Constraints on dark matter self-interaction from velocity distribution function in isolated halos

Self-interactions facilitate inter-particle redistribution of energy within the dense regions of galactic halos, implying modifications in the density and velocity distribution of dark matter. Simulating dark-matter only isolated halos for a wide range of mass and specific self-scattering cross-sections, we make a systematic study of the impact of self-scattering on the velocity distribution profiles. We report a conservative bound on $\sigma/m$ $\leq 2.7 \rm cm^2/gm$ at $95\%$ C.L. from observations of rotation curves in Milky-Way size galaxies. Sub-leading bounds from LSB galaxy and clusters are also presented.