Constraints on Neutron Star Properties from X-ray Observations of Millisecond Pulsars

We present model spectra and lightcurves of thermal emission from hot spots on the surface of a compact star with an unmagnetized light-element atmosphere. An application to X-ray observations of the nearest known rotation-powered millisecond pulsar (MSP) PSR J0437--4715 reveals that the thermal emission from this pulsar is fully consistent with such a model, enabling constraints on important properties of the underlying neutron star. We demonstrate that the observed thermal X-ray pulsations from J0437--4715 are incompatible with blackbody emission and require the presence of a limb-darkened, light element (most likely hydrogen) atmosphere on the neutron star surface. The morphology of the X-ray pulse profile is consistent with a global dipole configuration of the pulsar magnetic field but suggests an off-center magnetic axis, with a displacement of $\gtrsim$1 km from the stellar center. For an assumed mass of 1.4 M$_{\odot}$, the model restricts the allowed stellar radii to R=6.8-13.8 km (90% confidence) and R>6.7 km (99.9% confidence), which is consistent with standard NS equations of state and rules out an ultra-compact star. Deeper spectroscopic and timing observations of this and other nearby radio MSPs with current and future X-ray facilities (e.g., Constellation-X and XEUS) can provide further insight into the fundamental properties of neutron stars.