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

TL;DR

This paper details the modeling and verification of parameter estimation methods for NICER X-ray data of neutron stars, aiming to constrain their mass-radius relation and dense matter equation of state.

Contribution

It introduces verified pulse profile models and cross-validated parameter estimation codes for analyzing NICER observations of neutron stars.

Findings

Credible regions in mass-radius space are consistent across codes.

Parameter estimates are reliable and match synthetic data inputs.

Analysis shows how pulsar properties affect measurement precision.

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) and Riley 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.