Structure formation in gas-rich galactic discs with finite thickness: from discs to rings

Gravitational instabilities play an important role in structure formation of gas-rich high-redshift disc galaxies. In this paper, we revisit the axisymmetric perturbation theory and the resulting growth of structure by taking the realistic thickness of the disc into account. In the unstable regime, which corresponds for thick discs to a Toomre parameter below the critical value Q_0,crit = 0.696, we find a fastest growing perturbation wavelength that is always a factor 1.93 times larger than in the classical razor-thin disc approximation. This result is independent of the adopted disc scaleheight and by this independent of temperature and surface density. In order to test the analytical theory, we compare it with a high-resolution hydrodynamical simulation of an isothermal gravitationally unstable gas disc with the typical vertical sech^2 density profile and study its break up into rings that subsequently fragment into dense clumps. In the first phase, rings form, that organize themselves discretely, with distances corresponding to the local fastest growing perturbation wavelength. We find that the disc scaleheight has to be resolved initially with five or more grid cells in order to guarantee proper growth of the ring structures, which follow the analytical prediction. These rings later on contract to a thin and dense line, while at the same time accreting more gas from the inter-ring region. It is these dense, circular filaments, that subsequently fragment into a large number of clumps. Contrary to what is typically assumed, the clump sizes are therefore not directly determined by the fastest growing wavelength.