On the existence of a tight planar relation between stellar specific angular momentum, mass and effective surface brightness for ALFALFA galaxies

Measurements of the dependence of stellar specific angular momentum ($j_*$) on stellar mass ($M_*$) are presented for large samples of ALFALFA galaxies spanning the stellar mass range $\sim 10^8$-$10^{11}$ M$_{\odot}$. Accurate estimates of $j_*$ are generated using measurements of $I$-band effective radius and velocity width of the HI line profile. While the full sample ($N=3~607)$ of galaxies yields a $j_*$-$M_*$ relation with power-law index $\alpha = 0.404\pm 0.03$, it is shown that various sub-samples have indices that are very similar to the best literature results, yet with comparatively lower intrinsic scatters. A galaxy's mean $I$-band surface brightness within its effective radius ($<\mu_\mathrm{eff}>$) is shown to significantly correlate with $j_*$-$M_*$ scatter. A 3D plane fit to all $N=3~607$ galaxies in $\log_{10}j_*$-$\log_{10}M_*$-$<\mu_\mathrm{eff}>$ space yields $j_*\propto M_*^{0.589\pm 0.002}<\mu_\mathrm{eff}>^{0.193\pm 0.002}$ with scatter $\sigma=0.089$ dex. $<\mu_\mathrm{eff}>$-selected sub-samples of size up to $N=1~450$ yield power-law $j_*$-$M_*$ relations mostly consistent with $\alpha=0.55\pm 0.02$ from the literature and with intrinsic scatter ranging from 0.083 to 0.129 dex. Thus, this paper presents new, highly accurate measurements of the $j_*$-$M_*$ relation that can be used to better understand the important roles played by angular momentum in the formation and evolution of galaxies.