A Self-Consistent Model of the Ultra High-Energy Gamma-Ray Emission of Pulsar Wind Nebulae: Insights from LHAASO and ATNF Catalogs

TL;DR

The paper addresses how to model PWNe-driven UHE gamma-ray emission in the Galaxy by building a data-driven link between ATNF pulsars and LHAASO detections. It combines Galactic pulsar population synthesis with a censored regression framework to fit PWN spectra against spin-down power, while testing association robustness using an adapted Mattox method and exploring beaming-induced tensions. The analysis suggests that a large fraction of pulsars are misaligned or that many LHAASO associations may be with yet-undiscovered pulsars; with that assumption, unresolved PWNe contribute only a small fraction of the diffuse UHE gamma-ray background. Overall, the work provides a self-consistent, predictive model for PWNe UHE emission and offers a principled way to quantify the unresolved-source contribution as future data improve. This has practical implications for constraining the Galactic population of leptonic PeVatrons and for interpreting the UHE gamma-ray sky observed by LHAASO.

Abstract

Pulsar wind nebulae (PWNe) are the dominant Ultra-high-energy (UHE) gamma-ray sources in the LHAASO catalog suggesting that they are the dominant leptonic PeVatrons in our Galaxy. Despite this, still very little is known about their UHE gamma-ray emission, their number in the Galaxy, or their contribution to the gamma-ray emission of our Galaxy. In this work, we propose a self-consistent data-driven model of the UHE gamma-ray emission of PWNe based on the ATNF and LHAASO catalogs. More specifically, we build a model of the UHE gamma-ray emission of PWNe that preserves the statistical relationships in the ATNF catalog and reproduces the number of PWNe detected in the LHAASO catalog. To cope with the limited data available in the LHAASO catalog when performing fits on gamma-ray data, we introduce the concept of censored regression that allows to also use the information provided by unresolved sources. Using our model, we find that reproducing the number of PWNe detected by LHAASO requires either fractions of misaligned pulsars smaller ($\lesssim60\%$) than usually found in the literature, or that some of the associations of PWNe to ATNF pulsars made by LHAASO may not be true. In both cases, we find that in order to reach self-consistency between radio and gamma-ray data, it is necessary that the majority of the unidentified sources in the LHAASO catalog are PWNe associated to an unseen pulsar. Moreover, using our model we also find that the contribution of unresolved PWNe to the total (diffuse) gamma-ray background measured by LHAASO in the $1-1000\,\rm{TeV}$ range is always smaller than $\lesssim10\%$ ($\lesssim30\%$). We conclude that PWNe mostly contribute to the source component of the UHE gamma-ray sky, while having almost no imprint on its diffuse component.

Figures (5)

• Figure 1: Panel (a) shows the locations of radio-loud pulsars younger than $10\,\rm{Myr}$ with altitudes $|z|\leq1.7\,\rm{kpc}$ in the ATNF catalog. The pulsars between the two dashed lines in black that form an angle of $60^{\circ}$ at the Galactic center have been used to extract the local radial and age distributions of pulsars, assumed to be representative of the entire Galaxy. Panel (b) shows the locations radio-loud pulsars in the ATNF catalog together with the synthetic pulsars generated following our approach. The field of view of LHAASO goes counter-clockwise from the green dashed line to the red dashed line. In both panels the Sun is represented by a yellow diamond.
• Figure 2: Result of the standard (magneta line) and censored (green line) analyses performed on the ATNF and LHAASO data. The red points represent the intrinsic emission of the PWNe detected by KM2A and the blue points represent the upper limit on the intrinsic emission of undetected PWNe. The shaded areas represent the $68\%$ containment regions resulting from the fits.
• Figure 3: The left panel represents the number of detectable PWNe whose parent pulsar is part of the ATNF catalog as a function of the percentage of misaligned pulsars in the simulation. The right panel represents the total number of detected PWNe (whose parent pulsar is either in the ATNF catalog or synthetic) as a function of the percentage of misaligned pulsars in the simulation. In both panels the data points are the average over $1000$ simulations and the error bars represent $1\sigma$ (one standard deviation) over $1000$ simulations.
• Figure 4: Contribution of unresolved PWNe to the Galactic diffuse gamma-ray background. The upper left (right) panel shows the diffuse gamma-ray flux of lhaaso_diffuse_2 and our prediction for the gamma-ray flux from PWNe for the inner (outer) Galaxy using the same masks as LHAASO. The lower left (right) panel shows the contribution (in $\%$) of unresolved PWNe to the diffuse gamma-ray flux of the inner (outer) Galaxy. The data points represent the average over $1000$ simulations and the error bars represent $1\sigma$ (one standard deviation) over $1000$ simulations.
• Figure 5: Contribution of unresolved PWNe to the total Galactic gamma-ray flux. The upper left (right) panel shows the total gamma-ray flux of lhaaso_diffuse_2 and our prediction for the total gamma-ray flux from PWNe for the inner (outer) Galaxy. The lower left (right) panel shows the contribution (in $\%$) of unresolved PWNe to the total gamma-ray flux of the inner (outer) Galaxy. The data points represent the average over $1000$ simulations and the error bars represent $1\sigma$ (one standard deviation) over $1000$ simulations.