Its explained on the next page(it a simplification) In fact, by relaxing some of the assumptions made above, we have the more general relationship: L ∝ V 2/(+s

Its explained on the next page(it a simplification) In fact, by relaxing some of the assumptions made above, we have the more general relationship: L ∝ V 2/(+s+q−t) opt (here s, q and t can be band- dependent) that can be even more complex and non-linear when the scaling laws (2), (3), (4) are not just power laws. As a matter of fact, in several different large samples of galaxies it has been found that the TF has different slope and scatter in different bands: a I ≃ 10, s I ∼ 0.4mag, while a B ≃ 7.7, s B ∼ 0.5mag (Pierce & Tully 1992), (Salucci et al. 1993). Moreover, a non linearity in the TF is often found at low rotation velocities (Aaronson et al. 1982).