Measurements Of Neutron Star Radii Research Articles

Constraints on the Nuclear Symmetry Energy from Experiments, Theory and Observations

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

Constraining the Nuclear Symmetry Energy with Multimessenger Resonant Shattering Flares.

Much effort is devoted to measuring the nuclear symmetry energy through neutron star (NS) and nuclear observables. Since matter in the NS core may be nonhadronic, observables like radii and tidal deformability may not provide reliable constraints on properties of nucleonic matter. By performing the first consistent inference using ensembles of core and crust equations of state from astrophysical and nuclear data, we demonstrate that coincident timing of a resonant shattering flare (RSF) and gravitational wave signal during binary NS inspiral probes the crust-core transition region and provides constraints on the symmetry energy comparable to terrestrial nuclear experiments. We show that nuclear masses, RSFs, and measurements of NS radii and tidal deformabilities constrain different density ranges of the equation of state, providing complementary probes.

Velocity of sound beyond the high-density relativistic limit from lattice simulation of dense two-color QCD

Abstract We obtain the equation of state (EoS) for two-color quantum chromodynamics (QCD) at low temperature and high density from the lattice Monte Carlo simulation. We find that the velocity of sound exceeds the relativistic limit ($c_s^2/c^2=1/3$) after BEC-BCS (Bose-Einstein condensation–Bardeen–Cooper–Schrieffer) crossover in the superfluid phase. Such an excess of the sound velocity is previously unknown from any lattice calculations for QCD-like theories. This finding might have a possible relevance to the EoS of neutron star matter revealed by recent measurements of neutron star masses and radii.

Constraining scalar-tensor theories using neutron star mass and radius measurements

We use neutron star mass and radius measurements to constrain the spontaneous scalarization phenomenon in scalar-tensor theories using Bayesian analysis. Neutron star structures in this scenario can be significantly different from the case of general relativity, which can be used to constrain the theory parameters. We utilize this idea to obtain lower bounds on the coupling parameter $\beta$ for the case of massless scalars. These constraints are currently weaker than the ones coming from binary observations, and they have relatively low precision due to the approximations in our method. Nevertheless, our results clearly demonstrate the power of the mass-radius data in testing gravity, and can be further improved with future observations. The picture is different for massive scalars, for which the same data is considerably less effective in constraining the theory parameters in an unexpected manner. We identify the main reason for this to be a large high-likelihood region in the parameter space where deviations from general relativity are relatively small. We hope this initial study to be an invitation to use neutron star structure measurements more commonly to test alternative theories in general.

Decoding the density dependence of the nuclear symmetry energy

The large imbalance in the neutron and proton densities in very neutron rich systems increases the nuclear symmetry energy so that it governs many aspects of neutron stars and their mergers. Extracting the density dependence of the symmetry energy therefore constitutes an important scientific objective. Many analyses have been limited to extracting values for the symmetry energy, S0, and its “derivative”, L, at saturation density ρ0≈2.6×1014g/cm3≈0.16nucleons/fm3, resulting in constraints that appear contradictory. We show that most experimental observables actually probe the symmetry energy at densities far from ρ0, making the extracted values of S0 or L imprecise. By focusing on the densities these observables actually probe, we obtain a detailed picture of the density dependence of the symmetry energy from 0.25ρ0 to 2.0ρ0. From this experimentally derived density functional, we extract L01=54±6 MeV corresponding to the symmetry pressure of P01=1.8±0.2 MeV/fm3 at ρ≈0.10fm−3, a neutron skin thickness for P208b of Rnp=0.23±0.03 fm, and symmetry pressure at saturation density of P0=4.4±1.3 MeV/fm3. The extrapolated symmetry pressure at high density is consistent with results from recent measurements of neutron star radii from NICER and deformability from LIGO.

Uncertainty limits on neutron star radius measurements with gravitational waves

Upcoming observing campaigns with improved detectors will yield numerous detections of gravitational waves from neutron star binary inspirals. Rare loud signals together with numerous signals of moderate strength promise stringent constraints on the properties of neutron star matter, with a projected radius statistical uncertainty of $50-200$m with ${\cal{O}}(2000)$ sources. Given this precision we revisit all analysis assumptions and identify sources of systematic errors, quantify their impact on radius extraction, and discuss their relative importance and ways to mitigate them.

Can fermion-boson stars reconcile multimessenger observations of compact stars?

