Initial gradient in specific angular momentum ℓ for our 5 simulations (thick lines, ranked from coldest to hottest) compared to the Keplerian case. The width of the density “jump” region σ_j is adjusted in two steps. First, the critical value for which the global minimum in ∂_rℓ is exactly 0 (thin solid lines) is derived. Any value would give rise to a rotationally unstable region, characterized by ∂_rℓ < 0. An arbitrary5% margin was applied in our runs (thick dashed lines).