  We define a minimal model of dark matter with a fermion singlet $\chi$
coupled to the visible sector through the Higgs portal and with a heavy Dirac
neutrino $N$ that opens the annihilation channel $\chi \chi \to N \nu$. The
model provides the observed relic abundance consistently with bounds from
direct searches and implies a monochromatic neutrino signal at 10 GeV-1 TeV in
indirect searches. In particular, we obtain the capture rate of $\chi$ by the
Sun and show that the signal could be above the "neutrino floor" produced by
cosmic rays showering in the solar surface. In most benchmark models this solar
astrophysical background is above the expected dark matter signal, so the model
that we propose is a canonical example of WIMP not excluded by direct searches
that could be studied at neutrino telescopes and also at colliders.
