# Possible origin of the slow-diffusion region around Geminga

## TL;DR

This paper investigates the origin of slow cosmic-ray diffusion around Geminga, concluding that supernova remnant shock waves, rather than pulsar wind nebula activity, likely cause the observed slow diffusion region.

## Contribution

It proposes that the slow diffusion around Geminga is generated by supernova remnant shock waves, challenging previous ideas of self-generated turbulence from the pulsar wind nebula.

## Key findings

- Self-generated Alfvén waves cannot explain the slow diffusion when considering Geminga's proper motion.
- Supernova remnant shock waves can generate sufficient turbulence to account for the slow diffusion.
- The model also explains slow diffusion regions around other pulsars like PSR B0656+14 and Vela X.

## Abstract

Geminga pulsar is surrounded by a multi-TeV $\gamma$-ray halo radiated by the high energy electrons and positrons accelerated by the central pulsar wind nebula (PWN). The angular profile of the $\gamma$-ray emission reported by HAWC indicates an anomalously slow diffusion for the cosmic-ray electrons and positrons in the halo region around Geminga. In the paper we study the possible mechanism for the origin of the slow diffusion. At first, we consider the self-generated Alfv\'en waves due to the streaming instability of the electrons and positrons released by Geminga. However, even considering a very optimistic scenario for the wave growth, we find this mechanism DOES NOT work to account for the extremely slow diffusion at the present day if taking the proper motion of Geminga pulsar into account. The reason is straightforward as the PWN is too weak to generate enough high energy electrons and positrons to stimulate strong turbulence at the late time. We then propose an assumption that the strong turbulence is generated by the shock wave of the parent supernova remnant (SNR) of Geminga. Geminga may still be inside the SNR, and we find that the SNR can provide enough energy to generate the slow-diffusion circumstance. The TeV halos around PSR B0656+14, Vela X, and PSR J1826-1334 may also be explained under this assumption.