Angular momentum of disc galaxies with a lognormal density distribution

John Herbert Marr

Published 2015-07-16Version 1

Whilst most galaxy properties scale with galaxy mass, similar scaling relations for angular momentum are harder to demonstrate. A lognormal (LN) density distribution for disc mass provides a good overall fit to the observational data for disc rotation curves for a wide variety of galaxy types and luminosities. In this paper, the total angular momentum J and energy $\vert{}$E$\vert{}$ were computed for 38 disc galaxies from the published rotation curves and plotted against the derived disc masses, with best fit slopes of 1.683$\pm{}$0.018 and 1.643$\pm{}$0.038 respectively, using a theoretical model with a LN density profile. The derived mean disc spin parameter was $\lambda{}$=0.423$\pm{}$0.014. Using the rotation curve parameters V$_{max}$ and R$_{max}$ as surrogates for the virial velocity and radius, the virial mass estimator $M_{disc}\propto{}R_{max}V_{max}^2$ was also generated, with a log-log slope of 1.024$\pm{}$0.014 for the 38 galaxies, and a proportionality constant ${\lambda{}}^*=1.47\pm{}0.20\times{}{10}^5\ M_{sun\ }{kpc}^{-1}{km}^{-2}\ s^2$. This relationship was close to the theoretical slope of 1, and had less scatter than the corresponding Tully Fisher relation, $M\propto{}{\left(V_{rot}\right)}^{\alpha{}}$, suggesting that the virial mass estimator may provide an alternative method to determine disc masses.