Empirical distributions of galactic λ spin parameters from the Sloan Digital Sky Survey

Using simple dimensional arguments for both spiral and elliptical galaxies, we present formulae to derive an estimate of the halo spin parameter λ for any real galaxy, in terms of common observational parameters. This allows a rough estimate of λ, which we apply to a large volume-limited sample of galaxies taken from the Sloan Digital Sky Survey data base. The large numbers involved (11 597) allow the derivation of reliable λ distributions, as signal adds up significantly in spite of the errors in the inferences for particular galaxies. We find that if the observed distribution of λ is modelled with a lognormal function, as often done for this distribution in dark matter haloes that appear in cosmological simulations, we obtain parameters  λ₀= 0.04 ± 0.005  and  σ_λ= 0.51 ± 0.05  , interestingly consistent with values derived from simulations. For spirals, we find a good correlation between empirical values of λ and visually assigned Hubble types, highlighting the potential of this physical parameter as an objective classification tool.