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We describe the X-ray pulse profile models we use, and how we use them, toanalyze Neutron Star Interior Composition Explorer (NICER) observations ofrotation-powered millisecond pulsars to obtain information about themass-radius relation of neutron stars and the equation of state of the densematter in their cores. Here we detail our modeling of the observed profile ofPSR 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 astar with R/M 3, in case stars this compact need to be considered in futureanalyses. We also present our early cross-verification efforts of the parameterestimation procedures used by Miller et al. (2019) and Riley et al. (2019) byanalyzing two distinct synthetic data sets. Both codes yielded credible regionsin the mass-radius plane that are statistically consistent with one another andboth gave posterior distributions for model parameter values consistent withthe values that were used to generate the data. We also summarize theadditional tests of the parameter estimation procedure of Miller et al. (2019)that used synthetic pulse profiles and the NICER pulse profile of PSRJ0030+0451. We then illustrate how the precision of mass and radius estimatesdepends on the pulsar's spin rate and the size of its hot spot by analyzingfour different synthetic pulse profiles. Finally, we assess possible sources ofsystematic error in these estimates made using this technique, some of whichmay warrant further investigation.

the astrophysical journal. letters

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