  High spatial and spectral resolution observations of star formation and
kinematics in early galaxies have shown that two-thirds are massive rotating
disk galaxies with the remainder being less massive non-rotating objects. The
line of sight averaged velocity dispersions are typically five times higher
than in today's disk galaxies. This has suggested that
gravitationally-unstable, gas-rich disks in the early Universe are fuelled by
cold, dense accreting gas flowing along cosmic filaments and penetrating hot
galactic gas halos. However these accreting flows have not been observed, and
cosmic accretion cannot power the observed level of turbulence. Here we report
on a new sample of rare high-velocity-dispersion disk galaxies we have
discovered in the nearby Universe where cold accretion is unlikely to drive
their high star-formation rates. We find that the velocity dispersion is most
fundamentally correlated with their star-formation rates, and not their mass
nor gas fraction, which leads to a new picture where star formation itself is
the energetic driver of galaxy disk turbulence at all cosmic epochs.
