TeV cosmic-ray proton and helium spectra in the myriad model Ⅱ

Recent observations show that the spectra of cosmic ray nuclei start to harden above ～ 102 GeV, which contradicts the conventional steady-state cosmic ray model. We had suggested that this anomaly is due to the propagation effect of cosmic rays released from local young cosmic ray sources; the total flux of cosmic rays should be computed with the Myriad Model, where a contribution from sources in the local catalog is added to the background. However, although the hardening could be elegantly explained in this model, the model parameters obtained from the fit are skewed toward a region with fast diffusion and a low supernova rate in the Galaxy, in disagreement with other observations. We further explore this model in order to set up a concordant picture. Two possible improvements related to cosmic ray sources are considered. First, instead of the usual axisymmetric disk model, we examine a spiral model for the source distribution. Second, for nearby and young sources which are necessary to explain the hardening, we allow for an energy-dependent escape. We find that a major improvement comes from incorporating an energy-dependent escape time for local sources, and with both modifications not only are the cosmic ray proton and helium anomalies resolved, but also the parameters attain values in a reasonable range compatible with other analyses.