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 radio sky survey. We begin with a discussion of the non-intuitive relationship between the mean and median values of a non-Gaussian distribution in which measurements of the members of the distribution are dominated by noise. Following a detailed examination of the systematic effects present in the 20 cm VLA snapshot images that comprise FIRST, we demonstrate that image stacking allows us to recover the average properties of source populations with flux densities a factor of 30 or more below the rms noise level. With the calibration described herein, mean estimates of radio flux density, luminosity, radio loudness, etc. are derivable for any undetected source class having arcsecond positional accuracy. We demonstrate the utility of this technique by exploring the radio properties of quasars found in the Sloan Digital Sky Survey. We compute the mean luminosities and radio-loudness parameters for 41,295 quasars in the SDSS DR3 catalog. There is a tight correlation between optical and radio luminosity, with the radio luminosity increasing as the 0.72 power of optical luminosity. This implies declining radio-loudness with optical luminosity, with the most luminous objects (M{sub UV} = -30) having on average ten times lower radio-to-optical ratios than the least luminous objects (M{sub UV} = -21). 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. Quasars having g-r {approx} 0.8 magnitudes redder than the SDSS composite spectrum are found to have radio-loudness ratios that are higher by a factor of 8. We examine the radio properties of the subsample of quasars with broad absorption lines, finding, surprisingly, that BAL quasars have higher mean radio flux densities at all redshifts, with the greatest disparity arising in the rare low-ionization BAL subclass. We conclude with examples of other problems for which the stacking analysis developed here is likely to be of use