Cosmic clocks: A Tight Radius - Velocity Relationship for HI-Selected Galaxies

Abstract: HI-Selected galaxies obey a linear relationship between their maximum detected radius Rmax and rotational velocity. This result covers measurements in the optical, ultraviolet, and HI emission in galaxies spanning a factor of 30 in size and velocity, from small dwarf irregulars to the largest spirals. Hence, galaxies behave as clocks, rotating once a Gyr at the very outskirts of their discs. Observations of a large optically-selected sample are consistent, implying this relationship is generic to disc galaxies in the low redshift Universe. A linear RV relationship is expected from simple models of galaxy formation and evolution. The total mass within Rmax has collapsed by a factor of 37 compared to the present mean density of the Universe. Adopting standard assumptions we find a mean halo spin parameter lambda in the range 0.020 to 0.035. The dispersion in lambda, 0.16 dex, is smaller than expected from simulations. This may be due to the biases in our selection of disc galaxies rather than all halos. The estimated mass densities of stars and atomic gas at Rmax are similar (~0.5 Msun/pc^2) indicating outer discs are highly evolved. The gas consumption and stellar population build time-scales are hundreds of Gyr, hence star formation is not driving the current evolution of outer discs. The estimated ratio between Rmax and disc scale length is consistent with long-standing predictions from monolithic collapse models. Hence, it remains unclear whether disc extent results from continual accretion, a rapid initial collapse, secular evolution or a combination thereof.