Empirical predictions for (sub-)millimeter line and continuum deep
  fields
  [abridged] Modern (sub-)millimeter/radio interferometers will enable us to
measure the dust and molecular gas emission from galaxies that have
luminosities lower than the Milky Way, out to high redshifts and with
unprecedented spatial resolution and sensitivity. This will provide new
constraints on the star formation properties and gas reservoir in galaxies
throughout cosmic times through dedicated deep field campaigns targeting the
CO/[CII] lines and dust continuum emission. In this paper, we present empirical
predictions for such (sub-)millimeter line and continuum deep fields. We base
these predictions on the deepest available optical/near-infrared ACS and NICMOS
data on the Hubble Ultra Deep Field. Using a physically-motivated spectral
energy distribution model, we fit the observed optical/near-infrared emission
of 13,099 galaxies with redshifts up to z=5, and obtain median likelihood
estimates of their stellar mass, star formation rate, dust attenuation and dust
luminosity. We derive statistical constraints on the dust emission in the
infrared and (sub-)millimeter which are consistent with the observed
optical/near-infrared emission in terms of energy balance. This allows us to
estimate, for each galaxy, the (sub-)millimeter continuum flux densities in
several ALMA, PdBI/NOEMA and JVLA bands. Using empirical relations between the
observed CO/[CII] line luminosities and the infrared luminosity, we infer the
flux of the CO(1-0) and [CII] lines from the estimated infrared luminosity of
each galaxy in our sample. We then predict the fluxes of higher CO transition
lines CO(2-1) to CO(7-6) bracketing two extreme gas excitation scenarios. We
use our predictions to discuss possible deep field strategies with ALMA. The
predictions presented in this study will serve as a direct benchmark for future
deep field campaigns in the (sub-)millimeter regime.
