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PSR J0030+0451 Mass and Radius from NICER Data and Implications for the Properties of Neutron Star Matter

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 Added by M. Coleman Miller
 Publication date 2019
  fields Physics
and research's language is English




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Neutron stars are not only of astrophysical interest, but are also of great interest to nuclear physicists, because their attributes can be used to determine the properties of the dense matter in their cores. One of the most informative approaches for determining the equation of state of this dense matter is to measure both a stars equatorial circumferential radius $R_e$ and its gravitational mass $M$. Here we report estimates of the mass and radius of the isolated 205.53 Hz millisecond pulsar PSR J0030+0451 obtained using a Bayesian inference approach to analyze its energy-dependent thermal X-ray waveform, which was observed using the Neutron Star Interior Composition Explorer (NICER). This approach is thought to be less subject to systematic errors than other approaches for estimating neutron star radii. We explored a variety of emission patterns on the stellar surface. Our best-fit model has three oval, uniform-temperature emitting spots and provides an excellent description of the pulse waveform observed using NICER. The radius and mass estimates given by this model are $R_e = 13.02^{+1.24}_{-1.06}$ km and $M = 1.44^{+0.15}_{-0.14} M_odot$ (68%). The independent analysis reported in the companion paper by Riley et al. (2019) explores different emitting spot models, but finds spot shapes and locations and estimates of $R_e$ and $M$ that are consistent with those found in this work. We show that our measurements of $R_e$ and $M$ for PSR J0030$+$0451 improve the astrophysical constraints on the equation of state of cold, catalyzed matter above nuclear saturation density.

