Detection of Far-Infrared Emission from Galaxies and Quasars in the Galactic Extinction Map by Stacking Analysis

We performed stacking image analyses of galaxies over a Galactic extinction map constructed by Schlegel, Finkbeiner, and Davis (1998, AJ, 500, 525). We selected $ \sim$ 10 $ ^{7}$ galaxies in total from the Sloan Digital Sky Survey (SDSS) DR7 photometric catalog. We detected clear signatures of the enhancement of the extinction in the $ r$ -band, $ \Delta A_r$ , around galaxies, indicating that the extinction map is contaminated by their FIR (far-infrared) emission. The average amplitude of the contamination per galaxy was well-fitted to $ \Delta A_r$ ( $ m_r$ ) $ =$ 0.64 $ \times$ 10 $ ^{0.17(18-m_r)}$ [mmag]. While this value is very small, it is directly associated with galaxies, and may have a systematic effect on galaxy statistics. Indeed, this correlated contamination leads to a relatively large anomaly of galaxy surface number densities against the SFD extinction, $ A_{\rm SFD}$ , discovered by Yahata et al. (2007, PASJ, 59, 205). We modeled the radial profiles of stacked galaxy images, and found that the FIR signal around each galaxy does not originate from the central galaxy alone, but is dominated by the contributions of nearby galaxies via galaxy angular clustering. The separation of the single galaxy and the clustering terms enables us to infer the statistical relation of the FIR and $ r$ -band fluxes of galaxies, and also to probe the flux-weighted cross-correlation of galaxies, down to magnitudes that are difficult to probe directly for individual objects. We repeated the same stacking analysis for SDSS DR6 photometric quasars, and discovered similar signatures, but with weaker amplitudes. The implications of the present results for galaxy and quasar statistics, and for corrections to the Galactic extinction map, are briefly discussed.