A Molecular Line Scan in the Hubble Deep Field North: Constraints on the CO Luminosity Function and the Cosmic H2 Density

We present direct constraints on the CO luminosity function at high redshift and the resulting cosmic evolution of the molecular gas density, $\rho_{\rm H2}$(z), based on a blind molecular line scan in the Hubble Deep Field North (HDF-N) using the IRAM Plateau de Bure Interferometer. Our line scan of the entire 3mm window (79-115 GHz) covers a cosmic volume of ~7000 Mpc$^3$, and redshift ranges z<0.45, 1.01<z<1.89 and z>2. We use the rich multiwavelength and spectroscopic database of the HDF-N to derive some of the best constraints on CO luminosities in high redshift galaxies to date. We combine the blind CO detections in our molecular line scan (presented in a companion paper) with stacked CO limits from galaxies with available spectroscopic redshifts (slit or mask spectroscopy from Keck and grism spectroscopy from HST) to give first blind constraints on high-z CO luminosity functions and the cosmic evolution of the H2 mass density $\rho_{\rm H2}$(z) out to redshifts z~3. A comparison to empirical predictions of $\rho_{\rm H2}$(z) shows that the securely detected sources in our molecular line scan already provide significant contributions to the predicted $\rho_{\rm H2}$(z) in the redshift bins <z>~1.5 and <z>~2.7. Accounting for galaxies with CO luminosities that are not probed by our observations results in cosmic molecular gas densities $\rho_{\rm H2}$(z) that are higher than current predictions. We note however that the current uncertainties (in particular the luminosity limits, number of detections, as well as cosmic volume probed) are significant, a situation that is about to change with the emerging ALMA observatory.