Mixed fermion-boson stars are stable, horizonless, everywhere regular solutions of the coupled Einstein-(complex, massive) Klein-Gordon-Euler system. While isolated neutron stars and boson stars are uniquely determined by their central energy density, mixed configurations conform an extended parameter space that depends on the combination of the number of fermions and (ultra-light) bosons. The wider possibilities offered by fermion-boson stars could help explain the tension in the measurements of neutron star masses and radii reported in recent multi-messenger observations and nuclear-physics experiments. In this work we construct equilibrium configurations of mixed fermion-boson stars with realistic equations of state for the fermionic component and different percentages of bosonic matter. We show that our solutions are in excellent agreement with multi-messenger data, including gravitational-wave events GW170817 and GW190814 and X-ray pulsars PSR J0030+0451 and PSR J0740+6620, as well as with nuclear physics constraints from the PREX-2 experiment.

Spectral analysis of the quiescent low-mass X-ray binary in the globular cluster M30

ABSTRACT We present a recent Chandra observation of the quiescent low-mass X-ray binary containing a neutron star (NS), located in the globular cluster M30. We fit the thermal emission from the NS to extract its mass and radius. We find no evidence of flux variability between the two observations taken in 2001 and 2017, nor between individual 2017 observations, so we analyse them together to increase the signal-to-noise ratio. We perform simultaneous spectral fits using standard light-element composition atmosphere models (hydrogen or helium), including absorption by the interstellar medium, correction for pile-up of X-ray photons on the detector, and a power law for count excesses at high photon energy. Using a Markov chain Monte Carlo approach, we extract mass and radius credible intervals for both chemical compositions of the atmosphere: $\mbox{$R_{\rm NS}$}=7.94\mbox{{$\scriptstyle ^{ + 0.76}_{- 1.21}$}}$ km and $\mbox{$M_{\rm NS}$}\lt 1.19$ M⊙ assuming pure hydrogen, and $\mbox{$R_{\rm NS}$}=10.50\mbox{{$\scriptstyle ^{ + 2.88}_{- 2.03}$}}$ km and $\mbox{$M_{\rm NS}$}\lt 1.78$ M⊙ for helium, where the uncertainties represent the 90 per cent credible regions. For H, the small radius is difficult to reconcile with most current nuclear physics models (especially for nucleonic equations of state) and with other measurements of NS radii, with recent preferred values generally in the 11–14 km range. Whereas for He, the measured radius is consistent with this range. We discuss possible sources of systematic uncertainty that may result in an underestimation of the radius, identifying the presence of surface temperature inhomogeneities as the most relevant bias. According to this, we conclude that either the atmosphere is composed of He or it is anH atmosphere with a significant contribution of hotspots to the observed radiation.

Neutron star radius measurement from the ultraviolet and soft X-ray thermal emission of PSR J0437−4715

ABSTRACT We analysed the thermal emission from the entire surface of the millisecond pulsar PSR J0437−4715 observed in the ultraviolet and soft X-ray bands. For this, we calculated non-magnetized, partially ionized atmosphere models of hydrogen, helium, and iron compositions and included plasma frequency effects that may affect the emergent spectrum. This is particularly true for the coldest atmospheres composed of iron (up to a few per cent changes in the soft X-ray flux). Employing a Markov chain Monte Carlo method, we found that the spectral fits favour a hydrogen atmosphere, disfavour a helium composition, and rule out iron atmosphere and blackbody models. By using a Gaussian prior on the dust extinction, based on the latest 3D map of Galactic dust, and accounting for the presence of hot polar caps found in the previous work, we found that the hydrogen atmosphere model results in a well-constrained neutron star radius ${R_{\rm NS}}= 13.6^{+0.9}_{-0.8}{\, {\rm km}}$ and bulk surface temperature ${T_{\rm eff}^{\infty }}=\left(2.3\pm 0.1\right){\times 10^{5}}{\, {\rm K}}$. This relatively large radius favours a stiff equation of state and disfavours a strange quark composition inside neutron stars.

