Signals from the Noise: Image Stacking for Quasars in the FIRST Survey

We present a technique to explore the radio sky into the nanojansky regime by employing image stacking using the FIRST survey. We first discuss the nonintuitive relationship between the mean and median values of a non-Gaussian distribution that is dominated by noise, followed by an analysis of the systematic effects present in FIRST's 20 cm VLA snapshot images. Image stacking allows us to recover the properties of source populations with flux densities a factor of 30 or more below the rms noise level. Mean estimates of radio flux density, luminosity, etc. are derivable for any source class having arcsecond positional accuracy. We use this technique to compute the mean radio properties for 41,295 quasars from the SDSS DR3 catalog. There is a tight correlation between optical and radio luminosity, with the radio luminosity increasing as the 0.85 power of optical luminosity. This implies declining radio loudness with optical luminosity: the most luminous objects (M_UV = -28.5) have average radio-to-optical ratios 3 times lower than the least luminous objects (M_UV = -20). There is also a striking correlation between optical color and radio loudness: quasars that are either redder or bluer than the norm are brighter radio sources, with objects 0.8 mag redder than the SDSS composite spectrum having radio loudness ratios that are higher by a factor of 10. We explore the long-standing question of whether a radio-loud/radio-quiet dichotomy exists in quasars, finding that optical selection effects probably dominate the distribution function of radio loudness, which has at most a modest (~20%) inflection between the radio-loud and radio-quiet ends of the distribution. We also find, surprisingly, that broad absorption line quasars have higher mean radio flux densities, with the greatest disparity arising in the rare low-ionization BAL subclass.