THE EVOLUTION OF A PULSARS POLAR-CAP GEOMETRY

Contrary to what one might expect for a random orientation of pulsar magnetic and rotation axes, measurements (Lyne & Manchester; Rankin) of pulsar inclination angles show that the distribution of inclination angles is skewed toward moderate values with a peak near 30-degrees. Since these measurements assumed that pulsar beams are circular in cross section, the contradiction may have originated in a failure to account for the quasi-elliptical geometry of the pulsar polar cap. The polar cap is elliptical because more magnetic field lines close in the plane defined by the pulsar rotation and magnetic axes than in the direction of rotation. An attempt is made to compensate Rankin's data for the polar cap ellipticity, and the resulting distribution of inclination angles, alpha, is consistent with the expected function, sin alpha. The braking torque which causes pulsar periods to increase with time may be due to vacuum dipole radiation or plasma currents flowing along open magnetic field lines. In addition to slowing pulsar rotation, the vacuum-wave torque aligns the pulsar magnetic and rotation axes while the plasma-current torque causes the axes to counteralign. The hypotheses of alignment and counteralignment of the magnetic and rotation axes predict distinctly different analytical relationships between a pulsar's period and its inclination angle. Consequently, the angular width of the ellipse minor axis has a period dependence which varies as the inclination angle evolves. If the observed beam widths are affected by the axial ratio of the polar cap ellipse, the beam width-period dependence of pulsars with aligned rotation and magnetic axes may be very different from those with orthogonal axes and can be used to test the hypotheses. The width-period dependences determined from the measured pulsar periods and inclination angles imply that neither pure alignment nor pure counteralignment occur. The widths vary as p-1/2, suggesting that the limiting corotation radius of pulsar magnetospheres varies linearly with pulsar period.