The Size Function of Galaxy Disks out to z ~ 1 from the Canada-France-Hawaii-Telescope Legacy Survey

Abstract

The formation and growth of galaxy disks over cosmic time is crucial to our understanding of galaxy formation. Despite steady improvements in the size and quality of disk samples over the last decade, many aspects of galaxy disk evolution remain unclear. Using two square degrees of deep, wide-field i'-band imaging from the Canada-France-Hawaii Telescope Legacy Survey, we compute size functions for 6000 disks from z=0.2 to z=1 and explore luminosity and number density evolution scenarios with an emphasis on the importance of selection effects on the interpretation of the data. We also compute the size function of a very large sample of disks from the Sloan Digital Sky Survey to use as a local (z ~ 0.1) comparison. CFHTLS size functions computed with the same fixed luminosity-size selection window at all redshifts exhibit evolution that appears to be best modelled by a pure number density evolution. The z = 0.3 size function is an excellent match to the z = 0.9 one if disks at the highest redshift are a factor of 2.5 more abundant than in the local universe. The SDSS size function would also match the z = 0.9 CFHTLS size function very well with a similar change in number density. On the other hand, the CFHTLS size functions computed with a varying luminosity-size selection window with redshift remain constant if the selection window is shifted by 1.0$-$1.5 mag towards fainter magnitudes with decreasing redshift. There is a weak dependence on disk scale length with smaller ($h \lesssim $ 4 kpc) disks requiring more luminosity evolution than larger ones. Given that changes in number density are primarily due to mergers and that current estimates of merger rates below z = 1 are low, luminosity evolution appears to be a more plausible scenario to explain the observations.