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We study the density structures of dark matter subhalos for both cold darkmatter and self-interacting dark matter models using high-resolutioncosmological $N$-body simulations. We quantify subhalo's central density at 150pc from the center of each subhalo at the classical dwarf spheroidal andultrafaint dwarf scales found in Milky-Way sized halos. By comparing them withobservations, 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 smallpericenter shows a noticeable difference between the cold and theself-interacting models, indicating that Milky-Way satellites with smallpericenter are ideal sites to further constrain the nature of dark matter byfuture large spectroscopic surveys.

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