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

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