The Radius of PSR J0740+6620 from NICER and XMM-Newton Data
University of Maryland, College Park1, University of Illinois at Urbana–Champaign2, Columbia University3, Goddard Space Flight Center4, Hoffmann-La Roche5, University of Toulouse6, Haverford College7, Stony Brook University8, University of Alberta9, United States Naval Research Laboratory10, University of Orléans11, Centre national de la recherche scientifique12, Cornell University13, Max Planck Society14, National Radio Astronomy Observatory15, Eötvös Loránd University16, University of British Columbia17
TL;DR: In this article, the authors reported 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) observations.
Abstract: PSR J0740$+$6620 has a gravitational mass of $2.08\pm 0.07~M_\odot$, 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 $\pm 1\sigma$ credible intervals of all the radius estimates in the three frameworks is $12.45\pm 0.65$ km for a $1.4~M_\odot$ neutron star and $12.35\pm 0.75$ km for a $2.08~M_\odot$ neutron star.
Citations
More filters
University of Amsterdam1, United States Naval Research Laboratory2, Columbia University3, University of Toulouse4, Hoffmann-La Roche5, University of Alberta6, ASTRON7, Goddard Space Flight Center8, Los Alamos National Laboratory9, Haverford College10, Stony Brook University11, University of Maryland, College Park12, California Institute of Technology13, University of New Hampshire14, Vassar College15, Cornell University16, Eötvös Loránd University17, National Radio Astronomy Observatory18, Max Planck Society19, University of British Columbia20, University of Orléans21, Centre national de la recherche scientifique22
TL;DR: In this article, the authors estimate the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740$+$6620, conditional on pulse profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument (NICER XTI) event data.
Abstract: We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740$+$6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument (NICER XTI) event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint NANOGrav and CHIME/Pulsar wideband radio timing measurements of arXiv:2104.00880. We use XMM European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740$+$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.
353 citations
TL;DR: In this paper, the authors study the impact of the mass and radius of a 1.4 solar mass neutron star on the EOS of a binary binary neutron star, 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.
Abstract: 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.
125 citations
TL;DR: In this article, a lower bound for nuclear symmetry energy at densities above 2.5 was derived from 9 new analyses of neutron star observables consistent with results from earlier analyses of heavy-ion reactions and the latest predictions of the state-of-the-art nuclear many-body theories.
Abstract: New observational data of neutron stars since GW170817 have helped improve our knowledge about nuclear symmetry energy especially at high densities. We have learned particularly: (1) The slope parameter $L$ of nuclear symmetry energy at saturation density $\rho_0$ of nuclear matter from 24 new analyses is about $L\approx 57.7\pm 19$ MeV at 68\% confidence level consistent with its fiducial value, (2) The curvature $K_{\rm{sym}}$ from 16 new analyses is about $K_{\rm{sym}}\approx -107\pm 88$ MeV, (3) The magnitude of nuclear symmetry energy at $2\rho_0$, i.e. $E_{\rm{sym}}(2\rho_0)\approx 51\pm 13$ MeV at 68\% confidence level, has been extracted from 9 new analyses of neutron star observables consistent with results from earlier analyses of heavy-ion reactions and the latest predictions of the state-of-the-art nuclear many-body theories, (4) while the available data from canonical neutron stars do not provide tight constraints on nuclear symmetry energy at densities above about $2\rho_0$, the lower radius boundary $R_{2.01}=12.2$ km from NICER's very recent observation of PSR J0740+6620 of mass $2.08\pm 0.07$ $M_{\odot}$ and radius $R=12.2-16.3$ km at 68\% confidence level sets a tight lower limit for nuclear symmetry energy at densities above $2\rho_0$, (5) Bayesian inferences of nuclear symmetry energy using models encapsulating a first-order hadron-quark phase transition from observables of canonical neutron stars indicate that the phase transition shift appreciably both the $L$ and $K_{\rm{sym}}$ to higher values but with larger uncertaintie , (6) The high-density behavior of nuclear symmetry energy affects significantly the minimum frequency necessary to rotationally support GW190814's secondary component of mass (2.50-2.67) $M_{\odot}$ as the fastest and most massive pulsar discovered so far.
60 citations
TL;DR: In this article , the authors use Bayesian inference to combine data from astrophysical multi-messenger observations of neutron stars and from heavy-ion collisions of gold nuclei at relativistic energies with microscopic nuclear theory calculations.
Abstract: Interpreting high-energy, astrophysical phenomena, such as supernova explosions or neutron-star collisions, requires a robust understanding of matter at supranuclear densities. However, our knowledge about dense matter explored in the cores of neutron stars remains limited. Fortunately, dense matter is not probed only in astrophysical observations, but also in terrestrial heavy-ion collision experiments. Here we use Bayesian inference to combine data from astrophysical multi-messenger observations of neutron stars1-9 and from heavy-ion collisions of gold nuclei at relativistic energies10,11 with microscopic nuclear theory calculations12-17 to improve our understanding of dense matter. We find that the inclusion of heavy-ion collision data indicates an increase in the pressure in dense matter relative to previous analyses, shifting neutron-star radii towards larger values, consistent with recent observations by the Neutron Star Interior Composition Explorer mission5-8,18. Our findings show that constraints from heavy-ion collision experiments show a remarkable consistency with multi-messenger observations and provide complementary information on nuclear matter at intermediate densities. This work combines nuclear theory, nuclear experiment and astrophysical observations, and shows how joint analyses can shed light on the properties of neutron-rich supranuclear matter over the density range probed in neutron stars.
