Uncertainties of Modeling Gamma-Ray Pulsar Light Curves with Vacuum Dipole Magnetic Field

TL;DR

This paper examines the uncertainties in modeling gamma-ray pulsar light curves using vacuum dipole magnetic fields, highlighting the impact of relativistic aberration corrections and polar cap shape assumptions on model predictions.

Contribution

It identifies inconsistencies in previous models, corrects the aberration formula, and assesses the sensitivity of light curves to magnetic field and polar cap shape variations.

Findings

Corrected aberration formula reduces peak sharpness in TPC models.

Polar cap shape significantly affects the number of emission peaks in TPC models.

Vacuum field assumptions introduce large uncertainties, suggesting the need for force-free field models.

Abstract

Current models of pulsar gamma-ray emission use the magnetic field of a rotating dipole in vacuum as a first approximation to the shape of plasma-filled pulsar magnetosphere. In this paper we revisit the question of gamma-ray light-curve formation in pulsars in order to ascertain the robustness of the "two-pole caustic" (TPC) and "outer gap" (OG) models based on the vacuum magnetic field. We point out an inconsistency in the literature on the use of the relativistic aberration formula, where in several works the vacuum field was treated as known in the instantaneously corotating frame, rather than in the laboratory frame. With the corrected formula, we find that the peaks in the light curves predicted from the TPC model using the vacuum field are less sharp. The sharpness of the peaks in the OG model is less affected by this change, but the range of magnetic inclination angles and viewing geometries resulting in double-peaked light curves is reduced. In a realistic magnetosphere, the modification of field structure near the light cylinder due to plasma effects may change the shape of the polar cap and the location of the emission zones. We study the sensitivity of the light curves to different shapes of the polar cap for static and retarded vacuum dipole fields. In particular, we consider polar caps traced by the last open field lines and compare them to circular polar caps. We find that the TPC model is very sensitive to the shape of the polar cap, and a circular polar cap can lead to four peaks of emission. The OG model is less affected by polar cap shapes, but is subject to big uncertainties of applying the vacuum field near the light cylinder. We conclude that deviations from vacuum field can lead to large uncertainties in the pulse shapes, and a more realistic force-free field should be applied to the study of pulsar high energy emission.