Spatial Dependent Diffusion of Cosmic Rays and the Excess of Primary Electrons Derived from High Precision Measurements by AMS-02

The precise spectra of Cosmic Ray (CR) electrons and positrons have been published by the measurement of AMS-02. It is reasonable to regard the difference between the electrons and positrons spectra ( $triangle Phi= Phi_{e^-}-Phi_{e^+}$ ) as being dominated by primary electrons. Noticing that the resulting electron spectrum shows no sign of spectral softening above 20 GeV, which is in contrast with the prediction of standard model. In this work, we generalize the analytic one dimensional two-halo model of diffusion to a three dimensional realistic calculation by implementing a spatial variant diffusion coefficients in DRAGON package. As a result, we can reproduce the spectral hardening of protons observed by several experiments, and predict an excess of high energy primary electrons which agrees with the measurement reasonably well. Unlike the break spectrum obtained for protons, the model calculation predicts a smooth electron excess and thus slightly over predicts the flux from tens of GeV to 100GeV. To understand this issue, further experimental and theoretical studies are necessary.

On the Contribution of Fresh Cosmic Rays to the Excesses of Secondary Particles

The standard model of cosmic ray propagation has been very successful in explaining all kinds of the Galactic cosmic ray spectra. However, high precision measurement recently revealed the appreciable discrepancy between data and model expectation, from spectrum observations of $gamma$-rays, $e^+/e^-$ and probably the $B/C$ ratio starting from $sim$10 GeV energy. In this work, we propose that the fresh cosmic rays, which are supplied by the young accelerators and detained by local magnetic field, can contribute additional secondary particles interacting with local materials. As this early cosmic ray has a hard spectrum, the model calculation results in a two-component $gamma$-ray spectrum, which agree very well with the observation. Simultaneously, the expected neutrino number from the galactic plane could contribute $sim60%$ of IceCube observation neutrino number below a few hundreds of TeV. The same pp-collision process can account for a significant amount of the positron excesses. Under this model, it is expected that the excesses in $overline p/p$ and $B/C$ ratio will show up when energy is above $sim$10 GeV. We look forward that the model will be tested in the near future by new observations from AMS02, IceCube, AS$gamma$, HAWC and future experiments such as LHASSO, HiSCORE and CTA.

Pinpointing the knee of cosmic rays with diffuse PeV gamma-rays and neutrinos

The origin of the knee in cosmic ray spectrum remains to be an unsolved fundamental problem. There are various kinds of models which predict different break positions and the compositions of the knee. In this work, we suggest to use diffuse $gamma$-rays and neutrinos as probes to test these models. Based on several typical types of the composition models, the diffuse $gamma$-ray and neutrino spectra are calculated, which show distinctive cutoff behaviours at energies from tens of TeV to multi-PeV. The expected flux will be observable by the newly upgraded Tibet-AS$gamma$+MD (muon detector) experiment as well as more sensitive future projects, such as LHAASO and HiSCORE. By comparing the neutrino spectrum with the recent observations by IceCube experiment, we find that the diffuse neutrinos from interactions between the cosmic rays and the interstellar medium may not be responsible to the majority of the IceCube events. Future measurements of the neutrinos may be able to identify the Galactic diffuse component and further shed light on the problem of the knee of cosmic rays.