In 2023, the Third Fermi Large Area Telescope Pulsar Catalogue presented 294 light curves associated with known pulsars, including 143 millisecond pulsars. It provides a wealth of information about the mechanisms that generate pulsar beams. A study led by the Institute of Space Sciences (ICE-CSIC), recently published in The Astrophysical Journal Letters, introduces a new methodology to compare the whole set of gamma-ray light curves reported in that catalogue.

Gamma rays are the highest-energy form of light, and the gamma-ray sky is spectacularly different from the one we perceive with our own eyes. NASA's Fermi Gamma-ray Space Telescope is a space observatory that allows scientists to answer questions about supermassive black hole systems, pulsars, and the origin of cosmic rays and search for signals of new physics. The ICE-CSIC has been involved in Fermi since 2007, before its launch in 2008, as part of its scientific team.

Changes in brightness observed in light curves help astronomers explore how gamma-ray pulsars emit radiation and how their beams sweep across our line of sight. The method applied by ICE-CSIC in this study is based on dynamic time warping (DTW) to compare the whole set of gamma-ray light curves reported in the Third Fermi-Large Area Telescope Pulsar Catalogue. Scientists could quantitatively measure the degree of global similarity between two light curves beyond comparing indicators, such as how many peaks there are, their separation, and their width and height. 

“By studying the shapes of gamma-ray light curves, we gain insights into how pulsars emit radiation and how the geometry of their magnetic fields influences what we observe. One of the most striking findings in our study is that some light curves are remarkably similar, even among pulsars that differ significantly in age, magnetic field strength, or spin period”, says Carlos R. García, predoctoral researcher at ICE-CSIC. “This suggests that similar mechanisms may be at play in shaping gamma-ray emission across different types of pulsars despite their varying physical properties”, he adds.

In time series analysis, dynamic time warping is an algorithm employed to measure the similarity between two sequences that may vary in speed. DTW is also employed in different fields, such as medicine, seismology, financial market analysis, and speech recognition. 

The DTW method has recently started to be used in astrophysics, including applications for gamma-ray bursts or gravitational waves studies. This methodology is used for comparing pulsar light curves for the first time providing astronomers with a technique to study whether pulsars having similar light curves (now quantitatively measured) have similarities in other features too. Up to measurements of similarity were mostly done in an artisanal way. 

Pulsar clusters and all members are related by at least one similarity at a 3σ significance level. Each node represents a pulsar, and each colored edge connecting the nodes shows the similarity significance of the corresponding light curves (black for <1σ and green for >3σ). Credits:García, C. R., Torres, D. F (2025). Quantitative Exploration of the Similarity of Gamma-Ray Pulsar Light Curves. The Astrophysical Journal Letters, 982.

Looking into pulsars

Researchers found surprising that millisecond pulsars -pulsars with a rotational period less than about 10 milliseconds- and young pulsars share detailed light curve morphology up to minute details, despite the many orders of magnitude difference in their physical parameters. This has implications for the understanding of pulsar magnetospheres. 

“A relevant implication is that different kinds of pulsars (e.g., millisecond and regular) -and even pulsars of the same type but with orders of magnitude differences in their physical characteristics or spectra- have curves that can now be quantitatively flagged as being similar. Then, light curves must be dominantly influenced by geometry and both geometry and the underlying physical processes in the magnetospheres should roughly be the same”, explains Diego F. Torres, researcher from the Catalan Institution for Research and Advanced Studies (ICREA) at ICE-CSIC and the Institute of Space Studies of Catalonia (IEEC). 

This new method allows astronomers to cluster pulsars according to light similarity. They can study how pulsars with similar light curves behave regarding other aspects, like their spectra. In future studies, this new method can be used to understand and quantify similarities of transitional pulsars or to compare fast radio bursts, gamma radio bursts or magnetar light curves.

“This work highlights how data-driven techniques—such as dynamic time warping—can uncover subtle similarities between sources that may seem unrelated at first glance. It represents a step towards creating a new framework for pulsar classification based on observable emission patterns rather than solely on physical parameters, which could help identify new families of gamma-ray sources and enhance our understanding of the high-energy sky”, concludes Carlos R. García.