Neutron Star Mass-Radius Constraints of the Quiescent Low-mass X-ray Binaries X7 and X5 in the Globular Cluster 47 Tuc

We present Chandra ACIS-S sub-array observations of the quiescent neutron star low-mass X-ray binaries X7 and X5 in the globular cluster 47 Tuc. The large reduction in photon pile-up compared to previous deep exposures enables a substantial improvement in the spectroscopic determination of the neutron star radius and mass of these neutron stars. Modeling the thermal emission from the neutron star surface with a non-magnetized hydrogen atmosphere and accounting for numerous sources of uncertainties, we obtain for the neutron star in X7 a radius of $R=11.1^{+0.8}_{-0.7}$ km for an assumed stellar mass of $M=1.4$ M$_{\odot}$ (68% C.L.). We argue, based on astrophysical grounds, that the presence of a He atmosphere is unlikely for this source. Due to eclipses and variable absorption, the quiescent low-mass X-ray binary X5 provides less stringent constraints, leading to a radius of $R=9.6^{+0.9}_{-1.1}$ km, assuming a hydrogen atmosphere and a mass of $M=1.4$ M$_{\odot}$. When combined with all other existing spectroscopic radius measurements, these measurements strongly favor radii in the 9.9-11.2 km range for a ~1.5 M$_{\odot}$ neutron star and point to a dense matter equation of state that is somewhat softer than the nucleonic ones that are consistent with laboratory experiments at low densities.