Contours of integrated intensities and integrated intensity ratios to estimate gas density and methanol column density. Left: contours of the integrated intensity W(A⁺ 2_0,2 → 1_0,1) (vertical dashed lines) and the integrated intensity ratio W(E₂)/W(E₁) (horizontal dashed lines) intersect on a grid of RADEX models to yield gas density n_H2 and N(A-CH₃OH) in offsets from 0″ to +135″ in Barnard 1b. Right: contours of the integrated intensity W(E₂) (vertical dashed lines) and the contours of the integrated intensity ratio W(A⁺ 2_0,2 → 1_0,1)/W(A⁺ 1_0,1 → 0_0,0) (horizontal dashed lines) intersect on a grid of RADEX models to yield gas density n_H2 and N(E-CH₃OH) in offsets from +150″ to +210″ in Barnard 1b.