A Determination of Pulsar Emission Geometry from Polarization Observations

Abstract

One of the important problems in pulsar studies is to determine the magnetic inclination angle α, the intrinsic width of the radiation beam (2ρ) and the angle (α + β) between the observer's direction and the rotation axis. In this paper we solve this problem for individual pulses by using the observed pulse width (2Δ𝜙), the swing of polarization angle (2Δψ), and its central gradient (dψ/d𝜙)_max.

From the polar cap model we establish three basic geometrical relations, a complete set of equations from which explicit solutions can be obtained using the observed data. This is the first time that the orientation of pulsar emission is solved analytically solely on the basis of a geometrical model. However, the results are shown to be sensitively connected to the polarization-angle swing (2Δψ), which is not well measured for most pulsars. So the number of pulsars to which our method can be applied is limited. The importance of the measurement of Δψ is seen from our method. To ensure the credibility of our results, we have discussed the conditions to be satisfied by all reliable pulsar measurements. Our method is shown to be more favorable for pulsars with large pulse width 2Δ𝜙, large central gradient (dψ/d𝜙)_max and large magnetic inclination angle α. Out of 120 pulsars (from Lyne and Manchester 1988), 40 are solvable, and 7 are believed to be reliable. We discuss our method for the determination of pulsar geometry in comparison with other methods.