Galaxy And Mass Assembly (GAMA): Stellar-to-Dynamical Mass Relation II. Peculiar Velocities

Empirical correlations connecting starlight to galaxy dynamics (e.g., the fundamental plane (FP) of elliptical/quiescent galaxies and the Tully--Fisher relation of spiral/star-forming galaxies) provide cosmology-independent distance estimation and are central to local Universe cosmology. In this work, we introduce the mass hyperplane (MH), which is the stellar-to-dynamical mass relation $(M_\star/M_\mathrm{dyn})$ recast as a linear distance indicator. Building on recent FP studies, we show that both star-forming and quiescent galaxies follow the same empirical MH, then use this to measure the peculiar velocities (PVs) for a sample of 2496 galaxies at $z<0.12$ from GAMA. The limiting precision of MH-derived distance/PV estimates is set by the intrinsic scatter in size, which we find to be $\approx$0.1~dex for both quiescent and star-forming galaxies (when modeled independently) and $\approx$0.11~dex when all galaxies are modeled together; showing that the MH is as good as the FP. To empirically validate our framework and distance/PV estimates, we compare the inferred distances to groups as derived using either quiescent or star-forming galaxies. A good agreement is obtained with no discernible bias or offset, having a scatter of $\approx$0.05~dex $\approx$12\% in distance. Further, we compare our PV measurements for the quiescent galaxies to the previous PV measurements of the galaxies in common between GAMA and the Sloan Digital Sky Survey (SDSS), which shows similarly good agreement. Finally, we provide comparisons of PV measurements made with the FP and the MH, then discuss possible improvements in the context of upcoming surveys such as the 4MOST Hemisphere Survey (4HS).