Test of the superdiffusion model in the interstellar medium around the Geminga pulsar

TL;DR

This study tests the superdiffusion model for cosmic-ray propagation around the Geminga pulsar, finding that near-normal diffusion explains the halo morphology but predicts higher positron flux, impacting cosmic-ray origin interpretations.

Contribution

It introduces and tests the superdiffusion model against observational data, providing constraints on the diffusion index and implications for cosmic-ray propagation models.

Findings

Superdiffusion with alpha close to 2 fits the halo morphology.

Models with alpha<1.32 are disfavored at 95% confidence.

Superdiffusion predicts higher positron flux than normal diffusion.

Abstract

The TeV $\gamma$-ray halo around the Geminga pulsar is an important indicator of cosmic-ray (CR) propagation in the local zone of the Galaxy as it reveals the spatial distribution of the electrons and positrons escaping from the pulsar. Considering the intricate magnetic field in the interstellar medium (ISM), it is proposed that superdiffusion model could be more realistic to describe the CR propagation than the commonly used normal diffusion model. In this work, we test the superdiffusion model in the ISM around the Geminga pulsar by fitting to the surface brightness profile of the Geminga halo measured by HAWC. Our results show that the chi-square statistic monotonously increases as $\alpha$ decreases from 2 to 1, where $\alpha$ is the characteristic index of superdiffusion describing the degree of fractality of the ISM and $\alpha=2$ corresponds to the normal diffusion model. We find that model with $\alpha<1.32$ (or $<1.4$, depending on the data used in fit) is disfavored at 95\% confidence level. Superdiffusion model with $\alpha$ close to 2 can well explain the morphology of the Geminga halo, while it predicts much higher positron flux on the Earth than the normal diffusion model. This has important implication for the interpretation of the CR positron excess.