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I present an analysis of the deepest X-ray exposure of a radio millisecondpulsar (MSP) to date, an X-ray Multi Mirror-Newton European Photon ImagingCamera spectroscopic and timing observation of the nearest known MSP, PSRJ0437--4715. The timing data clearly reveal a secondary broad X-ray pulseoffset from the main pulse by $\sim$0.55 in rotational phase. In the context ofa model of surface thermal emission from the hot polar caps of the neutronstar, this can be plausibly explained by a magnetic dipole field that issignificantly displaced from the stellar center. Such an offset, if commonplacein MSPs, has important implications for studies of the pulsar population, highenergy pulsed emission, and the pulsar contribution to cosmic ray positrons.The continuum emission shows evidence for at least three thermal components,with the hottest radiation most likely originating from the hot magnetic polarcaps and the cooler emission from the bulk of the surface. I present pulsephase-resolved X-ray spectroscopy of PSR J0437--4715, which for the first time,properly accounts for the system geometry of a radio pulsar. Such an approachis essential for unbiased measurements of the temperatures and emission areasof polar cap radiation from pulsars. Detailed modelling of the thermal pulses,including relativistic and atmospheric effects, provides a constraint on theredshift-corrected neutron star radius of R>11.1 km (at 3 sigma conf.) for thecurrent radio timing mass measurement of 1.76 M_sun. This limit favors "stiff'"equations of state.

The Nearest Millisecond Pulsar Revisited with XMM-Newton: Improved Mass-Radius Constraints for PSR J0437-4715