Probability distribution functions (PDFs) of the column density for G0.253+0.016, assuming a value of β = 1.75. The black line shows the PDF for the combined image (4.3′′ × 2.7′′ resolution, or 0.18 × 0.11 pc for d = 8.4 kpc), and the grey line the SCUBA-only PDF (8′′ or 0.33 pc resolution). The left y-axis shows the number of pixels per logarithmic bin N_pix, and the right y-axis is the normalised probability p(η). The top x-axis is displays the dimensionless parameter η = ln(N/ ⟨ N ⟩). The dashed line shows the column density corresponding to the 3σ noise level, assuming a temperature of 30 K. The Poisson errors are shown as error bars. The grey filled area corresponds to a by-eye fit to the combined PDF, giving the fit parameters σ_η, describing the PDF width, and ⟨ N_H2 ⟩, the average density, whose values are shown in the figure.