  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.
