The last few years have seen tremendous progress in the observation of the global properties of neutron stars (NSs), e.g. masses, radii and tidal deformabilities. Such properties provide information about possible phase transitions in the inner cores of NSs, provided the connection between observed masses and radii and the equation of state (EoS) is well understood. We focus the present study on first-order phase transitions, which often softens the EoS and consequently reduces the maximum mass as well as the radii of NSs. Here, we challenge this conventional expectation by constructing explicit examples of EoSs undergoing a first-order phase transition, but which are much stiffer that their purely hadronic counterparts. We also provide comparisons with the recently proposed quarkyonic EoS which suggests a strong repulsion in the core of NSs, and we show that their stiffness can be realistically masqueraded by first-order phase transitions to exotic matter.
At present, neutron star radii from both observations and model predictions remain very uncertain. Whereas different models can predict a wide range of neutron star radii, it is not possible for most models to predict radii that are smaller than about 10 km, thus if such small radii are established in the future they will be very difficult to reconcile with model estimates. By invoking a new term in the equation of state that enhances the energy density, but leaves the pressure unchanged we simulate the current uncertainty in the neutron star radii. This new term can be possibly due to the exc…
Precise and reliable measurements of the masses and radii of neutron stars with a variety of masses would provide valuable guidance for improving models of the properties of cold matter with densities above the saturation density of nuclear matter. Several different approaches for measuring the masses and radii of neutron stars have been tried or proposed, including analyzing the X-ray fluxes and spectra of the emission from neutron stars in quiescent low-mass X-ray binary systems and thermonuclear burst sources; fitting the energy-dependent X-ray waveforms of rotation-powered millisecond puls…
An isovector-scalar meson is incorporated self-consistently into the quark-meson coupling description of nuclear matter and its most prominent effects on the structure of neutron stars are investigated. The recent measurement of GW170817 is used to constrain the strength of the isovector-scalar channel. With the imminent measurements of the neutron star radii in the NICER mission it is particularly notable that the inclusion of the isovector-scalar force has a significant impact. Indeed, the effect of this interaction on the neutron star radii and masses is larger than the uncertainties introd…
Measuring neutron star radii with spectroscopic and timing techniques relies on the combination of multiple observables to break the degeneracies between the mass and radius introduced by general relativistic effects. Here, we explore a previously used frequentist and a newly proposed Bayesian framework to obtain the most likely value and the uncertainty in such a measurement. We find that, for the expected range of masses and radii and for realistic measurement errors, the frequentist approach suffers from biases that are larger than the accuracy in the radius measurement required to distingu…
Recent experimental and ab initio theory investigations of the 208Pb neutron skin thickness are sufficiently precise to inform the neutron star equation of state. In particular, the strong correlation between the 208Pb neutron skin thickness and the pressure of neutron matter at normal nuclear densities leads to modified predictions for the radii, tidal deformabilities, and moments of inertia of typical 1.4 solar-mass neutron stars. In the present work, we study the relative impact of these recent analyses of the 208Pb neutron skin thickness on bulk properties of neutron stars within a Bayesia…
Recent neutron star observations suggest that the masses and radii of neutron stars may be smaller than previously considered, which would disfavor a purely nucleonic equation of state. In our model, we use a the flavor SU(3) sigma model that includes delta resonances and hyperons in the equation of state. We find that if the coupling of the delta resonances to the vector mesons is slightly smaller than that of the nucleons, we can reproduce both the measured mass-radius relationship and the extrapolated equation of state.
