Visualizing the pulsar population using graph theory

TL;DR

This paper reevaluates pulsar population visualization by applying principal components analysis and graph theory, revealing limitations of the traditional $P ext{--}\dot P$ diagram and introducing a new pulsar tree visualization tool.

Contribution

It introduces a novel analysis using PCA and graph theory to better understand pulsar similarities beyond the traditional $P ext{--}\dot P$ diagram, including a new visualization website.

Findings

$P$ and $\dot P$ are not principal components of pulsar data.

Distance measures based solely on $P$ and $\dot P$ can be misleading.

The pulsar tree reveals similarities not visible in the traditional diagram.

Abstract

The $P\dot P$ 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 $P\dot P$-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 components analysis over magnitudes depending on the intrinsic pulsar's timing properties (proxies to relevant physical pulsar features), to analyze 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 $\dot P$, we show that $P\dot P$ are not principal components. Thus, any distance ranking or visualization based only on $P$ and $\dot P$ 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 $\dot P$, and are thus naturally difficult to read from the $P\dot P$-diagram. We use this work to introduce the pulsar tree website http://www.pulsartree.ice.csic.es containing visualization tools and data to allow users to gather information in terms of MST and distance ranking.