Column density τ₈₅₀ as a function of effective temperature T for four R09 cores with clear linear relations. Left panels: column-density map with the core indicated by black contours. The R09 core number is given in the top left corner. Other R09 cores in the field are indicated by grey contours. Right panels: each data point corresponds to one pixel in the HP2 maps. The black line is a power-law fit to the data points. The blue line is a power-law function with the exponent k_Fisher and the normalisation chosen such that the function passes through the reference data point indicated by a blue circle.