Origin of the Joint Distribution of Structural Parameters in Disc Galaxies

We use a simple model of disc-galaxy formation in the LCDM cosmology to simultaneously reproduce the slopes, zero-points, scatter and uncorrelated residuals in the observed velocity-luminosity (VL) and radius-luminosity (RL) relations. Observed I-band luminosities are converted to stellar masses using the IMF-dependent relation between stellar mass-to-light ratio, M/L, and color. The model treats halo concentration, spin parameter, and disc mass fraction as independent log-normal random variables. Our main conclusion is that the VL and RL zero-points and the uncorrelated residuals can only be reproduced simultaneously if adiabatic contraction is avoided. One or the other could be fixed by appealing to unrealistic values for M/L, halo concentration c, and spin parameter lambda, but not all together. The small VL scatter is naturally determined by the predicted scatter in c and in M/L, quite independent of the large scatter in lambda. However, the RL scatter, driven by the scatter in lambda, can be as low as observed only if sigma_lambda simeq 0.25, about half the value predicted for CDM haloes. This may indicate that discs form in a special subset of haloes. The VL slope is reproduced once star formation occurs only above a threshold surface density, and the RL slope implies that the disc mass fraction is increasing with halo mass, consistent with feedback effects. A model that incorporates the above ingredients provides a simultaneous fit to all the observed features. In particular, the elimination of adiabatic contraction allows 80% disc contribution to the observed rotation velocity of bright discs at 2.2 disc scale lengths. The lack of halo contraction may indicate that disc formation is not as smooth as typically envisioned, but instead may involve clumpy, cold streams.