Constraining Self-Interacting Dark Matter with Dwarf Spheroidal Galaxies and High-resolution Cosmological $N$-body Simulations

We study the density structures of dark matter subhalos for both cold dark matter and self-interacting dark matter models using high-resolution cosmological $N$-body simulations. We quantify subhalo's central density at 150 pc from the center of each subhalo at the classical dwarf spheroidal and ultrafaint dwarf scales. By comparing them with observations, we find that the self-interacting scattering cross-section of $\sigma/m<3\ \rm{cm^{2}g^{-1}}$ is favored. Due to the combination of hosts' tide and self-interactions, the central density of subhalos with small pericenter shows a noticeable difference between the cold and the self-interacting models, indicating that dwarf satellites with small pericenter are ideal sites to further constrain the nature of dark matter by future large spectroscopic surveys.