A Bayesian statistical analysis of 897 pulsar flux density spectra

TL;DR

The paper tackles the question of whether pulsar radio spectra are well described by simple power laws or require more complex forms. It analyzes a large, curated dataset of calibrated flux densities (897 pulsars) using a Bayesian framework with six spectral forms, incorporating per-reference uncertainty upscaling and frequency re-scaling to compute robust model evidences via dynamic nested sampling. The results show that curved or broken spectra are the norm (68.8% decisively favored over simple power laws; broken power law is the most common at 60.1%), a substantial GPS population (74 pulsars), and notable spectral curvature among millisecond pulsars, challenging the long-standing view of spectral simplicity and highlighting the importance of data quality and statistical methodology. These findings provide a solid, model-classified foundation for future theoretical work on pulsar emission and propagation physics, and demonstrate that previous inferences drawn from smaller, noisier datasets and biased criteria were partially artifacts of the analysis method.

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.

Figures (8)

• Figure 1: Distributions of relative uncertainties in flux density measurements from several major references and of the full 2,310-pulsar dataset. In Hobbs_2004a, 38.2% of the measurements adopt an assumed 10% relative uncertainty where no estimates were reported. Jankowski_2018 derive uncertainties using modulation indices, producing a broad distribution. Johnston_2018 do not provide uncertainties, so a 20% relative uncertainty was assigned by pulsar_spectra. Posselt_2023 employ an unconventional flux density measurement method that yields relatively small uncertainties for most pulsars. Across all literature, 6.3% of the measurements have relative uncertainties of $\sim$10%, 3.5% have $\sim$20%, and 13.2% have $\sim$50%.
• Figure 2: Spectrum of PSR J1809--1917, which was previously classified as a simple power law Jankowski_2018 (lower panel), but our Bayesian analysis identifies the low-frequency turn-over power law as the best model (upper panel), with a $\ln\mathrm{BF}$ of 150 in its favor. The solid orange line and the shaded region display the posterior predictive distribution and its associated uncertainty, with the dark and light colored region showing the 1-$\sigma$ and 3-$\sigma$ credibility interval, respectively. Solid error bars denote the uncertainties reported in the literature, while dashed error bars represent the rescaled uncertainties with inferred $e_{\text{fac}}$ parameters.
• Figure 3: As Fig. \ref{['fig:J1809-1917']}, but for the broken power law spectrum of PSR J1406--6121, one of the newly identified GPS pulsars in this work. Both its observed data peak and the peak of the best-fit broken power law model lie near 1 GHz. Solid error bars show the uncertainties reported in the literature, while dashed error bars indicate the rescaled uncertainties with inferred $e_{\text{fac}}$ parameters.
• Figure 4: Distribution of spectral indices for 121 pulsars best fit by the simple power law, and for 214 pulsars whose simple power law fits are not evidently worse than other models (any $\ln \mathrm{BF} \le 3$).
• Figure 5: Distribution of spectral indices for 20 MSPs and 101 non-MSPs best fit by the simple power law. MSPs exhibit a noticeably steeper mean spectral index.