Neutron stars, produced at the death of massive stars, are often regarded as giant neutron-rich nuclei. This picture is especially relevant for low-mass (below about solar mass) neutron stars, where non-nucleonic components are not expected to occur. Due to the saturation property of nucleonic matter, leading to the celebrated liquid-drop picture of atomic nuclei, empirical nuclear masses and radii can be approximately expressed as function of atomic mass number. It is, however, not straightforward to express masses and radii of neutron stars even in the low-mass range where the structure is d…
We determine an empirical dense matter equation of state from a heterogeneous dataset of six neutron stars: three type I X-ray bursters with photospheric radius expansion, studied by Ozel et al., and three transient low-mass X-ray binaries. We critically assess the mass and radius determinations from the X-ray burst sources and show explicitly how systematic uncertainties, such as the photospheric radius at touchdown, affect the most probable masses and radii. We introduce a parameterized equation of state and use a Markov Chain Monte Carlo algorithm within a Bayesian framework to determine nu…
The masses and radii of low-magnetic field neutron stars can be measured by combining different observable quantities obtained from their X-ray spectra during thermonuclear X-ray bursts. One of these quantities is the apparent radius of each neutron star as inferred from the X-ray flux and spectral temperature measured during the cooling tails of bursts, when the thermonuclear flash is believed to have engulfed the entire star. In this paper, we analyze 13,095 X-ray spectra of 446 X-ray bursts observed from 12 sources in order to assess possible systematic effects in the measurements of the ap…
We examine the correlations of neutron star radii with the nuclear matter incompressibility, symmetry energy, and their slopes, which are the key parameters of the equation of state (EoS) of asymmetric nuclear matter. The neutron star radii and the EoS parameters are evaluated using a representative set of 24 Skyrme-type effective forces and 18 relativistic mean field models, and two microscopic calculations, all describing 2$M_\odot$ neutron stars. Unified EoSs for the inner-crust-core region have been built for all the phenomenological models, both relativistic and non-relativistic. Our inve…
X-ray burst spectra have long been used to estimate neutron star masses and radii. These estimates assumed that burst spectra are accurately described by the model atmosphere spectra developed over the last three decades. We compared RXTE data from a superburst with these spectra and found that the spectra predicted by previously published model atmospheres are strongly inconsistent with these high-precision measurements. In contrast, a simple Bose-Einstein spectrum is fully consistent with the data, as are recently published model atmosphere spectra. We discuss the implications of our results…
A set of theoretical mass-radius relations for rigidly rotating neutron stars with exotic cores, obtained in various theories of dense matter, is reviewed. Two basic observational constraints are used: the largest measured rotation frequency (716 Hz) and the maximum measured mass ($2\;M_\odot$). Present status of measuring the radii of neutron stars is described. The theory of rigidly rotating stars in general relativity is reviewed and limitations of the slow rotation approximation are pointed out. Mass-radius relations for rotating neutron stars with hyperon and quark cores are illustrated u…
We perform a systematic analysis of neutron star radius constraints from five quiescent low-mass X-ray binaries and examine how they depend on measurements of their distances and amounts of intervening absorbing material, as well as their assumed atmospheric compositions. We construct and calibrate to published results a semi-analytic model of the neutron star atmosphere which approximates these effects for the predicted masses and radii. Starting from mass and radius probability distributions established from hydrogen-atmosphere spectral fits of quiescent sources, we apply this model to compu…
Exchange of dominance between twin kHz quasi-periodic oscillations (QPOs) observed in some low-mass-X-ray-binaries (LMXB) suggests the possibility of a resonance between two oscillatory modes. We study the behaviour of the effective gravitational potential around specific resonant radii, and estimate the role of the higher-order terms governing the non-linear, anharmonic forcing. We discuss the impact it has on the mode amplitude in the linear and non--linear regimes. We also discuss a related possibility of lowering of the neutron star mass estimates from the highest observed QPO frequencies.
We summarize our current knowledge of neutron star masses and radii. Recent instrumentation and computational advances have resulted in a rapid increase in the discovery rate and precise timing of radio pulsars in binaries in the last few years, leading to a large number of mass measurements. These discoveries show that the neutron star mass distribution is much wider than previously thought, with 3 known pulsars now firmly in the 1.9-2.0 Msun mass range. For radii, large, high quality datasets from X-ray satellites as well as significant progress in theoretical modeling led to considerable pr…
The properties of neutron stars are determined by the nature of the matter that they contain. These properties can be constrained by measurements of the star's size. We obtain stringent constraints on neutron-star radii by combining multimessenger observations of the binary neutron-star merger GW170817 with nuclear theory that best accounts for density-dependent uncertainties in the equation of state. We construct equations of state constrained by chiral effective field theory and marginalize over these using the gravitational-wave observations. Combining this with the electromagnetic observat…
The presence of strong magnetic fields in neutron stars, such as in magnetars, may significantly affect their crust-core transition properties and the crust size. This knowledge is crucial in the correct interpretation of astrophysical phenomena involving magnetars, such as glitches in observed rotation frequencies, cooling, bursts and possibly tidal polarizabilities. A recently developed meta-modelling technique allows exploring the model dependence of density functional theory equation of state calculations. In this work, we extend this meta-model to investigate the effect of strong magnetic…
We calculate neutron star's moment of inertia and deformabilities using various microscopic equations of state for nuclear and hybrid star configurations. Correlations between the various observables are examined and we confirm several universal relations. We focus in particular on the constraints for the neutron star radii imposed by a determination of the average tidal deformability of the binary neutron star system GW170817. We find compatible radii between 12 and 13 kilometers and identify the suitable equations of state.
