emerge properly from the disc for $N_{\mathrm{J}} \geq 18$ grid cells per Jeans length, which corresponds to five cells per scaleheight at all radii. Too low resolution effectively raises the $Q$ of the disc numerically and spiral-like features appear, as expected for values $Q \geq Q_{\mathrm{crit}}$, where axisymmetric modes are stable but nonaxisymmetric modes can still grow. The isothermal EoS keeps the disc scaleheight constant and therefore ensures, that it is sufficiently resolved until the structures begin to grow.\
The disc is isothermal with $10^4$ K. However to ensure the Jeans condition for higher densities also at maximum resolution, we add an artificial pressure floor [@2010MNRAS.409.1088B; @Agertz:2009wd] $$T \geq \frac{G \; m_{\mathrm{H}}}{\upi \; k_{\mathrm{B}} \gamma}  N^{2} \Delta x_{\mathrm{min}}^{2} \; \rho,$$ where $m_{\mathrm{H}}$ is the atomic mass of hydrogen, $k_{\mathrm{B}}$ the Boltzmann constant, $\gamma = 1$ the adiabatic index, $\rho$ the density and $N=18$ the number of resolution elements per Jeans length for the smallest scales $\Delta x_{\mathrm{min}}$. This does not affect the global ring formation but determines the thickness and pressure in the collapsed high-density ring structures and by this regulates their fragmentation into clumps. The effect of such a pressure floor on the clump numbers, final sizes and their 