The relationship between galaxy and dark matter halo size from z ~ 3 to the present

We explore empirical constraints on the statistical relationship between the radial size of galaxies and the radius of their host dark matter haloes from z ∼ 0.1–3 using the Galaxy And Mass Assembly (GAMA) and Cosmic Assembly Near Infrared Deep Extragalactic Legacy Survey (CANDELS) surveys. We map dark matter halo mass to galaxy stellar mass using relationships from abundance matching, applied to the Bolshoi–Planck dissipationless  N-body simulation. We define SRHR ≡ re/Rh as the ratio of galaxy radius to halo virial radius, and SRHRλ ≡ re/(λRh) as the ratio of galaxy radius to halo spin parameter times halo radius. At z ∼ 0.1, we find an average value of SRHR ≃ 0.018 and SRHRλ ≃ 0.5 with very little dependence on stellar mass. Stellar radius–halo radius (SRHR) and SRHRλ have a weak dependence on cosmic time since z ∼ 3. SRHR shows a mild decrease over cosmic time for low-mass galaxies, but increases slightly or does not evolve for more massive galaxies. We find hints that at high redshift (z ∼ 2–3), SRHRλ is lower for more massive galaxies, while it shows no significant dependence on stellar mass at z ≲ 0.5. We find that for both the GAMA and CANDELS samples, at all redshifts from z ∼ 0.1–3, the observed conditional size distribution in stellar mass bins is remarkably similar to the conditional distribution of λRh. We discuss the physical interpretation and implications of these results.