Contours at 68% and 95% c.l. on the normalization, r_L, of the infrared L_500,tot−M₅₀₀ relation and on the external slope, β, of the spatial profile of the dust emission. Constraints are obtained from the stacked profile (blue) and from the inverse-variance weighted average matched filter flux (green), both in the Planck 857 GHz band. The combined constraint is shown as filled orange and yellow contours. The blue and white crosses shows the best value for the profile and combined fits, respectively.