  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.
