  Interactions between dark matter (DM) and relativistic particles at early
times suppress structure formation on small scales. In particular, the
scattering process transfers heat and momentum from radiation to DM, ultimately
reducing the abundance of low-mass DM halos and the dwarf galaxies they host.
Herein, we derive limits on DM--photon and DM--neutrino scattering cross
section using the Milky Way (MW) satellite galaxy population. We consider
temperature-independent interactions parameterized by DM mass ($m_\chi$) and
DM--radiation interaction cross section ($\sigma_{\chi\text{--}i}$, where $i$
represents the target species). By requiring that the linear matter power
spectra are strictly less suppressed than in the case of a thermal-relic warm
DM, we derive the following $95\%$ upper limits at $m_\chi=1$ MeV:
$\sigma_{\chi\text{--}\gamma}<1.50\times10^{-38}\text{cm}^2$ and
$\sigma_{\chi\text{--}\nu}<2.41\times10^{-38}\text{cm}^2$. Our bounds on
$\sigma_{\chi\text{--}i}$ depend linearly on $m_\chi$ for $m_\chi \gtrsim
1~\mathrm{MeV}$ and improve upon previous limits by an order of magnitude. The
mass dependence of our limit approaches $m_\chi^3$ at lower masses due to the
effects of DM sound speed; at $m_{\chi}=100~\mathrm{keV}$, we arrive at an
upper limit over three orders of magnitude more stringent than achieved in
previous explorations. Upcoming dwarf galaxy surveys will further improve the
sensitivity of similar analyses, complementing laboratory and indirect
detection searches for DM--radiation interactions.
