Topology of Pulsar Profiles (ToPP). I. Graph theory method and classification of the EPN

Some of the most important information on a radio pulsar is derived from its average pulse profile. Many early pulsar studies were necessarily based on only few such profiles. There, discrete profile components were linked to emission mechanism models for individual stars through human interpretation. For the population as a whole, profiles morphology must reflect the geometry and overall evolution of the radio emitting regions. The problem, however, is that this population is becoming too large for intensive studies of all sources individually. Moreover, connecting profiles from a large collection of pulsars rapidly becomes cumbersome. In this article, we present ToPP, the first-ever unsupervised method to sort pulsars by profile-shape similarity, using graph topology. We apply ToPP to the publicly available European Pulsar Network profile database, providing the first organised visual overview of multi-frequency profiles representing 90 individual pulsars. We find discrete evolutionary tracks, varying from simple, single component profiles at all frequencies, towards diverse mixtures of more complex profiles with frequency evolution. The profile evolution is continuous, extending out to millisecond pulsars, and does not fall in sharp classes. We interpret the profiles as a mixture of pulsar core/cone emission type, spin-down energetics, and the line-of-sight impact angle towards the magnetic axis. We show how ToPP can systematically classify sources into the Rankin empirical profile scheme. ToPP forms one of the key unsupervised methods that will be essential to explore upcoming pulsar census data such as expected by the Square Kilometer Array.