We show that the stellar surface-brightness profiles in disc galaxies---observed to be approximately exponential---can be explained if radial migration efficiently scrambles the individual stars angular momenta while conserving the circularity of the orbits and the total mass and angular momentum. In this case the discs distribution of specific angular momenta $j$ should be near a maximum-entropy state and therefore approximately exponential, $dNproptoexp(-j/langle jrangle)dj$. This distribution translates to a surface-density profile that is generally not an exponential function of radius: $Sigma(R)proptoexp[-R/R_e(R)]/(RR_e(R))(1+dlog v_c(R)/dlog R)$, for a rotation curve $v_c(R)$ and $R_e(R)equivlangle jrangle/v_c(R)$. We show that such a profile matches the observed surface-brightness profiles of disc-dominated galaxies as well as the empirical exponential profile. Disc galaxies that exhibit population gradients cannot have fully reached a maximum-entropy state but appear to be close enough that their surface-brightness profiles are well-fit by this idealized model.
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