Analytical expressions for pulse profile of neutron stars in plasma environments

We present an analytical study of light curves of slowly rotating radio pulsars with emphasis on the chromatic effects derived from the presence of a plasma environment; analyzing the effects of the compactness, the metric model, and the electronic plasma density profile. After doing a numerical integration of the trajectories and luminosity curves of pulsars for different spherically symmetric metrics representing the exterior region of the pulsar, we generalize the approximate Beloborodov formula in order to include plasma corrections, obtaining simple analytical expressions for the trajectories and the observed flux and significantly simplifying the calculation of the pulse profiles by a drastic reduction of their computational cost. We study the errors committed by our approximation, comparing the numerical and analytical procedures. We also show how to use the new formalism to model the flux coming from different emission caps, not necessarily circular or antipodal and including the case of ring-shaped hot spots. Finally, we extend the classification introduced by Beloborodov to the case of two distinguishable, non-antipodal, finite size emission caps, showing the respective classification maps and some of the characteristic pulse profiles.

Automated summary

In this study, we analyze the light curves of slowly rotating radio pulsars and focus on the chromatic effects caused by the presence of a plasma environment. By numerically integrating the trajectories and luminosity curves of pulsars under different spherically symmetric metrics, we extend the Beloborodov formula to include plasma corrections and simplify the calculation of pulse profiles. We demonstrate how this new formalism can be used to model flux from various emission caps, including non-circular or antipodal caps and ring-shaped hot spots. Moreover, we apply the classification introduced by Beloborodov to the case of two distinguishable, non-antipodal emission caps and provide classification maps and characteristic pulse profiles.