Optimal Neutron-star Mass Ranges to Constrain the Equation of State of Nuclear Matter with Electromagnetic and Gravitational-wave Observations

Abstract Exploiting a very large library of physically plausible equations of state (EOSs) containing more than 107 members and yielding more than 109 stellar models, we conduct a survey of the impact that a neutron-star radius measurement via electromagnetic observations can have on the EOS of nuclear matter. Such measurements are soon to be expected from the ongoing Neutron Star Interior Composition Explorer mission and will complement the constraints on the EOS from gravitational-wave detections. Thanks to the large statistical range of our EOS library, we can obtain a first quantitative estimate of the commonly made assumption that the high-density part of the EOS is best constrained when measuring the radius of the most massive, albeit rare, neutron stars with masses M ≳ 2.1 M ⊙. At the same time, we find that radius measurements of neutron stars with masses M ≃ 1.7–1.85 M ⊙ can provide the strongest constraints on the low-density part of the EOS. Finally, we quantify how radius measurements by future missions can further improve our understanding of the EOS of matter at nuclear densities.

Inferring neutron star properties from GW170817 with universal relations

Because all neutron stars share a common equation of state, tidal deformability constraints from the compact binary coalescence GW170817 have implications for the properties of neutron stars in other systems. Using equation-of-state insensitive relations between macroscopic observables like moment of inertia ($I$), tidal deformability ($\Lambda$) and stellar compactness, we derive constraints on these properties as a function of neutron-star mass based on the LIGO-Virgo collaboration's canonical deformability measurement, $\Lambda_{1.4} = 190^{+390}_{-120}$. Specific estimates of $\Lambda$, $I$, dimensionless spin $\chi$, and stellar radius $R$ for a few systems targeted by radio or X-ray studies are extracted from the general constraints. We also infer the canonical neutron-star radius as $R_{1.4} = 10.9^{+1.9}_{-1.5}$ km at 90$\%$ confidence. We further demonstrate how a gravitational-wave measurement of $\Lambda_{1.4}$ can be combined with independent measurements of neutron-star radii to tighten constraints on the tidal deformability as a proxy for the equation of state. We find that GW170817 and existing observations of six thermonuclear bursters in low-mass X-ray binaries jointly imply $\Lambda_{1.4} = 196^{+92}_{-63}$ at the 90$\%$ confidence level.

Atmospheric oscillations provide simultaneous measurement of neutron star mass and radius

ABSTRACT Neutron stars with near-Eddington observable luminosities were shown to harbour levitating atmospheres, suspended above their surfaces. We report a new method to simultaneously measure the mass and radius of a neutron star based on oscillations of such atmospheres. In this paper, we present an analytic derivation of a family of relativistic, oscillatory, spherically symmetric eigenmodes of the optically and geometrically thin levitating atmospheres, including the damping effects induced by the radiation drag. We discover characteristic maxima in the frequencies of the damped oscillations and show that from a measurement of the frequency maximum and of the luminosity one can determine the mass and radius of the neutron star. In addition to the stellar parameters, observation of the variation of the oscillation frequencies with flux would allow us to estimate the stellar luminosity and therefore the distance to the source with an accuracy of a few per cent. We also show that the ratio of any two undamped eigenfrequencies depends only on the adiabatic index of the atmosphere, while for the damped eigenfrequencies, this ratio varies with the luminosity. The damping coefficient is independent of the mode number of the oscillations. Signatures of the dynamics of such atmospheres will be reflected in the source’s X-ray light curves.

Constraining nuclear matter parameters with GW170817

The tidal measurement of gravitational waves from the binary neutron star merger event GW170817 allows us to probe nuclear physics that suffers less from astrophysical systematics compared to neutron star radius measurements with electromagnetic wave observations. A recent work found strong correlation among neutron-star tidal deformabilities and certain combinations of nuclear parameters associated with the equation of state. These relations were then used to derive bounds on such parameters from GW170817 assuming that the relations and neutron star masses are known exactly. Here, we expand on this important work by taking into account a few new considerations: (1) a broader class of equations of state; (2) correlations with the mass-weighted tidal deformability that was directly measured with GW170817; (3) how the relations depend on the binary mass ratio; (4) the uncertainty from equation of state variation in the correlation relations; (5) adopting the updated tidal deformability measurement from GW170817. Upon these new considerations, we find GW170817 bounds on nuclear parameters (the incompressibility $K_0$, its slope $M_0$ and the curvature of symmetry energy $K_{\mathrm{sym},0}$ at nuclear saturation density) to be 81 MeV $\leq K_0 \leq$ 362 MeV, 1556 MeV $\leq M_0 \leq$ 4971 MeV, and -254 MeV $\leq K_\mathrm{sym,0} \leq$ 27 MeV, which are more conservative than previously found with systematic errors more properly taken into account.

