Euclid preparation: XXI. Intermediate-redshift contaminants in the
  search for $z>6$ galaxies within the Euclid Deep Survey
  (Abridged) The Euclid mission is expected to discover thousands of z>6
galaxies in three Deep Fields, which together will cover a ~40 deg2 area.
However, the limited number of Euclid bands and availability of ancillary data
could make the identification of z>6 galaxies challenging. In this work, we
assess the degree of contamination by intermediate-redshift galaxies (z=1-5.8)
expected for z>6 galaxies within the Euclid Deep Survey. This study is based on
~176,000 real galaxies at z=1-8 in a ~0.7 deg2 area selected from the
UltraVISTA ultra-deep survey, and ~96,000 mock galaxies with 25.3$\leq$H<27.0,
which altogether cover the range of magnitudes to be probed in the Euclid Deep
Survey. We simulate Euclid and ancillary photometry from the fiducial, 28-band
photometry, and fit spectral energy distributions (SEDs) to various
combinations of these simulated data. Our study demonstrates that identifying
z>6 with Euclid data alone will be very effective, with a z>6 recovery of
91(88)% for bright (faint) galaxies. For the UltraVISTA-like bright sample, the
percentage of z=1-5.8 contaminants amongst apparent z>6 galaxies as observed
with Euclid alone is 18%, which is reduced to 4(13)% by including ultra-deep
Rubin (Spitzer) photometry. Conversely, for the faint mock sample, the
contamination fraction with Euclid alone is considerably higher at 39%, and
minimized to 7% when including ultra-deep Rubin data. For UltraVISTA-like
bright galaxies, we find that Euclid (I-Y)>2.8 and (Y-J)<1.4 colour criteria
can separate contaminants from true z>6 galaxies, although these are applicable
to only 54% of the contaminants, as many have unconstrained (I-Y) colours. In
the most optimistic scenario, these cuts reduce the contamination fraction to
1% whilst preserving 81% of the fiducial z>6 sample. For the faint mock sample,
colour cuts are infeasible.
