Characterizing the Mid-IR Extragalactic Sky with WISE and SDSS
  The Wide-field Infrared Survey Explorer (WISE) has completed its all-sky
survey at 3.4-22 micron. We merge the WISE data with optical SDSS data and
provide a phenomenological characterization of mid-IR, extragalactic sources.
WISE is most sensitive at 3.4micron(W1) and least at 22micron(W4). The W1 band
probes massive early-type galaxies out to z\gtrsim1. This is more distant than
SDSS identified early-type galaxies, consistent with the fact that 28% of
3.4micron sources have faint or no r-band counterparts (r>22.2). In contrast,
92-95% of 12 and 22micron sources have SDSS optical counterparts with r<22.2.
WISE 3.4micron detects 89.8% of the entire SDSS QSO catalog at SNR(W1)>7, but
only 18.9% at 22micron with SNR(W4)>5. We show that WISE colors alone are
effective in isolating stars (or local early-type galaxies), star-forming
galaxies and strong AGN/QSOs at z<3. We highlight three major applications of
WISE colors: (1) Selection of strong AGN/QSOs at z<3 using W1-W2>0.8 and
W2<15.2 criteria, producing a census of this population. The surface density of
these strong AGN/QSO candidates is 67.5+-0.14/deg^2. (2) Selection of
dust-obscured, type-2 AGN/QSO candidates. We show that WISE W1-W2>0.8, W2<15.2
combined with r-W2>6 (Vega) colors can be used to identify type-2 AGN
candidates. The fraction of these type-2 AGN candidates is 1/3rd of all WISE
color-selected AGNs. (3) Selection of ULIRGs at z\sim2 with extremely red
colors, r-W4>14 or well-detected 22micron sources lacking detections in the 3.4
and 4.6micron bands. The surface density of z~2 r-W4>14 ULIRGs is
0.9+-0.07/deg^2 at SNR(W4)>5 (flux(W4)>=2.5mJy), which is consistent with that
inferred from smaller area Spitzer surveys. Optical spectroscopy of a small
number of these high-redshift ULIRGs confirms our selection, and reveals a
possible trend that optically fainter or r-W4 redder candidates are at higher
redshifts.
