Measuring galaxy environment with the synergy of future photometric and
  spectroscopic surveys
  We exploit the synergy between low-resolution spectroscopy and photometric
redshifts to study environmental effects on galaxy evolution in slitless
spectroscopic surveys from space. As a test case, we consider the future Euclid
Deep survey (~40deg$^2$), which combines a slitless spectroscopic survey
limited at H$\alpha$ flux $\geq5\times 10^{-17}$ erg cm$^{-2}$ s$^{-1}$ and a
photometric survey limited in H-band ($H\leq26$). We use Euclid-like galaxy
mock catalogues, in which we anchor the photometric redshifts to the 3D galaxy
distribution of the available spectroscopic redshifts. We then estimate the
local density contrast by counting objects in cylindrical cells with radius
from 1 to 10 h$^{-1}$Mpc over the redshift range 0.9<z<1.8. We compare this
density field with the one computed in a mock catalogue with the same depth as
the Euclid Deep survey (H=26) but without redshift measurement errors. We find
that our method successfully separates high from low density environments (the
last from the first quintile of the density distribution), with higher
efficiency at low redshift and large cell: the fraction of low density regions
mistaken by high density peaks is <1% for all scales and redshifts explored,
but for scales of 1 h$^{-1}$Mpc for which is a few percent. These results show
that we can efficiently study environment in photometric samples if
spectroscopic information is available for a smaller sample of objects that
sparsely samples the same volume. We demonstrate that these studies are
possible in the Euclid Deep survey, i.e. in a redshift range in which
environmental effects are different from those observed in the local universe,
hence providing new constraints for galaxy evolution models.
