Larson's scaling laws, and the gravitational instability of clumpy discs at high redshift

Gravitational instabilities play a primary role in shaping the clumpy structure and powering the star formation activity of gas-rich high-redshift galaxies. Here we analyse the stability of such systems, focusing on the size and mass ranges of unstable regions in the disc. Our analysis takes into account the mass-size and linewidth-size scaling relations observed in molecular gas, originally discovered by Larson. We show that such relations can have a strong impact on the size and mass of star-forming clumps, as well as on the stability properties of the disc at all observable scales, making the classical Toomre parameter a highly unreliable indicator of gravitational instability. For instance, a disc with Q=1 can be far from marginal instability, while a disc with Q<<1 can be marginally unstable. Our work raises an important caveat: if clumpy discs at high redshift have scale-dependent surface densities and velocity dispersions, as implied by the observed clump scaling relations, then we cannot thoroughly understand their stability and star formation properties unless we perform multi-scale observations. This will soon be possible thanks to dedicated ALMA surveys, which will explore the physical properties of super-giant molecular clouds at the peak of cosmic star formation and beyond.