Toward An Empirical Theory of Pulsar Emission. VII. On the Spectral Behavior of Conal Beam Radii and Emission Heights

In this paper we return to the old problem of conal component-pair widths and profile dimensions. Observationally, we consider a set of 10 pulsars with prominent conal component pairs, for which well measured profiles exist over the largest frequency range now possible. Apart from some tendency to narrow at high frequency, the conal components exhibit almost constant widths. We use all three profile measures, the component separation as well as the outside half-power and 10% widths, to determine conal beam radii, which are the focus of our subsequent analysis. These radii at different frequencies are well fitted by a relationship introduced by Thorsett (1991), but the resulting parameters are highly correlated. Three different types of behavior are found: one group of stars exhibits a continuous variation of beam radius which can be extrapolated down to the stellar surface along the ``last open field lines''; a second group exhibits beam radii which asymptotically approach a minimum high frequency value that is 3--5 times larger; and a third set shows almost no spectral change in beam radius at all. The first two behaviors are associated with outer-cone component pairs; whereas the constant separation appears to reflect inner-cone emission.