Analytical expressions for pulse profile of neutron stars in plasma environments

TL;DR

This paper develops analytical formulas for neutron star pulse profiles in plasma environments, accounting for chromatic effects and different emission geometries, reducing computational costs and enhancing modeling flexibility.

Contribution

It generalizes the Beloborodov formula to include plasma corrections, providing simple analytical expressions for pulse profiles with various emission geometries.

Findings

Analytical expressions accurately approximate numerical results.

Plasma effects introduce significant chromatic modifications.

The formalism accommodates complex emission cap configurations.

Abstract

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.