Multi-frequency Radio Profiles of PSR B1133+16: radiation location and particle energy

TL;DR

This study analyzes multi-frequency radio profiles of PSR B1133+16 using advanced fitting functions and beam models to determine radiation locations, particle energies, and emission regions, challenging traditional conal-double interpretations.

Contribution

It introduces a square hyperbolic secant function and a 2D beam model for better profile fitting, and derives radiation altitudes and particle Lorentz factors across frequencies.

Findings

The square hyperbolic secant best fits the profiles.

Radiation Lorentz factors decrease with altitude.

Emission likely occurs in an annular region rather than the core.

Abstract

The pulse profile of PSR B1133+16 is usually regarded as a conal-double structure. However, its multifrequency profiles cannot simply be fitted with two Gaussian functions, and a third component is always needed to fit the bridge region (between two peaks). This would introduce additional, redundant parameters. In this paper, through a comparison of five fitting functions (Gaussian, von Mises, hyperbolic secant, square hyperbolic secant, and Lorentz), it is found that the square hyperbolic secant function can best reproduce the profile, yielding an improved fit. Moreover, a symmetric 2D radiation beam function, instead of a simple 1D Gaussian function, is used to fit the profile. Each profile with either well-resolved or not-so-well-resolved peaks could be fitted adequately using this beam function, and the bridge emission between the two peaks does not need to be a new component. Adopting inclination and impact angles based on polarization measurements, the opening angle ({\theta}_{\mu}0) of the radiation beam in a certain frequency band is derived from beam-function fitting. The corresponding radiation altitudes are then calculated. Based on multi-frequency profiles, we also computed the Lorentz factors of the particles and their dispersion at those locations in both the curvature-radiation (CR) and inverse-Compton-scattering (ICS) models. We found that the Lorentz factors of the particles decrease rapidly as the radiation altitude increases. Besides, the radiation prefers to be generated in annular region rather than core region, and this needs further validation.