Fig. 4: Solution of the transcendental equations predicting the max-size ratio (general atmospheric conditions).

For given environmental conditions, parametrized in terms of the dimensionless Galileo number Ga^(f) and grain-atmosphere density ratio s, reptation is only possible in a specific range of coarse-grain diameters d^(c), as encoded in the width of the coarse-grain peak of the surface GSD. For sufficiently large fine grains (s^1/4Ga^(f) ≳ 200), the analytical scaling function in Eq. (1) (solid line), implicitly predicting the max-size ratio \(\max ({d}^{({{{{{{{\rm{c}}}}}}}})})/\!\max ({d}^{({{{{{{{\rm{f}}}}}}}})})\), provides a perfect match to the full theory (symbols) for various combinations of Ga^(f) and s. Note the higher numerical sensitivity to s rather than Ga^(f) (inset) and the breakdown of the scaling for s^1/4Ga^(f) ≲ 200. Also, H depends on the planetary conditions primarily via s and the dimensionless settling velocity V_s.