Beyond the Simple Power Law: A Bayesian Analysis of 897 Pulsar Spectra

TL;DR

This study uses a large dataset and Bayesian analysis to show that most pulsar spectra are complex with curvature or breaks, challenging the previous belief that they are mostly simple power laws.

Contribution

It provides the first comprehensive Bayesian re-evaluation of pulsar spectra, revealing that broken power laws are more common than simple power laws and correcting prior misconceptions.

Findings

60% of pulsars have broken power law spectra

13.5% of pulsars are best described by simple power laws

74 pulsars have gigahertz-peaked spectra

Abstract

We present a comprehensive re-evaluation of pulsar radio spectra using the largest curated dataset of calibrated flux densities to date, comprising 897 pulsars, and employing a robust Bayesian framework for model comparison alongside frequentist methods. Contrary to the established consensus that pulsar spectra are predominantly simple power laws, our analysis reveals that complex spectral shapes with curvature or breaks are in fact the norm. The broken power law emerges as the most common spectral shape, accounting for 60\% of pulsars, while the simple power law describes only 13.5\%, with 68.8\% of pulsars decisively favoring curved or broken models. We further identify 74 confident gigahertz-peaked spectrum pulsars, and demonstrate that millisecond pulsars frequently exhibit spectral curvature. A key finding is that the previously reported dominance of the simple power law was largely a statistical artifact of the frequentist method used in earlier work. These findings substantially revise the prevailing view of pulsar spectra and establish a critical, model-classified foundation for future theoretical work.