Constraint on the velocity dependent dark matter annihilation cross section from gamma-ray and kinematic observations of ultrafaint dwarf galaxies

Searching for gamma rays from dwarf spheroidal galaxies (dSphs) is a promising approach to detect dark matter (DM) due to the high DM densities and low baryon components in dSphs. The Fermi-LAT observations from dSphs have set stringent constraints on the velocity independent annihilation cross section. However, the constraints from dSphs may change in velocity dependent annihilation scenarios because of the different velocity dispersions in galaxies. In this work, we study how to set constraints on the velocity dependent annihilation cross section from the combined Fermi-LAT observations of dSphs with the kinematic data. In order to calculate the gamma ray flux from the dSph, the correlation between the DM density profile and velocity dispersion at each position should be taken into account. We study such correlation and the relevant uncertainty from kinematic observations by performing a Jeans analysis. Using the observational results of three ultrafaint dSphs with large J-factors, including Willman 1, Reticulum II, and Triangulum II, we set constraints on the p-wave annihilation cross section in the Galaxy as an example.