An Explanation for the Observed Weak Size Evolution of Disk Galaxies

Surveys of distant galaxies with the Hubble Space Telescope and from the ground have shown that there is only mild evolution in the relationship between radial size and stellar mass for galactic disks from z ∼ 1 to the present day. Using a sample of nearby disk-dominated galaxies from the Sloan Digital Sky Survey (SDSS) and high-redshift data from the GEMS (Galaxy Evolution from Morphology and SEDs) survey, we investigate whether this result is consistent with theoretical expectations within the hierarchical paradigm of structure formation. The relationship between virial radius and mass for dark matter halos in the ΛCDM model evolves by about a factor of 2 over this interval. However, N-body simulations have shown that halos of a given mass have less centrally concentrated mass profiles at high redshift. When we compute the expected disk size-stellar mass distribution, accounting for this evolution in the internal structure of dark matter halos and the adiabatic contraction of the dark matter by the self-gravity of the collapsing baryons, we find that the predicted evolution in the mean size at fixed stellar mass since z ∼ 1 is about 15%-20%, in good agreement with the observational constraints from GEMS. At redshift z ∼ 2, the model predicts that disks at fixed stellar mass were on average only 60% as large as they are today. Similarly, we predict that the rotation velocity at a given stellar mass (essentially the zero point of the Tully-Fisher relation) is only about 10% larger at z ∼ 1 (20% at z ∼ 2) than at the present day.