  To illustrate the complementarity of the linear collider and astrophysics
bounds on the light (MeV-scale mass) dark matter (DM), we study the constraints
on the magnetic dipole DM from the DM-electron interactions at the proposed
International Linear Collider (ILC) and in supernova (SN) 1987A. We in
particular focus on the $e^+ e^-$ annihilation which is the common process for
producing DM pairs both at the ILC and in the SN. We estimate the bounds on the
DM magnetic dipole moment from the mono-photon signals at the ILC and also from
the energy loss rate due to the freely streaming DM produced in the SN. The SN
bounds can be more stringent than those from the ILC by as much as a factor
${\cal O}(10^5)$ for a DM mass below $10^2$ MeV. For larger DM masses, on the
other hand, SN rapidly loses its sensitivity and the collider constraints can
complement the SN constraints.
