The figure graphs the critical length l_⋆ of Eq. (D.4) as a function of the cylindrical radius, R. The Jeans lengths λ_J are shown in blue. The dotted line has λ_J= constant, the central value. The solid blue line recomputes the Jeans length using the local density ρ(R, 0). The dot-dash blue line is the situation when both the disc and halo are live components. Notice how l_⋆ ≈ λ_J around the origin. When l_⋆ <  λ_J, the differential rotation contributes to erode a fragmentation mode.