A Method for Testing Diffusive Shock Acceleration and Diffusion Propagation of 1-100 TeV Cosmic Electron with Multi-wavelength Observation of Geminga Halo and Pulsar Wind Nebula

Abstract

Diffusive shock acceleration and diffusion propagation are essential components of the standard cosmic ray model. These theories are based on extensive observations of high-energy solar processes, providing substantial direct evidence in the MeV energy range. Although the model is widely and successfully used to explain high-energy cosmic phenomena, direct validation has been elusive. The multi-wavelength spectra and angular profile measurements of the Geminga pulsar wind nebula and its pulsar halo, particularly the precise spectral observations by HAWC and LHAASO-KM2A in recent years, offer a rare opportunity to test these theories with cosmic rays energies between 1 TeV and several hundred TeV. These observations are expected to elevate the direct testing of theoretical models from multi-MeV to sub-PeV energies. In this work, a method is developed to test the diffusive shock acceleration and diffusion propagation model between one and several hundred TeV energies through the latest spectral and morphological data of the Geminga region from HAWC and Fermi-LAT. Our results show that the theories of diffusive shock acceleration and diffusion propagation are consistent with experimental observations. However, the published morphological data adopted rather wide energy bins and currently do not allow a high precision test of the inferred energy dependent diffusion coefficient by observed energy spectra with DSA theory. It is anticipated that future HAWC and LHAASO-KM2A observations will yield higher-precision results, and the confirmation of a rapidly increasing diffusion coefficient above 100 TeV would serve as important evidence supporting the diffusive shock acceleration and diffusion propagation theory. Similar tests would be both important and valuable for other models.

Figures (4)

• Figure 1: Electron density of the center derived from the measurement of Chandra (Orange Line) and HAWC (Blue Line). The orange region and blue region represents the 95% confidence interval inferred from Chandra and HAWC measurements. The unit of y-axis has been converted to $GeV^{-1} cm^{-3}$, with the radius of Geminga PWN $r_{PWN}=0.01pc$ and the magnetic field $B_{PWN}=20\mu G$. The diffusion coefficient in the Geminga halo is set to be $D^{H}=4.5\times10^{27}(E/100TeV)^{1/3}$
• Figure 2: Spectra fit of Geminga halo. The black data points are from Fermi-LAT and the red data points are from HAWC. Two different condition of electron acceleration in PWN with their best fit parameters and $\delta_1 =0.3$ are shown in figure. The blue line and green line shows the best fit zero-particle condition and zero-streaming condition respectively.
• Figure 3: The diffusion coefficients corresponding to the fitted parameters under the condition that $D_{100TeV} = 4.4^{+0.66}_{-0.57}\times 10^{27} cm^{2}~ s^{-1}$. The lines and shaded regions in different colors represent the best-fit diffusion coefficients and their corresponding 1-$\sigma$ uncertainty ranges for different $\delta_1$ values. The gray dashed line indicates the average diffusion coefficient within the Galaxy. (a) the zero-streaming condition. (b) the zero-particle condition.
• Figure 4: Brightness profile of Geminga halo measued by HAWC in two energy bins. The top two figures are profiles under zero-streaming condition, and the bottom two figures are profiles under zero-particle condition. The first energy bin is 17.8-31.6 TeV and the second energy bin is 31.6-316 TeV. Blue region is the gamma-ray profile predicted by this model. Combining with the background gamma-ray emission given by HAWC, the total profile is shown in red line, which describes the gamma-ray profile well.