We investigate constraints on neutron star structure arising from the assumptions that neutron stars have crusts, that recent calculations of pure neutron matter limit the equation of state of neutron star matter near the nuclear saturation density, that the high-density equation of state is limited by causality and the largest high-accuracy neutron star mass measurement, and that general relativity is the correct theory of gravity. We explore the role of prior assumptions by considering two classes of equation of state models. In a first, the intermediate- and high-density behavior of the equ…
We perform a joint Bayesian inference of neutron-star mass and radius constraints based on GW170817, observations of quiescent low-mass X-ray binaries (QLMXBs), photospheric radius expansion X-ray bursts (PREs), and X-ray timing observations of J0030+0451. With this data set, the form of the prior distribution still has an impact on the posterior mass-radius (MR) curves and equation of state (EOS), but this impact is smaller than recently obtained when considering QLMXBs alone. We analyze the consistency of the electromagnetic data by including an "intrinsic scattering" contribution to the unc…
Using a Bayesian approach, we combine measurements of neutron star macroscopic observables obtained by astrophysical and gravitational observations, to derive joint constraints on the equation of state (EoS) of matter at supranuclear density. In our analysis we use two sets of data: (i) the masses and tidal deformabilities measured in the binary neutron star event GW170817, detected by LIGO and Virgo; (ii) the masses and stellar radii measured from observations of nuclear bursts in accreting low-mass X-ray binaries. Using two different parametrizations of the equation of state, we compute the …
Intensity interferometry is a technique that has been used to measure the size of sources ranging from the quark-gluon plasma formed in heavy ion collisions to the radii of stars. We investigate using the same technique to measure proto-neutron star (PNS) radii with the neutrino signal received from a core-collapse supernovae. Using a full wave-packet analysis, including the neutrino mass for the first time, we derive criteria where the effect can be expected to provide the desired signal, and find that neutrinos from the next Galactic supernova should contain extractable PNS radius informatio…
Data selection and the determination of systematic uncertainties in the spectroscopic measurements of neutron star radii from thermonuclear X-ray bursts have been the subject of numerous recent studies. In one approach, the uncertainties and outliers were determined by a data-driven Bayesian mixture model, whereas in a second approach, data selection was performed by requiring that the observations follow theoretical expectations. We show here that, due to inherent limitations in the data, the theoretically expected trends are not discernible in the majority of X-ray bursts even if they are pr…
Time resolved X-ray spectroscopy of thermonuclear bursts observed from low mass X-ray binaries offer a unique tool to measure neutron star masses and radii. In this paper, we continue our systematic analysis of all the X-ray bursts observed with RXTE from X-ray binaries. We determine the events which show clear evidence for photospheric radius expansion and measure the Eddington limits for these accreting neutron stars using the bolometric fluxes attained at the touchdown moments of each X-ray burst. We employ a Bayesian technique to investigate the degree to which the Eddington limit for each…
We investigate the properties of dense matter and neutron stars. In particular we discuss model calculations based on the parity doublet picture of hadronic chiral symmetry. In this ansatz the onset of chiral symmetry restoration is reflected by the degeneracy of baryons and their parity partners. In this approach we also incorporate quarks as degrees of freedom to be able to study hybrid stars.
