We analyze the physical conditions in the interstellar gas of 11 actively star-forming galaxies at z~2, based on integral-field spectroscopy from the ESO-VLT and HST/NICMOS imaging. We concentrate on the high H-alpha surface brightnesses, large line widths, line ratios and the clumpy nature of these galaxies. We show that photoionization calculations and emission line diagnostics imply gas pressures and densities that are similar to the most intense nearby star-forming regions at z=0 but over much larger scales (10-20 kpc). A relationship between surface brightness and velocity dispersion can be explained through simple energy injection arguments and a scaling set by nearby galaxies with no free parameters. The high velocity dispersions are a natural consequence of intense star formation thus regions of high velocity dispersion are not evidence for mass concentrations such as bulges or rings. External mechanisms like cosmological gas accretion generally do not have enough energy to sustain the high velocity dispersions. In some cases, the high pressures and low gas metallicites may make it difficult to robustly distinguish between AGN ionization cones and star formation, as we show for BzK-15504 at z=2.38. We construct a picture where the early stages of galaxy evolution are driven by self-gravity which powers strong turbulence until the velocity dispersion is high. Then massive, dense, gas-rich clumps collapse, triggering star formation with high efficiencies and intensities as observed. At this stage, the intense star formation is likely self-regulated by the mechanical energy output of massive stars.
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