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, 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 that can be extrapolated down to the stellar surface along the "last open field lines," a second group exhibits beam radii that 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. The first group, remarkably, can be fitted by a Thorsett relation in which the constant term is constrained to be the field tangent direction at the edge of the polar cap ρpc, but the others cannot. The first group can also be fitted well using an index of - , but the second group cannot. We first compute heights from the conal beam radii, assuming dipolar fields and emission along the last open field lines, which we find are again well fitted by a suitable Thorsett relation. Here we find that the first group can be fitted using a constant term hpc of 10 km and also that the first two groups are remarkably well fitted by an index of - . We then argue that physical emission heights can be estimated using the component separation along an interior annulus of field lines having their "feet" about halfway out on the polar cap—such values agree well with most existing height values based on physical criteria. Therefore, we find that "radius-to-frequency" mapping is associated with outer-cone component pairs. The near constant behavior of inner cones is thus arresting. We explore possible interrelationships between the spectral behavior of the component and profile widths produced by both the field line flaring and the changing sight line geometry. We also attempt to understand the physical implications of the parameter values resulting from the Thorsett relation fits.