A precise moment of inertia measurement for PSR J0737-3039A in the double pulsar system is expected within the next five years. We present here a new method of mapping the anticipated measurement of the moment of inertia directly into the neutron star structure. We determine the maximum and minimum values possible for the moment of inertia of a neutron star of a given radius based on physical stability arguments, assuming knowledge of the equation of state only at densities below the nuclear saturation density. If the equation of state is trusted up to the nuclear saturation density, we find t…
The Neutron-star Interior Composition Explorer (NICER) is an X-ray astrophysics payload that will be placed on the International Space Station. Its primary science goal is to measure with high accuracy the pulse profiles that arise from the non-uniform thermal surface emission of rotation-powered pulsars. Modeling general relativistic effects on the profiles will lead to measuring the radii of these neutron stars and to constraining their equation of state. Achieving this goal will depend, among other things, on accurate knowledge of the source, sky, and instrument backgrounds. We use here sim…
We propose that the observed cooling of the neutron star in Cassiopeia A is due to enhanced neutrino emission from the recent onset of the breaking and formation of neutron Cooper pairs in the 3P2 channel. We find that the critical temperature for this superfluid transition is ~0.5x10^9 K. The observed rapidity of the cooling implies that protons were already in a superconducting state with a larger critical temperature. Our prediction that this cooling will continue for several decades at the present rate can be tested by continuous monitoring of this neutron star.
We present two recent parametrizations of the equation of state (FSU2R and FSU2H models) that reproduce the properties of nuclear matter and finite nuclei, fulfill constraints on high-density matter stemming from heavy-ion collisions, produce 2$M_{\odot}$ neutron stars, and generate neutron star radii below 13 km. Making use of these equations of state, cooling simulations for isolated neutron stars are performed. We find that two of the models studied, FSU2R (with nucleons) and, in particular, FSU2H (with nucleons and hyperons), show very good agreement with cooling observations, even without…
The equation of state (EOS) of dense matter has been a long-sought goal of nuclear physics. Equations of state generate unique mass versus radius (M-R) relations for neutron stars, the ultra-dense remnants of stellar evolution. In this work, we determine the neutron star mass-radius relation and, based on recent observations of both transiently accreting and bursting sources, we show that the radius of a 1.4 solar mass neutron star lies between 10.4 and 12.9 km, independent of assumptions about the composition of the core. We show, for the first time, that these constraints remain valid upon r…
The possibility of the appearance of the states with a nonzero average helicity in neutron matter is studied in the model with the Skyrme effective interaction. By providing the analysis of the self-consistent equations at zero temperature, it is shown that neutron matter with the Skyrme BSk18 effective force undergoes at high densities a phase transition to the state in which the degeneracy with respect to helicity of neutrons is spontaneously removed.
The nuclear symmetry energy is intimately connected with nuclear astrophysics. This contribution focuses on the estimation of the symmetry energy from experiment and how it is related to the structure of neutron stars. The most important connection is between the radii of neutron stars and the pressure of neutron star matter in the vicinity of the nuclear saturation density $n_s$. This pressure is essentially controlled by the nuclear symmetry energy parameters $S_v$ and $L$, the first two coefficients of a Taylor expansion of the symmetry energy around $n_s$. We discuss constraints on these p…
Modeling the amplitudes and shapes of the X-ray pulsations observed from hot, rotating neutron stars provides a direct method for measuring neutron-star properties. This technique constitutes an important part of the science case for the forthcoming NICER and proposed LOFT X-ray missions. In this paper, we determine the number of distinct observables that can be derived from pulse profile modeling and show that using only bolometric pulse profiles is insufficient for breaking the degeneracy between inferred neutron-star radius and mass. However, we also show that for moderately spinning (300-8…
We obtain a new equation of state for the nucleonic and hyperonic inner core of neutron stars that fulfills the 2$M_{\odot}$ observations as well as the recent determinations of stellar radii below 13 km. The nucleonic equation of state is obtained from a new parametrization of the FSU2 relativistic mean-field functional that satisfies these latest astrophysical constraints and, at the same time, reproduces the properties of nuclear matter and finite nuclei while fulfilling the restrictions on high-density matter deduced from heavy-ion collisions. On the one hand, the equation of state of neut…
