The Properties of the Star-Forming Interstellar Medium at z=0.8-2.2 from
  HiZELS - II: Star-Formation and Clump Scaling Laws in Gas Rich, Turbulent
  Disks
  We present adaptive optics assisted integral field spectroscopy of nine
Halpha-selected galaxies at z=0.84--2.23 selected from the HiZELS narrow-band
survey. Our observations map the star-formation and kinematics of these
representative star-forming galaxies on ~kpc-scales. We demonstrate that within
the ISM of these galaxies, the velocity dispersion of the star-forming gas
(\sigma) follows a scaling relation \sigma\propto\Sigma_SFR^(1/n)+constant
(where \Sigma_SFR is the star formation surface density and the constant
includes the stellar surface density). Assuming the disks are marginally stable
(Toomre Q=1), we show that this follows from the Kennicutt-Schmidt relation
(\Sigma_SFR = A\Sigma_gas^n), and we use the data to derive best fit parameters
of n=1.34+/-0.15 and A=3.4_(-1.6)^(+2.5)x10^(-4)Mo/yr/kpc^2, consistent with
the local relation and implying cold molecular gas masses of M_gas=10^(9-10)Mo
and molecular gas fractions M_gas/(M_gas+Mstars)=0.3+/-0.1, with a range of
10-75%. These values confirm the high gas fractions for high-redshift
star-forming galaxies, independent of CO-H_2 conversion factor. We also
identify eleven ~kpc-scale star-forming regions (clumps) within our sample and
show that their sizes are comparable to the wavelength of the fastest growing
unstable mode. The luminosities and velocity dispersions of these clumps follow
the same scaling relations as local HII regions, although their star formation
densities are a factor 15+/-5x higher than typically found locally. We discuss
how the clump properties are related to the disk, and show that their high
masses and luminosities are a consequence of the high disk surface density.
