Visualizing the pulsar population using graph theory

The PP˙ diagram is a cornerstone of pulsar research. It is used in multiple ways for classifying the population, understanding evolutionary tracks, identifying issues in our theoretical reach, and more. However, we have been looking at the same plot for more than five decades. A fresh appraisal may be healthy. Is the PP˙ -diagram the most useful or complete way to visualize the pulsars we know? Here we pose a fresh look at the information we have on the pulsar population. First, we use principal component analysis over magnitudes depending on the intrinsic pulsar’s timing properties (proxies to relevant physical pulsar features), to analyse whether the information contained by the pulsar’s period and period derivative is enough to describe the variety of the pulsar population. Even when the variables of interest depend on P and P˙⁠, we show that PP˙ are not principal components. Thus, any distance ranking or visualization based only on P and P˙ is potentially misleading. Next, we define and compute a properly normalized distance to measure pulsar nearness, calculate the minimum spanning tree of the population, and discuss possible applications. The pulsar tree hosts information about pulsar similarities that go beyond P and P˙⁠, and are thus naturally difficult to read from the PP˙-diagram. We use this work to introduce the pulsar tree website containing visualization tools and data to allow users to gather information in terms of MST and distance ranking.
This work has been supported by the grants PID2021-124581OB-I00 and PGC2018-095512-B-I00. CR is funded by the PhD FPI fellowship PRE2019-090828, and acknowledges the graduate program of the Universitat Autònoma of Barcelona. DFT acknowledges as well USTC and the Chinese Academy of Sciences Presidential Fellowship Initiative 2021VMA0001. AP acknowledges partial support from a Ramon y Cajal fellowship RYC-2017-21810. This work was also supported by the Spanish program Unidad de Excelencia María de Maeztu CEX2020-001058-M.