Using deep Chandra observations of the globular cluster M28, we study the quiescent X-ray emission of a neutron star in a low-mass X-ray binary in order to constrain the chemical composition of the neutron star atmosphere and the equation of state of dense matter. We fit the spectrum with different neutron star atmosphere models composed of hydrogen, helium or carbon. The parameter values obtained with the carbon model are unphysical and such a model can be ruled out. Hydrogen and helium models give realistic parameter values for a neutron star, and the derived mass and radius are clearly dist…
We study how the $Λ$ hyperon threshold influences the radius of the canonical $1.4 ~M_\odot$ neutron star in the light of the measurements found in the recent literature. We show that the onset of a new degree of freedom not only causes the well known reduction of the maximum mass, but also compacts the neutron stars with high central density. With the help of the strange mesons $ϕ$ and $σ^*$, we show that it is possible to simulate very compact neutron stars keeping realistic hyperon potentials, $U_Λ(n_0)= -28$ MeV and $ U_Λ^Λ(n_0/5)$ in agreement with recents measurements. In the end we gene…
Mergers of black hole (BH) and neutron star (NS) binaries are of interest since the emission of gravitational waves (GWs) can be followed by an electromagnetic (EM) counterpart, which could power short gamma-ray bursts. Until now, LIGO/Virgo has only observed a candidate BH-NS event, GW190426\_152155, which was not followed by any EM counterpart. We discuss how the presence (absence) of a remnant disk, which powers the EM counterpart, can be used along with spin measurements by LIGO/Virgo to derive a lower (upper) limit on the radius of the NS. For the case of GW190426\_152155, large measureme…
We use gravitational-wave observations of the binary neutron star merger GW170817 to explore the tidal deformabilities and radii of neutron stars. We perform Bayesian parameter estimation with the source location and distance informed by electromagnetic observations. We also assume that the two stars have the same equation of state; we demonstrate that for stars with masses comparable to the component masses of GW170817, this is effectively implemented by assuming that the stars' dimensionless tidal deformabilities are determined by the binary's mass ratio $q$ by $Λ_1/Λ_2 = q^6$. We investigat…
We explore constraints on the equation of state (EOS) of neutron-rich matter based on microscopic calculations up to nuclear densities and observations of neutron stars. In a previous work we showed that predictions based on modern nuclear interactions derived within chiral effective field theory and the observation of two-solar-mass neutron stars result in a robust uncertainty range for neutron star radii and the EOS over a wide range of densities. In this work we extend this study, employing both the piecewise polytrope extension from Hebeler et al. as well as the speed of sound model of Gre…
Measuring radii of merging neutron stars with interface-mode asteroseismology informed by nuclear theory and experiment
University of Bath（巴斯大学）；East Texas A&M University（东德克萨斯农工大学）；Texas A&M University（德克萨斯农工大学）；Ohio University（俄亥俄大学）；Michigan State University（密歇根州立大学）；CNRS（法国国家科学研究中心）
A number of properties of dense matter can be understood semiquantitatively in terms of simple physical arguments. We begin with the outer parts of neutron stars, and consider the density at which pressure ionization occurs, the density at which electrons become relativistic, the density at which neutrons drip out of nuclei, and the size of the equilibrium nucleus in dense matter. Subsequently, we treat the so-called "pasta" phases expected to occur at densities just below the density at which the transition from the crust to the liquid core of a neutron star occurs. We then consider aspects o…
Effects of the symmetry energy slope on magnetized neutron stars
Centro Federal de Educação Tecnológica de Minas Gerais（米纳斯吉拉斯州联邦技术教育学院）；Universidade Estadual da Região Tocantina do Maranhão, UEMASUL（马拉尼昂托坎蒂纳地区州立大学）；Universidade Federal do Maranhão（马拉尼昂联邦大学）；Universidade Federal de Santa Catarina（圣卡塔琳娜联邦大学）
The masses and radii of neutron stars are discussed in general relativity and scalar-tensor theory of gravity and the differences are compared with the current uncertainties stemming from the nuclear equation of state in the relativistic mean-field framework. It is shown that astrophysical and gravitational waves observations of radii of neutron stars with masses $M \lesssim 1.4 M_{\odot}$ constrain only the nuclear equation of state, and in particular the density dependence of the nuclear symmetry energy. Future observations of massive neutron stars may constrain the coupling parameters of th…
The role of dense-matter properties in the tidal deformability of a cold nonaccreted neutron star is further investigated. Using the set of Brussels-Montreal unified equations of state, we have computed the gravitoelectric Love numbers $k_\ell$ and the gravitomagnetic Love numbers $j_\ell$ up to $\ell=5$. Their relative importance and their sensitivity to the symmetry energy and the neutron-matter stiffness are numerically assessed. Their impact on the phase of the gravitational-wave signal emitted by binary neutron star inspirals is also discussed.
