Angular momentum of disc galaxies with a lognormal density distribution

By postulating that the majority of the mass and angular momentum of a disc galaxy is confined to the disc with a lognormal surface density distribution, and that galactic discs are substantially, if not fully, self-gravitating, it may be shown that the resultant rotation curves (RCs) display a good overall fit to observational data for a wide range of galaxy types. With this hypothesis, the total angular momentum $J$, and total energy |$E$| of 38 disc galaxies was computed and plotted against the derived disc masses, with best fit slopes for $J$ of $1.683\pm0.018$ and |$E$| of $1.643\pm0.038$, and a universal disc spin parameter $\lambda=0.423\pm0.014$. Using the disc parameters $V_{max}$ and $R_{max}$ as surrogates for the virial velocity and radius, a virial mass estimator $M_{disc}\propto{}R_{max}V_{max}^2$ was generated, with a log-log slope of $1.024\pm0.014$ for the 38 galaxies, and a proportionality constant $\lambda^*=1.47\pm0.20\times10^5M_\odot{}kpc^{-1}km^{-2}s^2$. This relationship has less scatter than $M_\odot\propto{}V^\alpha$, and may provide an alternative to the Tully-Fisher relation in determining virial disc masses.