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Register a new userThe Radius of PSR J0740+6620 from NICER and XMM-Newton Data
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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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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.
X-ray pulse profile modeling of PSR J0740+6620, the most massive known pulsar, with data from the NICER and XMM-Newton observatories recently led to a measurement of its radius. We investigate this measurements implications for the neutron star equation of state (EoS), employing a nonparametric EoS model based on Gaussian processes and combining information from other x-ray, radio and gravitational-wave observations of neutron stars. Our analysis mildly disfavors EoSs that support a disconnected hybrid star branch in the mass-radius relation, a proxy for strong phase transitions, with a Bayes factor of $6.9$. For such EoSs, the transition mass from the hadronic to the hybrid branch is constrained to lie outside ($1,2$) $M_{odot}$. We also find that the conformal sound-speed bound is violated inside neutron star cores, which implies that the core matter is strongly interacting. The squared sound speed reaches a maximum of $0.75^{+0.25}_{-0.24}, c^2$ at $3.60^{+2.25}_{-1.89}$ times nuclear saturation density at 90% credibility. Since all but the gravitational-wave observations prefer a relatively stiff EoS, PSR J0740+6620s central density is only $3.57^{+1.3}_{-1.3}$ times nuclear saturation, limiting the density range probed by observations of cold, nonrotating neutron stars in $beta$-equilibrium.
We report the detection of X-ray pulsations from the rotation-powered millisecond-period pulsars PSR J0740+6620 and PSR J1614-2230, two of the most massive neutron stars known, using observations with the Neutron Star Interior Composition Explorer (NICER). We also analyze X-ray Multi-Mirror Mission (XMM-Newton) data for both pulsars to obtain their time-averaged fluxes and study their respective X-ray fields. PSR J0740+6620 exhibits a broad double-peaked profile with a separation of ~0.4 in phase. PSR J1614-2230, on the other hand, has a broad single-peak profile. The broad modulations with soft X-ray spectra of both pulsars are indicative of thermal radiation from one or more small regions of the stellar surface. We show the NICER detections of X-ray pulsations for both pulsars and also discuss the phase relationship to their radio pulsations. In the case of PSR J0740+6620, this paper documents the data reduction performed to obtain the pulsation detection and prepare for pulse profile modeling analysis.
In recent years our understanding of the dense matter equation of state (EOS) of neutron stars has significantly improved by analyzing multimessenger data from radio/X-ray pulsars, gravitational wave events, and from nuclear physics constraints. Here we study the additional impact on the EOS from the jointly estimated mass and radius of PSR J0740+6620, presented in Riley et al. (2021) by analyzing a combined dataset from X-ray telescopes NICER and XMM-Newton. We employ two different high-density EOS parameterizations: a piecewise-polytropic (PP) model and a model based on the speed of sound in a neutron star (CS). At nuclear densities these are connected to microscopic calculations of neutron matter based on chiral effective field theory interactions. In addition to the new NICER data for this heavy neutron star, we separately study constraints from the radio timing mass measurement of PSR J0740+6620, the gravitational wave events of binary neutron stars GW190425 and GW170817, and for the latter the associated kilonova AT2017gfo. By combining all these, and the NICER mass-radius estimate of PSR J0030+0451 we find the radius of a 1.4 solar mass neutron star to be constrained to the 95% credible ranges 12.33^{+0.76}_{-0.81} km (PP model) and 12.18^{+0.56}_{-0.79} km (CS model). In addition, we explore different chiral effective field theory calculations and show that the new NICER results provide tight constraints for the pressure of neutron star matter at around twice saturation density, which shows the power of these observations to constrain dense matter interactions at intermediate densities.
By directly inverting several neutron star observables in the three-dimensional parameter space for the Equation of State of super-dense neutron-rich nuclear matter, we show that the lower radius limit for PSR J0740+6620 of mass $2.08pm 0.07~M_{odot}$ from Neutron Star Interior Composition Explorer (NICER)s very recent observation sets a much tighter lower boundary than previously known for nuclear symmetry energy in the density range of $(1.0sim 3.0)$ times the saturation density $rho_0$ of nuclear matter. The super-soft symmetry energy leading to the formation of proton polarons in this density region of neutron stars is clearly disfavoured by the first radius measurement for the most massive neutron star observed reliably so far.
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