  Electromagnetically neutral dark sector particles may directly couple to the
photon through higher dimensional effective operators. Considering electric and
magnetic dipole moment, anapole moment, and charge radius interactions, we
derive constraints from stellar energy loss in the Sun, horizontal branch and
red giant stars, as well as from cooling of the proto-neutron star of SN1987A.
We provide the exact formula for in-medium photon-mediated pair production to
leading order in the dark coupling, and compute the energy loss rates
explicitly for the most important processes, including a careful discussion on
resonances and potential double counting between the processes. Stringent
limits for dark states with masses below $3\,$keV ($40\,$MeV) arise from red
giant stars (SN1987A), implying an effective lower mass-scale of approximately
$10^9\,$GeV ($10^7\,$GeV) for mass-dimension five, and $100\,$GeV ($2.5\,$TeV)
for mass-dimension six operators as long as dark states stream freely; for the
proto-neutron star, the trapping of dark states is also evaluated. Together
with direct limits previously derived by us in Chu et al. (2018), this provides
the first comprehensive overview of the viability of effective electromagnetic
dark-state interactions below the GeV mass-scale.