59 citations
TL;DR: In this paper , the authors constructed more than 107 equations of state (EOSs) with continuous sound speed and built more than 108 nonrotating stellar models consistent with nuclear theory and perturbative QCD, but also with astronomical observations.
Abstract: Determining the sound speed c s in compact stars is an important open question with numerous implications on the behavior of matter at large densities and hence on gravitational-wave emission from neutron stars. To this scope, we construct more than 107 equations of state (EOSs) with continuous sound speed and build more than 108 nonrotating stellar models consistent not only with nuclear theory and perturbative QCD, but also with astronomical observations. In this way, we find that EOSs with subconformal sound speeds, i.e., with cs2<1/3 within the stars, are possible in principle but very unlikely in practice, being only 0.03% of our sample. Hence, it is natural to expect that cs2>1/3 somewhere in the stellar interior. Using our large sample, we obtain estimates at 95% credibility of neutron-star radii for representative stars with 1.4 and 2.0 solar masses, R1.4=12.42−0.99+0.52km , R2.0=12.12−1.23+1.11km , and for the binary tidal deformability of the GW170817 event, Λ˜1.186=485−211+225 . Interestingly, our lower bounds on the radii are in very good agreement with the prediction derived from very different arguments, namely, the threshold mass. Finally, we provide simple analytic expressions to determine the minimum and maximum values of Λ˜ as a function of the chirp mass.
54 citations
References
More filters
TL;DR: Matplotlib is a 2D graphics package used for Python for application development, interactive scripting, and publication-quality image generation across user interfaces and operating systems.
Abstract: Matplotlib is a 2D graphics package used for Python for application development, interactive scripting,and publication-quality image generation across user interfaces and operating systems
23,312 citations
01 Jan 1986
TL;DR: The Kernel Method for Multivariate Data: Three Important Methods and Density Estimation in Action.
Abstract: Introduction. Survey of Existing Methods. The Kernel Method for Univariate Data. The Kernel Method for Multivariate Data. Three Important Methods. Density Estimation in Action.
15,499 citations
Book•
23 Nov 2005TL;DR: The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics, and deals with the supervised learning problem for both regression and classification.
Abstract: A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.
11,357 citations
TL;DR: The emcee algorithm as mentioned in this paper is a Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (2010).
Abstract: We introduce a stable, well tested Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (2010). The code is open source and has already been used in several published projects in the astrophysics literature. The algorithm behind emcee has several advantages over traditional MCMC sampling methods and it has excellent performance as measured by the autocorrelation time (or function calls per independent sample). One major advantage of the algorithm is that it requires hand-tuning of only 1 or 2 parameters compared to ~N2 for a traditional algorithm in an N-dimensional parameter space. In this document, we describe the algorithm and the details of our implementation. Exploiting the parallelism of the ensemble method, emcee permits any user to take advantage of multiple CPU cores without extra effort. The code is available online at http://dan.iel.fm/emcee under the GNU General Public License v2.
8,805 citations
TL;DR: The association of GRB 170817A, detected by Fermi-GBM 1.7 s after the coalescence, corroborates the hypothesis of a neutron star merger and provides the first direct evidence of a link between these mergers and short γ-ray bursts.
Abstract: On August 17, 2017 at 12∶41:04 UTC the Advanced LIGO and Advanced Virgo gravitational-wave detectors made their first observation of a binary neutron star inspiral. The signal, GW170817, was detected with a combined signal-to-noise ratio of 32.4 and a false-alarm-rate estimate of less than one per 8.0×10^{4} years. We infer the component masses of the binary to be between 0.86 and 2.26 M_{⊙}, in agreement with masses of known neutron stars. Restricting the component spins to the range inferred in binary neutron stars, we find the component masses to be in the range 1.17-1.60 M_{⊙}, with the total mass of the system 2.74_{-0.01}^{+0.04}M_{⊙}. The source was localized within a sky region of 28 deg^{2} (90% probability) and had a luminosity distance of 40_{-14}^{+8} Mpc, the closest and most precisely localized gravitational-wave signal yet. The association with the γ-ray burst GRB 170817A, detected by Fermi-GBM 1.7 s after the coalescence, corroborates the hypothesis of a neutron star merger and provides the first direct evidence of a link between these mergers and short γ-ray bursts. Subsequent identification of transient counterparts across the electromagnetic spectrum in the same location further supports the interpretation of this event as a neutron star merger. This unprecedented joint gravitational and electromagnetic observation provides insight into astrophysics, dense matter, gravitation, and cosmology.
7,327 citations