Constraining anisotropic diffusion between Geminga and Earth with the cosmic-ray electron and positron spectrum

TL;DR

This paper investigates how anisotropic cosmic-ray diffusion around Geminga affects the electron and positron flux observed at Earth, using gamma-ray observations and DAMPE data to constrain the diffusion parameters and explain spectral features.

Contribution

It introduces an anisotropic diffusion model for Geminga's cosmic rays and constrains its parameters using observational data, explaining the TeV excess and gamma-ray halo.

Findings

The Alfvén Mach number must be ≥0.75 to match observations.

Anisotropic diffusion can produce a 1 TeV peak in the spectrum.

Geminga's diffusion anisotropy influences the observed cosmic-ray flux.

Abstract

The gamma-ray halo surrounding Geminga suggests a notable reduction in cosmic-ray diffusion. One potential explanation for this phenomenon is the projection effect of slow diffusion perpendicular to the average magnetic field (represented by the diffusion coefficient $D_\perp$) within an anisotropic diffusion framework. In this context, the diffusion coefficient parallel to the mean field ($D_\parallel$) may remain substantial, allowing electrons and positrons ($e^\pm$) generated by Geminga to effectively propagate towards Earth along magnetic field lines, potentially leading to an observable $e^\pm$ flux. This study initially establishes the fundamental parameters of the anisotropic model based on the morphology and spectral observations of the Geminga halo, and subsequently forecasts the $e^\pm$ flux generated by Geminga at Earth's location. Our findings indicate that the $e^-+e^+$ spectrum obtained by DAMPE can provide critical constraints on the anisotropic diffusion model: to ensure that the projected spectrum does not surpass the observational data, the Alfv\'en Mach number of the turbulent magnetic field ($M_A$) should not fall below 0.75, corresponding to $D_\parallel/D_\perp\lesssim3$ given $D_\perp=D_\parallel M_A^4$. This suggests that a substantial reduction in $D_\parallel$ relative to the Galactic average may still be necessary. Additionally, our analysis reveals that within the anisotropic diffusion framework, Geminga could generate a distinct peak around 1 TeV in the $e^-+e^+$ spectrum, potentially accounting for the anomalous 1.4 TeV excess tentatively detected by DAMPE.