Compact galaxies and the size-mass galaxy distribution from a colour-selected sample at 0.04 < z < 0.15 supplemented by ugrizYJHK photometric redshifts

The size-mass galaxy distribution is a key diagnostic for galaxy evolution. Massive compact galaxies are potential surviving relics of a high-redshift phase of star formation. Some of these could be nearly unresolved in SDSS imaging and thus not included in galaxy samples. To overcome this, a sample was selected from the combination of SDSS and UKIDSS photometry to r<17.8. This was done using colour-colour selection, and then by obtaining accurate photometric redshifts (photo-z) using scaled flux matching (SFM). Compared to spectroscopic redshifts (spec-z), SFM obtained a 1-sigma scatter of 0.0125 with only 0.3% outliers (Delta:ln(1+z)>0.06). A sample of 163186 galaxies was obtained with 0.04<z<0.15 over 2300 sq.deg. using a combination of spec-z and photo-z. Following Barro et al., log:Sigma_1.5=log:M_*-1.5log:reff was used to define compactness. The spectroscopic completeness was 76% for compact galaxies (log:Sigma_1.5>10.5) compared to 92% for normal-size galaxies. This difference is primarily attributed to SDSS `fibre collisions' and not the completeness of the main galaxy sample selection. Using environmental overdensities, this confirms that compact quiescent galaxies are significantly more likely to be found in high-density environments compared to normal-size galaxies. By comparison with a high-redshift sample from 3D-HST, log:Sigma_1.5 distribution functions show significant evolution, with this being a compelling way to compare with simulations such as EAGLE. The number density of compact quiescent galaxies drops by a factor of about 30 from z~2 to log(n/Mpc^-3)=-5.3+-0.4 in the SDSS-UKIDSS sample. The uncertainty is dominated by the steep cut off in log:Sigma_1.5, which is demonstrated conclusively using this complete sample.