The elastic scattering between dark matter (DM) and radiation can potentially explain
small-scale observations that the cold dark matter faces as a challenge, as damping density
fluctuations via dark acoustic oscillations in the early universe erases small-scale structure.
We study a semi-analytical subhalo model for interacting dark matter with radiation, based on the
extended Press-Schechter formalism and subhalos' tidal evolution prescription. We also test the
elastic scattering between DM and neutrinos using observations of Milky-Way satellites from the
Dark Energy Survey and PanSTARRS1. We conservatively impose strong constraints on the DM-neutrino
scattering cross section of σ
DM–ν,n ∝ En
ν
(n = 0,2,4) at 95%
confidence level (CL), σ
DM–ν,0 < 10-32 cm2 (m
DM/
GeV), σ
DM–ν,2 < 10-43 cm2 (m
DM/
GeV)(Eν
/Eν
0)2 and σ
DM–ν,4 < 10-54 cm2 (m
DM
/GeV)(Eν
/Eν
0)4, where Eν
0 is the neutrino energy and Eν
0 is the
average momentum of relic cosmic neutrinos today, Eν
0 ≃ 6.1 K. By imposing a
satellite forming condition, we obtain the strongest upper bounds on the DM-neutrino cross section
at 95% CL, σ
DM–ν,0 < 4 × 10-34 cm2 (m
DM/
GeV), σ
DM–ν,2 < 10-46 cm2 (m
DM/
GeV)(Eν
/Eν
0)2 and σ
DM–ν,4 < 7 × 10-59
cm2 (m
DM/GeV)(Eν
/Eν
0)4.