Emission-rotation correlation in pulsars: new discoveries with optimal techniques

Pulsars are known to display short-term variability. Recently, examples of longer-term emission variability have emerged that are often correlated with changes in the rotational properties of the pulsar. To further illuminate this relationship, we have developed techniques to identify emission and rotation variability in pulsar data, and determine correlations between the two. Individual observations may be too noisy to identify subtle changes in the pulse profile. We use Gaussian process (GP) regression to model noisy observations and produce a continuous map of pulse profile variability. Generally, multiple observing epochs are required to obtain the pulsar spin frequency derivative ($\dot{\nu}$). GP regression is, therefore, also used to obtain $\dot{\nu}$, under the hypothesis that pulsar timing noise is primarily caused by unmodelled changes in $\dot{\nu}$. Our techniques distinguish between two types of variability: changes in the total flux density versus changes in the pulse shape. We have applied these techniques to 168 pulsars observed by the Parkes radio telescope, and see that although variations in flux density are ubiquitous, substantial changes in the shape of the pulse profile are rare. We reproduce previously published results and present examples of profile shape changing in seven pulsars; in particular, a clear new example of correlated changes in profile shape and rotation is found in PSR~J1602$-$5100. In the shape changing pulsars, a more complex picture than the previously proposed two state model emerges. We conclude that our simple assumption that all timing noise can be interpreted as $\dot{\nu}$ variability is insufficient to explain our dataset.