Observed stellar surface density distribution for the six UFDs analyzed in this work as worked out in Sánchez Almeida et al. (2024a, their Fig. 1). It is well reproduced by the line-of-sight projection of the SIDM profile used in Sect. 3. The magenta line corresponds to the best fit using one such profile. The figure also includes the polynomial fit to Σ_★(R) given by Sánchez Almeida et al. (2024a, the solid cyan line). Here R stands for the projected radial distance from the center of the galaxy, and b is a radial scaling factor, different for the different dwarfs, that allows the whole set of dwarfs to collapse to a single shape.