Constraining the Neutron Star Mass--Radius Relation and Dense Matter Equation of State with NICER. III. Model Description and Verification of Parameter Estimation Codes

Abstract

We describe the X-ray pulse profile models we use, and how we use them, to analyze Neutron Star Interior Composition Explorer (NICER) observations of rotation-powered millisecond pulsars to obtain information about the mass-radius relation of neutron stars and the equation of state of the dense matter in their cores. Here we detail our modeling of the observed profile of PSR J0030+0451 that we analyzed in Miller et al. (2019) andRiley et al. (2019) and describe a cross-verification of computations of the pulse profiles of a star with R/M ∼ 3, in case stars this compact need to be considered in future analyses. We also present our early cross-verification efforts of the parameter estimation procedures used by Miller et al. (2019) and Riley et al. (2019) by analyzing two distinct synthetic data sets. Both codes yielded credible regions in the mass-radius plane that are statistically consistent with one another and both gave posterior distributions for model parameter values consistent with the values that were used to generate the data. We also summarize the additional tests of the parameter estimation procedure of Miller et al. ( 2019) that used synthetic pulse profiles and the NICER pulse profile of PSR J0030+0451. We then illustrate how the precision of mass and radius estimates depends on the pulsar's spin rate and the size of its hot spot by analyzing four different synthetic pulse profiles. Finally, we assess possible sources of systematic error in these estimates made using this technique, some of which may warrant further investigation.

A NICER View of the Massive Pulsar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy

“…The methodology in this Letter is largely shared with that of Riley et al (2019), Bogdanov et al (2019b), and Bogdanov et al (2021). In this section, we summarize that methodology and give a more detailed report of the new model components.…”

“…Due to the expectation that PSR J0740+6620 could be very compact, the X-PSI code was extended to allow multiple rays from any point to reach the telescope. This improvement to X-PSI as well as details of code validation are discussed in Bogdanov et al (2021). X-PSI sums over the primary and the visible higher-order images of any regions on a star that lie in a multiplyimaged region.…”

“…The specific intensity is determined from lookup tables generated using the NSX atmosphere code assuming either fully ionized hydrogen or helium (Ho & Lai 2001) or partially ionized hydrogen (Ho & Heinke 2009). 19 In this work, we consider only fully ionized models since the limited parameter ranges of existing opacity tables (Iglesias & Rogers 1996;Badnell et al 2005;Colgan et al 2016) reduce the accuracy of atmosphere models employing these tables (see Bogdanov et al 2021 andMiller et al 2021 for further discussion and comparisons).…”

“…It is important to remark that our posterior computation procedure has not been validated in any meaningful way via simulation-based calibration because at present it is basically intractable for any one group to calibrate credible region coverage on a model-by-model basis (see the discussion in chapter 3 of Riley 2019 and in Riley et al 2019). For discussion on the level of calibra-tion we have attained by cross-checking against independent calculations performed by another group (Miller et al 2019), we refer to Bogdanov et al (2021). However, we open-source the entire analysis package for this Letter, so another group with resources is free to modify, cross-check, and improve upon the posterior computation.…”

Impact of Dynamical Tides on the Reconstruction of the Neutron Star Equation of State

“…Gravitational waves carry characteristic information about the composition of neutron stars, providing a unique means to infer their elusive equation of state (EOS) [3]. Observations with the current ground-based GW detector network of Advanced LIGO [4] and Advanced Virgo [5] have yielded the first direct constraints on the EOS [6,7], with recent complementary information obtained from pulsar observations [8] and terrestrial experiments [9].…”