Normalised SG kernels, $\pi d_g{H}_g^2\mathrm{K}$, for light (top) and massive (bottom) discs. For light discs, the prescriptions of Müller et al. (2012) and Rendon Restrepo & Barge (2023) are insensitive to the Toomre’s parameter. This is in contrast with the Bessel prescription, which scale as 1/Q_g in the limit of massive discs. When a constant SL prescription is used, the kernel vanishes at short distances, whereas for a vanishing SL, the kernel diverges, suggesting an overestimation of SG. The Bessel prescription is the unique prescription that is simultaneously inversely proportional to Q_g for massive discs, does not vanish at the singularity and permits a smooth transition between massive and light discs.