  The Metis coronagraph is one of the remote sensing instruments hosted on
board the ESA/NASA Solar Orbiter mission. Metis is devoted to carry out the
first simultaneous imaging of the solar corona in both visible light (VL) and
ultraviolet (UV). High-energy particles penetrate spacecraft materials and may
limit the performance of on-board instruments. A study of galactic cosmic-ray
(GCR) tracks observed in the first VL images gathered by Metis during the
commissioning phase for a total of 60 seconds of exposure time is presented
here. A similar analysis is planned for the UV channel. A prediction of the GCR
flux up to hundreds of GeV is made here for the first part of the Solar Orbiter
mission to study the Metis coronagraph performance. GCR model predictions are
compared to observations gathered on board Solar Orbiter by the EPD/HET
experiment in the range 10 MeV-100 MeV in the summer 2020 and with previous
measurements. Estimated cosmic-ray fluxes above 70 MeV n$^{-1}$ have been also
parameterized and used for Monte Carlo simulations aiming at reproducing the
cosmic-ray track observations in the Metis coronagraph VL images. The same
parameterizations can also be used to study the performance of other detectors.
By comparing observations of cosmic-ray tracks in the Metis VL images with
FLUKA Monte Carlo simulations of cosmic-ray interactions in the VL detector, it
is found that cosmic rays fire a fraction of the order of 10$^{-4}$ of the
whole image pixel sample. Therefore, cosmic rays do not affect sensibly the
quality of Metis VL images. It is also found that the overall efficiency for
cosmic-ray identification in the Metis VL images is approximately equal to the
contribution of Z$>$2 particles. As a result, the Metis coronagraph may play
the role of a proton monitor for long-term GCR variations during the overall
mission duration.
