Pioneering use of graph theory to study neutron stars

Scientists have used graph theory for the first time to analyze rapidly spinning neutron stars that emit periodic radiation.

A study by the Higher Council for Scientific Research (CSIC) in Spain makes it possible to represent a population of pulsars using graph theory, a technique that had not been applied in this field to date.

Researchers from the Institute of Space Sciences (ICE) of the CSIC Carlos R. García, Diego F. Torres -also a member of the Institute for Space Studies of Catalonia (IEEC)- and Alessandro Patruno offer a new approach when studying pulsars , very rapidly rotating neutron stars that emit periodic radiation from the radio wave band to the gamma ray band.

This study also presents the website The Pulsar Tree, which allows visualizing the entire population of known pulsars in a tree-like graph, in which each branch corresponds to a set of pulsars with particular characteristics. This website contains tools and data that allow research staff to analyze the similarities between one pulsar and another based on its location in the tree.

As they radiate, pulsars lose rotational kinetic energy. The P-dP/dt diagram shows the spin period (P), or how many times a pulsar spins on itself per second, and the rate of change of this spin period (spin period derivative or dP/dt, from its notation). mathematics).

“Until now, the P-dP/dt diagram has been a key part of pulsar research and is used in multiple ways to classify populations or understand the evolutionary footprints of these systems, among others,” says Carlos R. García, predoctoral researcher at ICE and lead author of the study.

The graph theory techniques used in The Pulsar Tree have been applied in different fields: from engineering problems -beginning with maximizing the efficiency in the distribution of electricity in Moravia in 1926- to the analysis of cognitive deterioration, going through the risk in the financial markets. “In astronomy, they have been used to study the grouping of galaxies, analyze data from particle or cosmic ray colliders, among other examples. However, they had not been used until now for the analysis of pulsar populations”, says Torres.

The Vela Pulsar, 1,000 light-years from Earth, imaged by NASA’s Chandra X-ray Observatory. (Photo: NASA)

With this new approach, the researchers show that any classification of pulsars that uses only spin period (P) and rate of change of spin period (dP/dt) can be potentially misleading. In this way, The Pulsar Tree holds information about similarities of pulsars that would be difficult to read by the P-dP/dt diagram.

The graphical approach of the pulsar tree offers applications related to the connections between the different classes that exist. “It can be used -according to Patruno- to record the discovery of a new class of pulsars or, in the case of synthetic populations of pulsars, to evaluate the quality of the population synthesis model that created them”.

“Graph theory is elegant and robust, and allows us to find relationships between objects in a natural way. Using it for the first time to analyze the population of pulsars opens the door to multiple applications that we hope to explore in future works on the subject”, says the main author.

This method can also be generalized to consider other variables when defining the distance between pulsars, allowing different problems to be addressed. For example, it would allow further study of binary pulsars and their environmental and orbital parameters, the analysis of distances that contain spectral parameters in a given energy range, or the properties of the light curve.

Carlos R. García’s team exposes the mathematical details of The Pulsar Tree in the academic journal Monthly Notices of the Royal Astronomical Society, under the title “Visualizing the pulsar population using graph theory”. (Source: ICE / CSIC)