Until now there is no experimental evidence to prove the existence of a supersymmetric Dark Matter candidate. We have developed a tool applying the Chi2 least method to constrain the Dark Matter particle models by confronting the effective field theory with data from indirect detection, direct detection and collider-based experiments and relic density. We found most of the parameter space in the low mass range has been excluded out in several models. The velocity-dependent annihilating Dark Matter candidates could not been ruled out by the existing data, and we constrain this type of models by taking into account the Sommerfeld Enhanced self-annihilation and inverse Compton scattering to fit the FermiLAT IGRB data. Additional constraint from the CMB data helps to exclude a large area in the parameter space. We make a prediction of the photon flux from systems with different velocity dispersion profiles, this could be a tool to rule out the p-wave Dark Matter particle candidate or reveal its properties with only astrophysical data if we could get higher resolutions in the future to observe the dSphs and the other targets. A dynamical solution to the Boltzmann Equation is accomplished to show a different freeze-out scenario for a dark sector with multiple particles.
