The frequency-dependent behaviour of subpulse drifting: I. Carousel geometry and emission heights of PSR B0031-07

The carousel model of pulsar emission attributes the phenomenon of subpulse drifting to a set of discrete sparks located very near the stellar surface rotating around the magnetic axis. Here, we investigate the subpulse drifting behaviour of PSR B0031-07 in the context of the carousel model. We show that B0031-07's three drift modes (A, B, and C) can be understood in terms of a single carousel rotation rate if the number of sparks is allowed to change by an integral number, and where the different drift rates are due to (first-order) aliasing effects. This also results in harmonically-related values for P 3 (the time it takes a subpulse to reappear at the same pulse phase), which we confirm for B0031-07. A representative solution has [n_A, n_B, n_C] = [15, 14, 13] sparks and a carousel rotation period of P_4 = 16.4 P_1. We also investigate the frequency dependence of B0031-07's subpulse behaviour. We extend the carousel model to include the dual effects of aberration and retardation, including the time it takes the information about the surface spark configuration to travel from the surface up to the emission point. Assuming these effects dominate at B0031-07's emission heights, we derive conservative emission height differences of $\lesssim 2000$ km for mode A and $\lesssim 1000$ km for modes B and C as seen between 185 MHz and 610 MHz. This new method of measuring emission heights is independent of others that involve average profile components or the polarisation position angle curve, and thus provides a potentially strong test of the carousel model.