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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 (σ) follows a scaling relation σ\proptoΣ_SFR^(1/n)+constant (where Σ_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 (Σ_SFR = AΣ_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.