Constraint On The Velocity Dependent Dark Matter Annihilation Cross Section From Fermi-Lat Observations Of Dwarf Galaxies

The gamma-ray observation of dwarf spheroidal satellites (dSph's) is an ideal approach for probing the dark matter (DM) annihilation signature. The latest Fermi-LAT dSph searches have set stringent constraints on the velocity independent annihilation cross section in the small DM mass range, which gives very strong constraints on the scenario to explain the AMS-02 positron excess by DM annihilation. However, the dSph constraints would change in the velocity dependent annihilation scenarios, because the velocity dispersion in the dSph's varies from that in the Milky Way. In this work, we use a likelihood map method to set constraints on the velocity dependent annihilation cross section from the Fermi-LAT observation of six dSph's. We consider three typical forms of the annihilation cross section, i.e. p-wave annihilation, Sommerfeld enhancement, and Breit-Wigner resonance. For the p-wave annihilation and Sommerfeld enhancement, the dSph limits would become much weaker and stronger compared with those for the velocity independent annihilation, respectively. For the Breit-Wigner annihilation, the dSph limits would vary depending on the model parameters. We show that the scenario to explain the AMS-02 positron excess by DM annihilation is still viable in the velocity dependent cases.