Coloured lines represent the average stellar radial number density profiles of each of the five Aquarius halos considered, as seen by 16 observers, 3 of whom are located along the principal axis of the respective dark matter halo, while the rest are arranged in a regular pattern spanning one hemisphere centred on the target galaxy (see text for details). The black line shows the stellar radial profile of metal-poor stars in the halo of M 31, represented by a power law with index of − 3.34 (Ibata et al. 2014). For reference, two generic power laws having indices of − 3 and − 4 are plotted with dashed lines.