The relation between the galaxy velocity dispersions or maximal velocities and their V-band luminosities. Filled circles correspond to the results of this work and those of N-body simulations. The observations of low-mass galaxies are displayed with open symbols. The gray area indicates how the Guo et al. (2011)’s relation between stellar and dark halo masses, further extrapolated by Sawala et al. (2011), translates into luminosities and velocity dispersions for a minimum and maximum value of the NFW concentration parameter. Below a stellar mass of 10^8.3   M_⊙, two faint end slopes of stellar mass functions are considered (see text), splitting in two different branches the gray area. The dashed black lines are obtained when considering the Aquarius project’s relation between the maximal velocity and halo mass (Springel et al. 2008). The minimum stellar mass (10^8.3   M_⊙ ) for the original Guo et al. (2011)’s fit and its correspondence in terms of range of velocities is indicated with black arrows.