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As a basic characteristic of cosmic ray (CR) propagation, the diffusive halocan advance our understanding of many CR-related studies and indirect darkmatter. The method to derive the halo size usually has degeneracy problems thusaffected by large uncertainties. The diffusion gamma ray from high-latitudeclouds might shed light on the halo size independently. Since the spatiallydependent propagation (SDP) model has a better agreement with the observed CRs,compared with conventional propagation model, in this work, we investigate thehalo thickness based on SDP model with Fermi-LAT $\rm\gamma$-ray observation onthe high- and intermediate-velocity clouds. As a result, in order not to exceedthe relative $\gamma$-ray emissivity in the high-latitude clouds, halothickness should be in the range of $\rm ~3.3\sim9~ kpc$. Moreover, the spatialmorphology of $\rm\gamma$-rays estimated based on SDP model under differentvalues of halo thickness are distinctive, which provides us a tool to determinethe halo size. We hope that our model could be tested and tuned bymulti-wavelength observations in the future.

Constraining the cosmic ray propagation halo thickness using Fermi-LAT observations of high-latitude clouds