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 multiscale observations. This will soon be possible thanks to dedicated Atacama Large Millimeter/submillimeter Array surveys, which will explore the physical properties of supergiant molecular clouds at the peak of cosmic star formation and beyond.