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 lambda for any real galaxy, in terms of common observational parameters. This allows a rough estimate of lambda, 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 lambda 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 lambda is modelled with a lognormal function, as often done for this distribution in dark matter haloes that appear in cosmological simulations, we obtain parameters lambda(0) = 0.04 +/- 0.005 and sigma(lambda) = 0.51 +/- 0.05, interestingly consistent with values derived from simulations. For spirals, we find a good correlation between empirical values of lambda and visually assigned Hubble types, highlighting the potential of this physical parameter as an objective classification tool.