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Both the mass and radius of the millisecond pulsar PSR J0030+0451 have been inferred via pulse-profile modeling of X-ray data obtained by NASAs NICER mission. In this Letter we study the implications of the mass-radius inference reported for this source by Riley et al. (2019) for the dense matter equation of state (EOS), in the context of prior information from nuclear physics at low densities. Using a Bayesian framework we infer central densities and EOS properties for two choices of high-density extensions: a piecewise-polytropic model and a model based on assumptions of the speed of sound in dense matter. Around nuclear saturation density these extensions are matched to an EOS uncertainty band obtained from calculations based on chiral effective field theory interactions, which provide a realistic description of atomic nuclei as well as empirical nuclear matter properties within uncertainties. We further constrain EOS expectations with input from the current highest measured pulsar mass; together, these constraints offer a narrow Bayesian prior informed by theory as well as laboratory and astrophysical measurements. The NICER mass-radius likelihood function derived by Riley et al. (2019) using pulse-profile modeling is consistent with the highest-density region of this prior. The present relatively large uncertainties on mass and radius for PSR J0030+0451 offer, however, only a weak posterior information gain over the prior. We explore the sensitivity to the inferred geometry of the heated regions that give rise to the pulsed emission, and find a small increase in posterior gain for an alternative (but less preferred) model. Lastly, we investigate the hypothetical scenario of increasing the NICER exposure time for PSR J0030+0451.
We report on Bayesian parameter estimation of the mass and equatorial radius of the millisecond pulsar PSR J0030$+$0451, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer (NICER) X-ray spectral-timing event data. We perform relativistic ray-tracing of thermal emission from hot regions of the pulsars surface. We assume two distinct hot regions based on two clear pulsed components in the phase-folded pulse-profile data; we explore a number of forms (morphologies and topologies) for each hot region, inferring their parameters in addition to the stellar mass and radius. For the family of models considered, the evidence (prior predictive probability of the data) strongly favors a model that permits both hot regions to be located in the same rotational hemisphere. Models wherein both hot regions are assumed to be simply-connected circular single-temperature spots, in particular those where the spots are assumed to be reflection-symmetric with respect to the stellar origin, are strongly disfavored. For the inferred configuration, one hot region subtends an angular extent of only a few degrees (in spherical coordinates with origin at the stellar center) and we are insensitive to other structural details; the second hot region is far more azimuthally extended in the form of a narrow arc, thus requiring a larger number of parameters to describe. The inferred mass $M$ and equatorial radius $R_mathrm{eq}$ are, respectively, $1.34_{-0.16}^{+0.15}$ M$_{odot}$ and $12.71_{-1.19}^{+1.14}$ km, whilst the compactness $GM/R_mathrm{eq}c^2 = 0.156_{-0.010}^{+0.008}$ is more tightly constrained; the credible interval bounds reported here are approximately the $16%$ and $84%$ quantiles in marginal posterior mass.
Very recently the NICER collaboration has published the first-ever accurate measurement of mass and radius together for PSR J0030+0451, a nearby isolated quickly-rotating neutron star (NS). In this work we set the joint constraints on the equation of state (EoS) and some bulk properties of NSs with the data of PSR J0030+0451, GW170817 and some nuclear experiments. The piecewise polytropic expansion method and the spectral decomposition method have been adopted to parameterize the EoS. The resulting constraints are consistent with each other. Assuming the maximal gravitational mass of non-rotating NS $M_{rm TOV}$ lies between $2.04 rm M_{odot}$ and $2.4 rm M_{odot}$, with the piecewise method the pressure at twice nuclear saturation density is measured to be $3.38^{+2.43}_{-1.50}times 10^{34}~{rm dyn~cm^{-2}}$ at the $90%$ level. For a NS with canonical mass of $1.4 rm M_odot$, we have the moment of inertia $I_{1.4} = {1.43}^{+0.28}_{-0.13} times 10^{38}~{rm kg cdot m^2}$, tidal deformability $Lambda_{1.4} = 390_{-140}^{+320}$, radius $R_{1.4} = 12.2_{-0.9}^{+1.0}~{rm km}$, and binding energy $BE_{1.4} = {0.16}^{+0.01}_{-0.02} rm M_{odot}$ at the $90%$ level, which are improved in comparison to the constraints with the sole data of GW170817.
In this work we investigate neutron stars (NS) in $f(mathtt{R,L_m})$ theory of gravity for the case $f(mathtt{R,L_m}) = mathtt{R} + mathtt{L_m} + sigmamathtt{R}mathtt{L_m}$, where $mathtt{R}$ is the Ricci scalar and $mathtt{L_m}$ the Lagrangian matter density. In the term $sigmamathtt{R}mathtt{L_m}$, $sigma$ represents the coupling between the gravitational and particles fields. For the first time the hydrostatic equilibrium equations in the theory are solved considering realistic equations of state and NS masses and radii obtained are subject to joint constrains from massive pulsars, the gravitational wave event GW170817 and from the PSR J0030+0451 mass-radius from NASAs Neutron Star Interior Composition Explorer (${it NICER}$) data. We show that in this theory of gravity, the mass-radius results can accommodate massive pulsars, while the general theory of relativity can hardly do it. The theory also can explain the observed NS within the radius region constrained by the GW170817 and PSR J0030+0451 observations for masses around $1.4~M_{odot}$.
PSR J0740$+$6620 has a gravitational mass of $2.08pm 0.07~M_odot$, which is the highest reliably determined mass of any neutron star. As a result, a measurement of its radius will provide unique insight into the properties of neutron star core matter at high densities. Here we report a radius measurement based on fits of rotating hot spot patterns to Neutron Star Interior Composition Explorer (NICER) and X-ray Multi-Mirror (XMM-Newton) X-ray observations. We find that the equatorial circumferential radius of PSR J0740$+$6620 is $13.7^{+2.6}_{-1.5}$ km (68%). We apply our measurement, combined with the previous NICER mass and radius measurement of PSR J0030$+$0451, the masses of two other $sim 2~M_odot$ pulsars, and the tidal deformability constraints from two gravitational wave events, to three different frameworks for equation of state modeling, and find consistent results at $sim 1.5-3$ times nuclear saturation density. For a given framework, when all measurements are included the radius of a $1.4~M_odot$ neutron star is known to $pm 4$% (68% credibility) and the radius of a $2.08~M_odot$ neutron star is known to $pm 5$%. The full radius range that spans the $pm 1sigma$ credible intervals of all the radius estimates in the three frameworks is $12.45pm 0.65$ km for a $1.4~M_odot$ neutron star and $12.35pm 0.75$ km for a $2.08~M_odot$ neutron star.
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