Multi-Frequency Radio Profiles of PSR B1133+16: Radiation Location and Particle Energy

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 (θ µ0 ) 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.

Study of Three Rotating Radio Transients with FAST

“…The conal beam shape was assumed as a square hyperbolic function. Although Lu et al [17] considered this function as the best-fit shape to the pulsar beam, it might not exactly represent the beam shape. The initial inclination angle was set to an acute value (45 • ), and the initial impact angle was positive (10 • ).…”

“…The mean pulse profile has two peaks separated by a bridge component, which characterizes a not-well-resolved conal-double profile [16] as the mean pulse profile of PSR B1133+16. We then attempted to fit the profiles by the modelling approach of Lu et al (2016) [17],…”

“…where φ is the pulse phase; A, φ 0 and σ are parameters describing the shape of the radiation cone; F sech square is defined as follows (which has been proved to be a good function to describe the shape of pulse peak in Lu et al (2016) [17]),…”

High-speed visual target tracking with mixed rotation invariant description and skipping searching

“…which is examined in Lu et al ( 2016) [22] to be the most appropriate function to describe the shape of the pulse profile wings. On the other hand, to fit profiles with a conal beam, the cone function discussed in Lu et al…”

Investigating the multifrequency pulse profiles of PSRs B0329+54 and B1642–03 in an inverse Compton scattering model

“…where θi is the angle between the outgoing direction (initial direction of photons moving from the sparking point, see sparking point A in Fig.1 in Qiao & Lin 1998) and incoming direction (radiation direction) of photons; ω0 = 2π × 10 6 rad/s (Lu et al 2016) is the initial angular frequency of the low frequency wave; γ is the Lorentz factor of particle with the value ≫ 1; η = v c ≈ 1. θi can be determined by the following equation (Qiao & Lin 1998):…”