MAP estimations of the sub-beam N-PDF parameters across our M51 test region. Top, from left to right : mean column density of the LN part of N-PDF (N₀ ), the pixel area filling factor (η) and the average gas density (including blank sky contributions). Bottom : width of the LN (σ), the column density of transition between the LN and PL parts of the N-PDF (N_thresh) and the PL index (α). Red contours in each panel indicate ¹³CO(J = 1 → 0) integrated intensities of 4 and 12 K km s⁻¹ (dashed and solid contours, respectively). The white arrow indicates the direction to the galactic centre. To first order, the gas is denser and more gravitationally unstable inside the spiral arm than outside it.