence level, consistent with its fiducial value from surveys of over 50 earlier analyses of both terrestrial and astrophysical data within error bars. (2) The curvature Ksym of nuclear symmetry energy at ρ0 from 16 new analyses of neutron star observables was about Ksym≈−107±88 MeV at a 68% confidence level, in very good agreement with the systematics of earlier analyses. (3) The magnitude of nuclear symmetry energy at 2ρ0, i.e., Esym(2ρ0)≈51±13 MeV at a 68% confidence level, was extracted from nine new analyses of neutron star observables, consistent with the results from earlier analyses of heavy-ion reactions and the latest predictions of the state-of-the-art nuclear many-body theories. (4) While the available data from canonical neutron stars did not provide tight constraints on nuclear symmetry energy at densities above about 2ρ0, the lower radius boundary R2.01=12.2 km from NICER’s very recent observation of PSR J0740+6620 of mass 2.08±0.07M⊙ and radius R=12.2–16.3 km at a 68% confidence level set a tight lower limit for nuclear symmetry energy at densities above 2ρ0. (5) Bayesian inferences of nuclear symmetry energy using models encapsulating a first-order hadron–quark phase transition from observables of canonical neutron stars indicated that the phase transition shifted appreciably both L and Ksym to higher values, but with larger uncertainties compared to analyses assuming no such phase transition. (6) The high-density behavior of nuclear symmetry energy significantly affected the minimum frequency necessary to rotationally support GW190814’s secondary component of mass (2.50–2.67) M⊙ as the fastest and most massive pulsar discovered so far. Overall, thanks to the hard work of many people in the astrophysics and nuclear physics community, new data of neutron star observations since the discovery of GW170817 have significantly enriched our knowledge about the symmetry energy of dense neutron-rich nuclear matter.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Neutron Skins: Weak Elastic Scattering and Neutron Stars

The recently completed PREX-2 campaign measured the density distribution of neutrons in the lead nucleus as a function of momentum transfer (the form factor), confirmed a relatively large extent of the neutrons beyond the protons in the nucleus (the neutron skin), and provided a precise determination of the density of protons and neutrons at the center of a heavy nucleus. In turn, the measured form factor can be related to various nuclear and neutron star properties. The NICER X-ray telescope has inferred the masses and radii of some X-ray pulsars (neutron stars), although complications arise when determining these quantities independently. Further improvements in NICER have enabled simultaneous mass–radius determinations that had not previously been possible. During the next decade, measurements in astrophysics, gravitational-wave astronomy, and nuclear physics are expected to provide a wealth of more precise data. In this review, we present an overview of the current state of neutron skin measurements and offer insights into prospects for the future.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2019

Dark halos around neutron stars and gravitational waves

Here, we find that models of MeV-GeV dark matter in which dark matter interacts strongly can be constrained by the observation of gravitational waves from binary neutron star (BNS) mergers. Trace amounts of dark matter, either produced during the supernova or accreted later, can alter the structure of neutron stars (NS) and influence their tidal deformability. We focus on models of dark matter interacting by the exchange of light vector gauge bosons that couple to a conserved dark charge. In these models, dark matter accumulated in neutron stars can extend to large radii. Gravitational waves detected from the first observed BNS merger GW170817 places useful constraints on such not-so compact objects. Dark halos, if present, further predict a greater variability of neutron star tidal deformabilities than expected for ordinary neutron stars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