The solar disk at high energies

High energy cosmic rays "illuminate" the Sun and produce an image that could be observed in up to five different channels: a cosmic ray shadow (whose energy dependence has been studied by HAWC); a gamma ray flux (observed at $E\le 200$ GeV by Fermi-LAT); a muon shadow (detected by ANTARES and IceCube); a neutron flux (undetected, as there are no hadronic calorimeters in space); and a flux of high energy neutrinos. Since these signals are correlated, the ones already observed can be used to reduce the uncertainty in the still undetected ones. Here we define a simple set up that uses the Fermi-LAT and HAWC observations to imply very definite fluxes of neutrons and neutrinos from the solar disk. In particular, we provide a fit of the neutrino flux at 10 GeV-10 TeV that includes its dependence on the zenith angle and on the period of the solar cycle. This flux represents a neutrino floor in indirect dark matter searches. We show that in some benchmark models the current bounds on the dark matter-nucleon cross section push the solar signal below this neutrino floor.