Optical and Radio Properties of Extragalactic Sources Observed by the FIRST and SDSS Surveys

We discuss the optical and radio properties of 30,000 FIRST sources positionally associated with an SDSS source in 1230 deg$^2$ of sky. The majority (83%) of the FIRST sources identified with an SDSS source brighter than r=21 are optically resolved. We estimate an upper limit of 5% for the fraction of quasars with broad-band optical colors indistinguishable from those of stars. The distribution of quasars in the radio flux -- optical flux plane supports the existence of the "quasar radio-dichotomy"; 8% of all quasars with i<18.5 are radio-loud and this fraction seems independent of redshift and optical luminosity. The radio-loud quasars have a redder median color by 0.08 mag, and a 3 times larger fraction of objects with red colors. FIRST galaxies represent 5% of all SDSS galaxies with r<17.5, and 1% for r<20, and are dominated by red galaxies. Magnitude and redshift limited samples show that radio galaxies have a different optical luminosity distribution than non-radio galaxies selected by the same criteria; when galaxies are further separated by their colors, this result remains valid for both blue and red galaxies. The distributions of radio-to-optical flux ratio are similar for blue and red galaxies in redshift-limited samples; this similarity implies that the difference in their luminosity functions, and resulting selection effects, are the dominant cause for the preponderance of red radio galaxies in flux-limited samples. We confirm that the AGN-to-starburst galaxy number ratio increases with radio flux, and find that radio emission from AGNs is more concentrated than radio emission from starburst galaxies (abridged).