The recent discovery by Bachetti et al. (2014) of a pulsar in M82 that can reach luminosities of up to 10^40 ergs s^-1, a factor of ~100 the Eddington luminosity for a 1.4 Msol compact object, poses a challenge for accretion physics. In order to better understand the nature of this source and its duty cycle, and in the light of several physical models that have been subsequently published, we conduct a spectral and temporal analysis of the 0.5-8 keV X-ray emission from this source from 15 years of Chandra observations. We fit the Chandra spectra of the pulsar with a power-law model and a disk black body model, subjected to interstellar absorption in M82. We carefully assess for the effect of pile-up in our observations, where 4/19 observations have a pile-up fraction >10%, which we account for during spectral modeling with a convolution model. When fitted with a power-law model, the average photon index when the source is at high luminosity (L_X>10^39 ergs s^-1) is Gamma=1.33+/-0.15. For the disk black body model, the average temperature is T=3.24+/-0.65 keV, consistent with other luminous X-ray pulsars. We also investigated the inclusion of a soft excess component and spectral break, finding that the spectra are also consistent with these features common to luminous X-ray pulsars. In addition, we present spectral analysis from NuSTAR over the 3-50 keV range where we have isolated the pulsed component. We find that the pulsed emission in this band is best fit by a power-law with a high-energy cut-off, where Gamma=0.6+/-0.3 and E_C=14^{+5}_{-3} keV. While the pulsar has previously been identified as a transient, we find from our longer-baseline study that it has been remarkably active over the 15-year period, where for 9/19 (47%) observations that we analyzed, the pulsar appears to be emitting at a luminosity in excess of 10^39 ergs s^-1, greater than 10 times its Eddington limit.
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