a), b) Two examples of the (T_colour, β_colour) distributions for the observations simulated in the Planck-HFI and IRAS 100 μm bands for the central pixels of the series of filaments described in Table 3. The red squares show the results of the fits for the clouds described in Sect. 3.1, containing DHGL grain populations and illuminated by the ISRF, extinguished or not, without noise (10 clouds  ×  7 radiation fields). The black crosses show the same after adding the estimated statistical noise to the simulated data (the length of the arms of the black crosses are the error bars). The green dashed lines are the power-law fits of these two particular realisations and the green solid line corresponds to the average relation over the 1000 cases. For clarity, the plot includes only every 50th of the 14   000 points (see Sect. 3.2 for details). The black line is the fit to the observed β_colour − T_colour relation measured by Planck Collaboration (2011c) towards cold clumps with Planck-HFI and IRAS 100 μm bands. c) Probability distribution of the B parameter obtained from 1000 cloud samples, similar to the two examples in the upper frames (with B defined as , see Sect. 3.2 for details).