GW170817: Measurements of Neutron Star Radii and Equation of State.

On 17 August 2017, the LIGO and Virgo observatories made the first direct detection of gravitational waves from the coalescence of a neutron star binary system. The detection of this gravitational-wave signal, GW170817, offers a novel opportunity to directly probe the properties of matter at the extreme conditions found in the interior of these stars. The initial, minimal-assumption analysis of the LIGO and Virgo data placed constraints on the tidal effects of the coalescing bodies, which were then translated to constraints on neutron star radii. Here, we expand upon previous analyses by working under the hypothesis that both bodies were neutron stars that are described by the same equation of state and have spins within the range observed in Galactic binary neutron stars. Our analysis employs two methods: the use of equation-of-state-insensitive relations between various macroscopic properties of the neutron stars and the use of an efficient parametrization of the defining function p(ρ) of the equation of state itself. From the LIGO and Virgo data alone and the first method, we measure the two neutron star radii as R_{1}=10.8_{-1.7}^{+2.0} km for the heavier star and R_{2}=10.7_{-1.5}^{+2.1} km for the lighter star at the 90% credible level. If we additionally require that the equation of state supports neutron stars with masses larger than 1.97 M_{⊙} as required from electromagnetic observations and employ the equation-of-state parametrization, we further constrain R_{1}=11.9_{-1.4}^{+1.4} km and R_{2}=11.9_{-1.4}^{+1.4} km at the 90% credible level. Finally, we obtain constraints on p(ρ) at supranuclear densities, with pressure at twice nuclear saturation density measured at 3.5_{-1.7}^{+2.7}×10^{34} dyn cm^{-2} at the 90% level.

Estimating the equation of state from measurements of neutron star radii with 5% accuracy

Context. Observations of heavy (⋍2 M⊙) neutron stars, such as PSR J1614−2230 and PSR J0348+0432, in addition to the recent measurement of tidal deformability from the binary neutron-star merger GW170817, place interesting constraints on theories of dense matter. Currently operating and future observatories, such as the Neutron star Interior Composition Explorer (NICER) and the Advanced Telescope for High ENergy Astrophysics (ATHENA), are expected to collect information on the global parameters of neutron stars, namely masses and radii, with an accuracy of a few percent. Such accuracy will allow for precise comparisons of measurements to models of compact objects and significantly improve our understanding of the physics of dense matter. Aims. The dense-matter equation of state is still largely unknown. We investigate how the accuracy of measurements expected from the NICER and ATHENA missions will improve our understanding of the dense-matter interior of neutron stars. Methods. We compared global parameters of stellar configurations obtained using three different equations of state: a reference (SLy4 EOS) and two piecewise polytropes manufactured to produce mass-radius relations indistinguishable from an observational point of view, i.e. within the predicted error of radius measurement. We assumed observational errors on the radius determination corresponding to the accuracies expected for the NICER and ATHENA missions. The effect of rotation was examined using high-precision numerical relativity computations. Because masses and rotational frequencies might be determined very precisely in the most optimistic scenario, only the influence of observational errors on radius measurements was investigated. Results. We show that ±5% errors in radius measurement lead to ~10% and ~40% accuracy in central parameter estimations for low-mass and high-mass neutron stars, respectively. Global parameters, such as oblateness and surface area, can be established with 8–10% accuracy, even if only compactness (instead of mass and radius) is measured. We also report on the range of tidal deformabilities corresponding to the estimated masses of GW170817 for the assumed uncertainty in radius.

Effects of Thermonuclear X-Ray Bursts on Non-burst Emissions in the Soft State of 4U 1728–34

Abstract It has recently been shown that the persistent emission of a neutron star low-mass X-ray binary (LMXB) evolves during a thermonuclear (type-I) X-ray burst. The reason of this evolution, however, is not fully known. This uncertainty can introduce significant systematics in the neutron star radius measurement using burst spectra, particularly if an unknown but significant fraction of the burst emission, which is reprocessed, contributes to the changes in the persistent emission during the burst. Here, by analyzing individual burst data of AstroSat/LAXPC from the neutron star LMXB 4U 1728–34 in the soft state, we show that the burst emission is not significantly reprocessed by a corona covering the neutron star. Rather, our analysis suggests that the burst emission enhances the accretion disk emission, possibly by increasing the accretion rate via disk. This enhanced disk emission, which is Comptonized by a corona covering the disk, can explain an increased persistent emission observed during the burst. This finding provides an understanding of persistent emission components and their interaction with the thermonuclear burst emission. Furthermore, as burst photons are not significantly reprocessed, non-burst and burst emissions can be reliably separated, which is required to reduce systematic uncertainties in the stellar radius measurement.

