We use the first systematic data sets of CO molecular line emission in z ∼ 1-3 normal star-forming galaxies (SFGs) for a comparison of the dependence of galaxy-averaged star formation rates on molecular gas masses at low and high redshifts, and in different galactic environments. Although the current high-z samples are still small and biased towards the luminous and massive tail of the actively star-forming 'main-sequence', a fairly clear picture is emerging. Independent of whether galaxy-integrated quantities or surface densities are considered, low-and high-z SFG populations appear to follow similar molecular gas-star formation relations with slopes 1.1 to 1.2, over three orders of magnitude in gas mass or surface density. The gas-depletion time-scale in these SFGs grows from 0.5 Gyr at z ∼ 2 to 1.5 Gyr at z ∼ 0. The average corresponds to a fairly low star formation efficiency of 2 per cent per dynamical time. Because star formation depletion times are significantly smaller than the Hubble time at all redshifts sampled, star formation rates and gas fractions are set by the balance between gas accretion from the halo and stellar feedback.In contrast, very luminous and ultraluminous, gas-rich major mergers at both low and high z produce on average four to 10 times more far-infrared luminosity per unit gas mass. We show that only some fraction of this difference can be explained by uncertainties in gas mass or luminosity estimators; much of it must be intrinsic. A possible explanation is a top-heavy stellar mass function in the merging systems but the most likely interpretation is that the star formation relation is driven by global dynamical effects. For a given mass, the more compact merger systems produce stars more rapidly because their gas clouds are more compressed with shorter dynamical times, so that they churn more quickly through the available gas reservoir than the typical normal disc galaxies. When the dependence on galactic dynamical Based on observations with the Plateau de Bure millimetre interferometre, operated by the Institute for Radio Astronomy in the Millimetre Range (IRAM), which is funded by a partnership of INSU/CNRS (France), MPG (Germany) and IGN (Spain).

This paper provides an update of our previous scaling relations (Genzel et al. 2015) between galaxy integrated molecular gas masses, stellar masses and star formation rates, in the framework of the star formation main-sequence (MS), with the main goal to test for possible systematic effects. For this purpose our new study combines three independent methods of determining molecular gas masses from CO line fluxes, far-infrared dust spectral energy distributions, and ~1mm dust photometry, in a large sample of 1444 star forming galaxies (SFGs) between z=0 and 4. The sample covers the stellar mass range log(M*/M)=9.0-11.8, and star formation rates relative to that on the MS, δMS=SFR/SFR(MS), from 10 -1.3 to 10 2.2 . Our most important finding is that all data sets, despite the different techniques and analysis methods used, follow the same scaling trends, once method-to-method zero point offsets are minimized and uncertainties are properly taken into account. The molecular gas depletion time tdepl, defined as the ratio of molecular gas mass to star formation rate, scales as (1+z) -0.6 × (δMS) -0.44 , and is only weakly dependent on stellar mass. The ratio of molecular-to-stellar mass μgas depends on (1+z) 2.5 × (δMS) 0.52 × (M*) -0.36 , which tracks the evolution of the specific star formation rate. The redshift dependence of μgas requires a curvature term, as may the mass-dependences of tdepl and μgas. We find no or only weak correlations of tdepl and μgas with optical size R or surface density once one removes the above scalings, but we caution that optical sizes may not be appropriate for the high gas and dust columns at high-z.

We present PHIBSS, the IRAM Plateau de Bure high-z blue sequence CO 3-2 survey of the molecular gas properties in normal star forming galaxies (SFGs) near the cosmic star formation peak. PHIBSS provides 52 CO detections in two redshift slices at z~1.2 and 2.2, with log(M * (M  )) ≥10.4 and log(SFR(M  /yr)) ≥ 1.5.Including a correction for the incomplete coverage of the M * -SFR plane, we infer average gas fractions of ~0.33 at z~1.2 and ~0.47 at z~2.2. Gas fractions drop with stellar mass, in agreement with cosmological simulations including strong star formation feedback. Most of the z~1-3 SFGs are rotationally supported turbulent disks. The sizes of CO and UV/optical emission are comparable. The molecular gasstar formation relation for the z=1-3 SFGs is near-linear, with a ~0.7 Gyrs gas depletion timescale; changes in depletion time are only a secondary effect. Since this timescale is much less than the Hubble time in all SFGs between z~0 and 2, fresh gas must be supplied with a fairly high duty cycle over several billion years. At given z and M * , gas fractions correlate strongly with the specific star formation rate. The variation of specific star formation rate between z~0 and 3 is mainly controlled by the fraction of baryonic mass that resides in cold gas.

2Stars form from cold molecular interstellar gas. Since this is relatively rare in the local Universe, galaxies like the Milky Way form only a few new stars per year. Typical massive galaxies in the distant Universe formed stars an order of magnitude more rapidly 1,2 . Unless star formation was significantly more efficient, this difference suggests that young galaxies were much more gas rich. Molecular gas observations in the distant Universe have so far been largely restricted to very luminous, rare objects, including mergers and quasars 3,4,5 . Here we report the results of a systematic survey of molecular gas in samples of typical massive star forming galaxies at ~1.2 and 2.3, when the Universe was 40% and 24% of its current age. Our measurements provide empirical evidence that distant star forming galaxies indeed were gas rich, and that the star formation efficiency is not strongly dependent on cosmic epoch. The average fraction of cold gas relative to total galaxy baryonic mass at z= 2.3 and z=1.2 is ~44% and 34%, three to ten times higher than in today's massive spiral galaxies 6 . The slow decrease between z~2 and 1 probably requires a mechanism of semi-continuous replenishment of fresh gas to the young galaxies.Direct observations of molecular gas in galaxies as a function of cosmic epoch are required to understand how galaxies have turned their gas into stars. To explore the evolution of cold gas fractions, we selected two samples of star forming galaxies (SFGs) spanning similar ranges in stellar mass and star formation rates: one at redshift z~1.2 (t o~5 .5 Gyr after the Big Bang) and the other at z~2.3 (t 0~3 Gyr). With recent improvements in instrumental sensitivity we can now sample the massive tail of the 3 typical, or 'normal' star forming galaxies in this epoch (Supplementary Information, section 1). These 'main-sequence' galaxies are believed to have high (40-70%) duty cycles of star formation, and most are probably not 'starbursts' in a brief period of activity, such as major dissipative mergers 1,2 . Figure 1 displays the source-integrated spectra in the CO J=3-2 transition for 19 of the galaxies observed, 10 at z~2 and 9 at z~1. For 14 SFGs we have solid (>4σ) detections in both redshift ranges, and for the first time for z>2 SFGs. In 5 galaxies the emission is marginally or not detected, or may be continuum rather than line emission. Table 1 summarizes the observed and derived galaxy properties.For EGS1305123 (z=1.12) and EGS1207881 (z=1.17) we also obtained high quality spatially resolved maps with FWHM resolutions of 0.65" and 1". Figure 2c shows the integrated CO 3-2 emission in EGS1305123, superposed on an optical image from the Hubble Space Telescope (HST). This map resolves for the first time the cold molecular gas distribution in a clearly non-merging high-z SFG. This system looks like a scaled-up version (in terms of star formation rate and gas mass) of normal z~0 gas rich disk galaxies. In the optical images EGS1305123 is a nearly face-on, large spiral disk. The clumpy CO emissio...