Observational constraints on disc galaxy formation

We use data from the literature to constrain theoretical models of galaxy formation. We show how to calculate the dimensionless spin parameter lambda of the haloes of disc galaxies, and we compare the distribution of lambda with that observed in cosmological N-body simulations. The agreement is excellent, which provides strong support for the hierarchical picture of galaxy formation. Assuming only that the radial surface density distribution of discs is exponential, we estimate crudely the maximum-disc mass-to-light ratio in the I band, and obtain [Y-I] less than or similar to 3.56 h, for a Hubble constant of 100 h km s(-1) Mpc(-1). We discuss this result and its limitations in relation to other independent determinations of Y-I. We also define a dimensionless form of the Tully-Fisher relation, and use it to derive a value of the baryon fraction in disc galaxies; the median value is m(d) = 0.084(Y-I/3.56 h). Assuming that the gas fraction in galactic haloes is at most as large as that in clusters, we also conclude that [Y-I] less than or similar to 2.56 h(-1/2).