The Wide-field Infrared Survey Explorer ( WISE ) has completed its all-sky survey in four channels at 3.4 - 22 \mu m , detecting hundreds of millions of objects .
We merge the \wise mid-infrared data with optical data from the Sloan Digital Sky Survey ( SDSS ) and provide a phenomenological characterization of \wise extragalactic sources . \wise is most sensitive at 3.4 \mu m ( W 1 ) and least sensitive at 22 \mu m ( W 4 ) .
The W 1 band probes massive early-type galaxies out to z \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \mathchar 536 $ } \hss } \raise 2.0 pt% \hbox { $ \mathchar 318 $ } } 1 .
This is more distant than SDSS identified early-type galaxies , consistent with the fact that 28 % of 3.4 \mu m sources have faint or no r -band counterparts ( r > 22.2 ) .
In contrast , 92 - 95 % of 12 \mu m and 22 \mu m sources have SDSS optical counterparts with r \leq 22.2 . \wise 3.4 \mu m detects 89.8 % of the entire SDSS QSO catalog at SNR _ { W 1 } > 7 \sigma , but only 18.9 % at 22 \mu m with SNR _ { W 4 } > 5 \sigma .
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 \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \mathchar 536 $ } \hss } \raise 2.0 pt% \hbox { $ \mathchar 316 $ } } 3 .
We highlight three major applications of \wise colors : ( 1 ) Selection of strong AGN/QSOs at z \leq 3 using W 1 - W 2 > 0.8 and W 2 < 15.2 criteria , producing a better census of this population .
The surface density of these strong AGN/QSO candidates is 67.5 \pm 0.14 per deg ^ { 2 } .
( 2 ) Selection of dust-obscured , type-2 AGN/QSO candidates .
We show that \wise W 1 - W 2 > 0.8 , W 2 < 15.2 combined with r - W 2 > 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 ultra-luminous infrared galaxies at z \sim 2 with extremely red colors , r - W 4 > 14 or well-detected 22 \mu m sources lacking detections in the 3.4 and 4.6 \mu m bands .
The surface density of z \sim 2 ULIRG candidates selected with r - W 4 > 14 is 0.9 \pm 0.07 per deg ^ { 2 } at SNR _ { W 4 } \geq 5 ( the corresponding , lowest flux density of 2.5 mJy ) , which is consistent with that inferred from smaller area Spitzer surveys .
Optical spectroscopy of a small number of these high-redshift ULIRG candidates confirms our selection , and reveals a possible trend that optically fainter or r - W 4 redder candidates are at higher redshifts .