We present an analytical study of light curves of slowly rotating pulsars
with emphasis on the chromatic effects derived from the presence of a plasma
environment; analyzing the effects of the compactness and charge of the star,
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.
Preprint
Subjects: Astrophysics - High Energy Astrophysical Phenomena; Astrophysics - Solar and Stellar Astrophysics; General Relativity and Quantum Cosmology