  (abridged) We have analyzed the properties of the rest-frame optical emission
lines of a sample of 53 intensely star forming galaxies at z=1.3 to 2.7
observed with SINFONI on the ESO-VLT. We find large velocity dispersions in the
lines, sigma=30-250 km/s. Our data agree well with simulations where we applied
beam-smearing and assumed a scaling relation of the form: velocity dispersion
is proportional to the square root of the star-formation intensity
(star-formation rate per unit area). We conclude that the dispersions are
primarily driven by star formation. To explain the high surface brightness and
optical line ratios, high thermal pressures in the warm ionized medium, WIM,
are required (log P/k (K/cm^3)>~6-7). Such thermal pressures in the WIM are
similar to those observed in nearby starburst galaxies, but occur over much
larger physical scales. Moreover, the relatively low ionization parameters
necessary to fit the high surface brightnesses and optical line ratios suggest
that the gas is not only directly associated with regions of star formation,
but is wide spread throughout the general ISM. Thus the optical emission line
gas is a tracer of the large scale dynamics of the bulk of the ISM. We present
a simple model for the energy input from young stars in an accreting galaxy, to
argue that the intense star-formation is supporting high turbulent pressure,
which roughly balances the gravitational pressure and thus enables distant gas
accreting disks to maintain a Toomre disk instability parameter Q~1. For a star
formation efficiency of 3%, only 5-15% of the mechanical energy from young
stars that is deposited in the ISM is needed to support the level of turbulence
required for maintaining this balance. Since this balance is maintained by
energy injected into the ISM by the young stars themselves, this suggests that
star formation in high redshift galaxies is self-regulating.