The theoretical status of the hyperon-nucleon and hyperon-hyperon interactions is reviewed, paying a special attention to chiral effective field theories. Results on hyperons in dense matter are presented and the consequences for the properties of neutron stars are analyzed.
Methods. We use both a Monte Carlo (MC) sampling and a Bayesian analysis to find the effects of the photospheric composition and the touchdown radius. We apply these two methods to six LMXBs that show PRE XRBs. In both methods, we solve the Eddington flux equation and the apparent angular area equation both of which include the correction terms. For the MC sampling, we have developed an iterative method in order to solve these two equations more efficiently. Results. We confirm that the effects of the photospheric composition and the touchdown radius are similar in the statistical and analytic…
Many techniques for measuring neutron star radii rely on absolute flux measurements in the X-rays. As a result, one of the fundamental uncertainties in these spectroscopic measurements arises from the absolute flux calibrations of the detectors being used. Using the stable X-ray burster, GS 1826-238, and its simultaneous observations by Chandra HETG/ACIS-S and RXTE/PCA as well as by XMM-Newton EPIC-pn and RXTE/PCA, we quantify the degree of uncertainty in the flux calibration by assessing the differences between the measured fluxes during bursts. We find that the RXTE/PCA and the Chandra grati…
Using the quantum field theory methods, we calculate the helicity flip of an electron scattering off protons in dense matter of a neutron star. The influence of the electroweak interaction between electrons and background nucleons on the helicity flip is examined. We also derive the kinetic equation for the chiral imbalance. The derived kinetic equation is compared with the results obtained by other authors.
The historic first detection of the binary neutron star merger GW170817 by the LIGO-Virgo collaboration has set a limit on the gravitational deformability of neutron stars. In contrast, radio observations of PSR J0740+6620 find a very massive neutron star. Tension between the small deformability and the large maximum mass may suggest that the pressure rises rapidly with density and thus the speed of sound in dense matter is likely a large fraction of the speed of light. We use these observations and simple constant sound-speed model equations of state to set a lower bound on the maximum speed …
We present a quantitative analysis of superfluidity and superconductivity in dense matter from observations of isolated neutron stars in the context of the minimal cooling model. Our new approach produces the best fit neutron triplet superfluid critical temperature, the best fit proton singlet superconducting critical temperature, and their associated statistical uncertainties. We find that the neutron triplet critical temperature is likely $2.09^{+4.37}_{-1.41} \times 10^{8}$ K and that the proton singlet critical temperature is $7.59^{+2.48}_{-5.81} \times 10^{9}$ K. However, we also show th…
Determining neutron star (NS) radii and masses can help to understand the properties of matter at supra-nuclear densities. Thermal emission during thermonuclear X-ray bursts from NSs in low-mass X-ray binaries provides a unique opportunity to study NS parameters, because of the high fluxes, large luminosity variations and the related changes in the spectral properties. The standard cooling tail method uses hot NS atmosphere models to convert the observed spectral evolution during cooling stages of X-ray bursts to the Eddington flux F_Edd and the stellar angular size Ω. These are then translate…
A moderately spinning neutron star acquires an oblate shape and a spacetime with a significant quadrupole moment. These two properties affect its apparent surface area for an observer at infinity, as well as the lightcurve arising from a hot spot on its surface. In this paper, we develop a ray-tracing algorithm to calculate the apparent surface areas of moderately spinning neutron stars making use of the Hartle-Thorne metric. This analytic metric allows us to calculate various observables of the neutron star in a way that depends only on its macroscopic properties and not on the details of its…
