Ratios r_peak/r_ns (thick solid lines) and r_∇/r_ns (thin dotted lines) depending on the coefficients (α, β) that define the cooling function in Eq. (1). The contour lines are calculated for γ = 4/3 in spherical geometry, with r_sh/r_ns = 10, without dissociation (ε = 0). The values of r_peak/r_ns and r_∇/r_ns are indicated with the same colour code. The cooling parameters (α, β) = (3/2, 5/2), (6, 1) and (5, 6) used in Fig. 3 are indicated with crosses for reference and are connected by grey lines. The black dotted line marks the threshold β = α above which the advection time from r_peak to r_ns is finite and r_∇ = r_ns.