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Register a new userA NICER View of PSR J0030+0451: Millisecond Pulsar Parameter Estimation
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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.
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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.
Modeling of the NICER X-ray waveform of the pulsar PSR J0030+0451, aimed to constrain the neutron star mass and radius, has inferred surface hot-spots (the magnetic polar caps) that imply significantly non-dipolar magnetic fields. To this end, we investigate magnetic field configurations that comprise offset dipole plus quadrupole components using static vacuum field and force-free global magnetosphere models. Taking into account the compactness and observer angle values provided by Miller et al. (2019) and Riley et al. (2019), we compute geodesics from the observer plane to the polar caps to compute the resulting X-ray light curve. We explore, through Markov chain Monte Carlo techniques, the detailed magnetic field configurations that can reproduce the observed X-ray light curve and have discovered degeneracies, i.e., diverse field configurations, which can provide sufficient descriptions to the NICER X-ray waveforms. Having obtained the force-free field structures, we then compute the corresponding synchronous gamma-ray light curves following Kalapotharakos et al. (2014) these we compare to those obtained by Fermi-LAT, to provide models consistent with both the X-ray and the gamma-ray data, thereby restricting further the multipole field parameters. An essential aspect of this approach is the proper computation of the relative phase between the synchronous X- and gamma-ray light curves. We conclude with a discussion of the broader implications of our study.
We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740$+$6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument (NICER XTI) event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint NANOGrav and CHIME/Pulsar wideband radio timing measurements of arXiv:2104.00880. We use XMM European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740$+$6620 to be $12.39_{-0.98}^{+1.30}$ km and $2.072_{-0.066}^{+0.067}$ M$_{odot}$ respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, conditional on surface hot regions that are non-overlapping spherical caps of fully-ionized hydrogen atmosphere with uniform effective temperature; a posteriori, the temperature is $log_{10}(T$ [K]$)=5.99_{-0.06}^{+0.05}$ for each hot region. All software for the X-ray modeling framework is open-source and all data, model, and sample information is publicly available, including analysis notebooks and model modules in the Python language. Our marginal likelihood function of mass and equatorial radius is proportional to the marginal joint posterior density of those parameters (within the prior support) and can thus be computed from the posterior samples.
We report on deep BVR-imaging of the field of the nearby millisecond pulsar PSR J0030+0451 obtained with the ESO/VLT/FORS2. We do not detect any optical counterpart down to B>27.3, V>27.0 and R>27.0 in the immediate vicinity of the radio pulsar position. The closest detected sources are offset by >3, and they are excluded as counterpart candidates by our astrometry. Using our upper limits in the optical, and including recent XMM-Newton X-ray data we show that any nonthermal power-law spectral component of neutron star magnetospheric origin, as suggested by the interpretation of X-ray data, must be suppressed by at least a factor of ~500 in the optical range. This either rules out the nonthermal interpretation or suggests a dramatic spectral break in the 0.003-0.1 keV range of the power-law spectrum. Such a situation has never been observed in the optical/X-ray spectral region of ordinary pulsars, and the origin of such a break is unclear. An alternative interpretation with a purely thermal X-ray spectrum is consistent with our optical upper limits. In this case the X-ray emission is dominated by hot polar caps of the pulsar.
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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