The Effect of Pulsar Geometry on the Observed Gamma-ray Spectrum of Millisecond Pulsars

Abstract

We analyse 13 yrs of $\textit{Fermi}$-LAT PASS 8 events from 127 gamma-ray emitting millisecond pulsars (MSPs) in the energy range 0.1$-$100 GeV and significantly detect 118 MSPs. We fit the stacked emission with a log parabola (LP) spectral model which we show is preferred to two previously published models. We consider the influence of pulsar properties and observer geometric effects on spectral features by defining energy flux colours for both the individual MSPs, and our stacked model as a baseline. There is no correlation of colours with pulsar luminosity, $\dot{E}$, surface magnetic field or magnetic impact angle. We also find that pulsar geometry has little effect on the observed gamma-ray spectrum which is in tension with previous modelling of gamma-ray emission with respect to pulsar geometry. Our LP MSP model is applicable to problems where an ensemble of gamma-ray MSPs is considered, such as that of the Galactic centre excess or in the case of emission from globular clusters.