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

The pulse profile of PSR B1133+16 is usually regarded as a conal double structure. However, its multi-frequency 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 and inverse-Compton-scattering 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 an annular region rather than the core region, and this needs further validation.