Cosmic clocks: a tight radius–velocity relationship for H i-selected galaxies

H I-selected galaxies obey a linear relationship between their maximum detected radius Rmax and rotational velocity. This result covers measurements in the optical, ultraviolet, and H I 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 radius–velocity relationship is expected from simple models of galaxy formation and evolution. The total mass within R_(max) 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 λ in the range 0.020–0.035. The dispersion in λ, 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 haloes. The estimated mass densities of stars and atomic gas at R_(max) are similar (∼0.5 M⊙ 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 R_(max) and disc scalelength 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.