True error σ on the stacked flux measurements as a function of the instrumental white noise level σ_inst. that is put on the image (here normalized to a “PSF” noise in mJy, i.e., the error on the flux measurement of a point source in the absence of confusion). We generated multiple simulations of the 250 μm maps using varying levels of white noise, and compute σ from the difference between the measured fluxes and their expected values. Left: evolution of the average total noise per source where N_stack is the number of stacked sources. This is the total error when extracting the flux of a single source on the map. When the instrumental noise (red line) is high, it dominates the error budget over the confusion noise. However, when reaching too low values, the measured total noise is dominated by the confusion noise σ_conf. (blue line). We fit this evolution as (orange line) to obtain σ_conf. = 4.6 mJy. The red circle marks the instrumental noise level reached in the real maps. Right: comparison between the estimated error from the stack residual σ_IMG and the true error σ. The points show the median of σ/σ_IMG, and the error bars are showing the 16th and 84th percentiles of the distribution. The green horizontal line is the line of perfect agreement, and the blue vertical line marks the confusion noise at 250 μm. The red circle marks the instrumental noise level reached in the real maps.