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

## TL;DR

This paper investigates the subpulse drifting behavior of pulsar PSR B0031-07 within the carousel model, explaining its drift modes through changes in spark numbers and aliasing effects, and extends the model to include frequency-dependent emission height estimates.

## Contribution

It introduces a unified carousel model explaining all drift modes via spark number changes and aliasing, and develops a new method to estimate emission heights using aberration and retardation effects.

## Key findings

- Drift modes can be explained by a single carousel rotation rate with varying spark numbers.
- Confirmed harmonic relation of P3 values across modes.
- Estimated emission height differences are less than 2000 km between 185 MHz and 610 MHz.

## Abstract

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.