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.