  Both the mass and radius of the millisecond pulsar PSR J0030+0451 have been
inferred via pulse-profile modeling of X-ray data obtained by NASA's NICER
mission. In this Letter we study the implications of the mass-radius inference
reported for this source by Riley et al. (2019) for the dense matter equation
of state (EOS), in the context of prior information from nuclear physics at low
densities. Using a Bayesian framework we infer central densities and EOS
properties for two choices of high-density extensions: a piecewise-polytropic
model and a model based on assumptions of the speed of sound in dense matter.
Around nuclear saturation density these extensions are matched to an EOS
uncertainty band obtained from calculations based on chiral effective field
theory interactions, which provide a realistic description of atomic nuclei as
well as empirical nuclear matter properties within uncertainties. We further
constrain EOS expectations with input from the current highest measured pulsar
mass; together, these constraints offer a narrow Bayesian prior informed by
theory as well as laboratory and astrophysical measurements. The NICER
mass-radius likelihood function derived by Riley et al. (2019) using
pulse-profile modeling is consistent with the highest-density region of this
prior. The present relatively large uncertainties on mass and radius for PSR
J0030+0451 offer, however, only a weak posterior information gain over the
prior. We explore the sensitivity to the inferred geometry of the heated
regions that give rise to the pulsed emission, and find a small increase in
posterior gain for an alternative (but less preferred) model. Lastly, we
investigate the hypothetical scenario of increasing the NICER exposure time for
PSR J0030+0451.
