Massive galaxies in the young Universe, ten billion years ago, formed stars at surprising intensities. Although this is commonly attributed to violent mergers, the properties of many of these galaxies are incompatible with such events, showing gas-rich, clumpy, extended rotating disks not dominated by spheroids. Cosmological simulations and clustering theory are used to explore how these galaxies acquired their gas. Here we report that they are 'stream-fed galaxies', formed from steady, narrow, cold gas streams that penetrate the shock-heated media of massive dark matter haloes. A comparison with the observed abundance of star-forming galaxies implies that most of the input gas must rapidly convert to stars. One-third of the stream mass is in gas clumps leading to mergers of mass ratio greater than 1:10, and the rest is in smoother flows. With a merger duty cycle of 0.1, three-quarters of the galaxies forming stars at a given rate are fed by smooth streams. The rarer, submillimetre galaxies that form stars even more intensely are largely merger-induced starbursts. Unlike destructive mergers, the streams are likely to keep the rotating disk configuration intact, although turbulent and broken into giant star-forming clumps that merge into a central spheroid. This stream-driven scenario for the formation of discs and spheroids is an alternative to the merger picture.

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.