Phase Resolved Spectroscopy of Millisecond Pulsars

Gamma-ray observations by Fermi-LAT have opened a new window into the acceleration of particles in the compact magnetospheres of millisecond pulsars. With 53 months of observation, photon statistics allow a first phase resolved spectroscopy of the gamma-ray emission. We studied the 16 brightest millisecond pulsars. They exhibit different light curve morphologies with single or double peaks. We will present spectra for the leading and trailing sides of the peaks, as well as in the inter-peak and off-peak intervals. We have also detected a significant continuous component of the emission for 5 objects. We will present our study of the spectral changes with respect to the rotational phase. In particular, we have found that the spectral energy distribution shifts through the first peak, with a SED maximum at significantly larger energy on the trailing side than on the leading side. No such changes occur across the second peak when present. We will show how stable the spectra are from one object to another across a wide range in spindown power or as a function of geometry (radio-to-gamma-ray lag, magnetic obliquity, aspect angle).