Diffusion of Cosmic Antiprotons Generated throughout the Dark Matter Halo -- A Semi-Analytical Solution for a Linear Galactic Wind Model

The public GALPROP code gives a fully numerical solution for the spectrum of cosmic rays propagating through a linear Galactic wind directed outwards from the Galactic plane in the framework of a cylindrical diffusion model. Alternatively, for the linear Galactic wind case, we present a semi-analytical solution of the two-zone cylindrical model which describes the spectrum of cosmic-ray antiprotons produced from the primary sources throughout the dark matter halo. While the secondary antiprotons can be generated by, e.g., the GALPROP WebRun, consistently using this semi-analytical solution for the primary ones would be helpful to build a suited dark matter (DM) model, which may be sophisticated, and then to perform a statistical analysis when confronting with data. As an example, using the obtained formula, we study the possible DM signal, through the channel $\text{DM DM} \to {\bar b}b$, and its constraint from the measurement of the AMS-02 antiproton-to-proton ratio. The indication of the DM signal is discussed. The advantage of the semi-analytical approach and its comparison with the GALPROP model are presented.