Euclid: The selection of quiescent and star-forming galaxies using
  observed colours
  The Euclid mission will observe well over a billion galaxies out to $z\sim6$
and beyond. This will offer an unrivalled opportunity to investigate several
key questions for understanding galaxy formation and evolution. The first step
for many of these studies will be the selection of a sample of quiescent and
star-forming galaxies, as is often done in the literature by using well known
colour techniques such as the `UVJ' diagram. However, given the limited number
of filters available for the Euclid telescope, the recovery of such rest-frame
colours will be challenging. We therefore investigate the use of observed
Euclid colours, on their own and together with ground-based u-band
observations, for selecting quiescent and star-forming galaxies. The most
efficient colour combination, among the ones tested in this work, consists of
the (u-VIS) and (VIS-J) colours. We find that this combination allows users to
select a sample of quiescent galaxies complete to above $\sim70\%$ and with
less than 15$\%$ contamination at redshifts in the range $0.75<z<1$. For
galaxies at high-z or without the u-band complementary observations, the
(VIS-Y) and (J-H) colours represent a valid alternative, with $>65\%$
completeness level and contamination below 20$\%$ at $1<z<2$ for finding
quiescent galaxies. In comparison, the sample of quiescent galaxies selected
with the traditional UVJ technique is only $\sim20\%$ complete at $z<3$, when
recovering the rest-frame colours using mock Euclid observations. This shows
that our new methodology is the most suitable one when only Euclid bands, along
with u-band imaging, are available.
