Neutron stars are not only of astrophysical interest, but are also of great interest to nuclear physicists because their attributes can be used to determine the properties of the dense matter in their cores. One of the most informative approaches for determining the equation of state (EoS) of this dense matter is to measure both a star's equatorial circumferential radius R e and its gravitational mass M . Here we report estimates of the mass and radius of the isolated 205.53 Hz millisecond pulsar PSR J0030+0451 obtained using a Bayesian inference approach to analyze its energy-dependent thermal X-ray waveform, which was observed using the Neutron Star Interior Composition Ex-Corresponding author: M. C. Miller miller@astro.umd.edu a Einstein Fellow arXiv:1912.05705v1 [astro-ph.HE] 12 Dec 2019 Miller, Lamb, Dittmann, et al. plorer (NICER). This approach is thought to be less subject to systematic errors than other approaches for estimating neutron star radii. We explored a variety of emission patterns on the stellar surface. Our best-fit model has three oval, uniform-temperature emitting spots and provides an excellent description of the pulse waveform observed using NICER. The radius and mass estimates given by this model are R e = 13.02 +1.24 −1.06 km and M = 1.44 +0.15 −0.14 M (68%). The independent analysis reported in the companion paper by Riley et al. explores different emitting spot models, but finds spot shapes and locations and estimates of R e and M that are consistent with those found in this work. We show that our measurements of R e and M for PSR J0030+0451 improve the astrophysical constraints on the EoS of cold, catalyzed matter above nuclear saturation density.

We present upper limits on the amplitude of r-mode oscillations, and gravitational-radiation-induced spin-down rates, in low mass X-ray binary neutron stars under the assumption that the quiescent neutron star luminosity is powered by dissipation from a steady-state r-mode. For masses < 2M ⊙ we find dimensionless r-mode amplitudes in the range from about 1 × 10 −8 to 1.5 × 10 −6 . For the accreting millisecond X-ray pulsar sources with known quiescent spin-down rates these limits suggest that 1% of the observed rate can be due to an unstable r-mode. Interestingly, the source with the highest amplitude limit, NGC 6440, could have an r-mode spin-down rate comparable to the observed, quiescent rate for SAX J1808-3658. Thus, quiescent spin-down measurements for this source would be particularly interesting. For all sources considered here our amplitude limits suggest that gravitational wave signals are likely too weak for detection with Advanced LIGO. Our highest mass model (2.21 M ⊙ ) can support enhanced, direct Urca neutrino emission in the core and thus can have higher r-mode amplitudes. Indeed, the inferred r-mode spin-down rates at these higher amplitudes are inconsistent with the observed spin-down rates for some of the sources, such as IGR J00291+5934 and XTE J1751-305. In the absence of other significant sources of internal heat, these results could be used to place an upper limit on the masses of these sources if they were made of hadronic matter, or alternatively it could be used to probe the existence of exotic matter in them if their masses were known.