Neutron star mass and radius measurements from atmospheric model fits to X-ray burst cooling tail spectra

Observations of thermonuclear X-ray bursts from accreting neutron stars (NSs) in low-mass X-ray binary systems can be used to constrain NS masses and radii. Most previous work of this type has set these constraints using Planck function fits as a proxy: both the models and the data are fit with diluted blackbody functions to yield normalizations and temperatures which are then compared against each other. Here, for the first time, we fit atmosphere models of X-ray bursting NSs directly to the observed spectra. We present a hierarchical Bayesian fitting framework that uses state-of-the-art X-ray bursting NS atmosphere models with realistic opacities and relativistic exact Compton scattering kernels as a model for the surface emission. We test our approach against synthetic data, and find that for data that are well-described by our model we can obtain robust radius, mass, distance, and composition measurements. We then apply our technique to Rossi X-ray Timing Explorer observations of five hard-state X-ray bursts from 4U 1702-429. Our joint fit to all five bursts shows that the theoretical atmosphere models describe the data well but there are still some unmodeled features in the spectrum corresponding to a relative error of 1-5% of the energy flux. After marginalizing over this intrinsic scatter, we find that at 68% credibility the circumferential radius of the NS in 4U 1702-429 is R = 12.4+-0.4 km, the gravitational mass is M=1.9+-0.3 Msun, the distance is 5.1 < D/kpc < 6.2, and the hydrogen mass fraction is X < 0.09.

Simultaneous Constraints on the Mass and Radius of Aql X–1 from Quiescence and X-Ray Burst Observations

Abstract The measurement of neutron star mass and radius is one of the most direct ways to distinguish between various dense matter equations of state. The mass and radius of accreting neutron stars hosted in low-mass X-ray binaries can be constrained by several methods, including photospheric radius expansion from type I X-ray bursts and from quiescent spectra. In this paper, we apply for the first time these two methods simultaneously to constrain the mass and radius of Aql X–1. The quiescent spectra from Chandra and XMM-Newton, and photospheric radius expansion bursts from RXTE are used. The determination of the mass and radius of Aql X–1 is also used to verify the consistency between the two methods and to narrow down the uncertainties of the neutron star mass and radius. It is found that the distance to Aql X–1 should be in the range of 4.0–5.75 kpc, based on the overlapping confidence regions between photospheric radius expansion burst and quiescent spectra methods. In addition, we show that the mass and radius determined for the compact star in Aql X–1 are compatible with strange star equations of state and conventional neutron star models.

SYSTEMATIC UNCERTAINTIES IN THE SPECTROSCOPIC MEASUREMENTS OF NEUTRON STAR MASSES AND RADII FROM THERMONUCLEAR X-RAY BURSTS. III. ABSOLUTE FLUX CALIBRATION

ABSTRACT 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 gratings measurements agree with each other within their formal uncertainties, increasing our confidence in these flux measurements. In contrast, XMM-Newton EPIC-pn measures 14.0 ± 0.3% less flux than the RXTE/PCA. This is consistent with the previously reported discrepancy with the flux measurements of EPIC-pn, compared with EPIC MOS1, MOS2, and ACIS-S detectors. We also show that any intrinsic time-dependent systematic uncertainty that may exist in the calibration of the satellites has already been implicity taken into account in the neutron star radius measurements.

Neutron matter, symmetry energy and neutron stars

Recent progress in quantum Monte Carlo with modern nucleon-nucleon interactions have enabled the successful description of properties of light nuclei and neutron- rich matter. Of particular interest is the nuclear symmetry energy, the energy cost of creating an isospin asymmetry, and its connection to the structure of neutron stars. Combining these advances with recent observations of neutron star masses and radii gives insight into the equation of state of neutron-rich matter near and above the saturation density. In particular, neutron star radius measurements constrain the derivative of the symmetry energy.