We present stacking analyses on our ALMA deep 1.1 mm imaging in the SXDF using 1.6 \mu m and 3.6 \mu m selected galaxies in the CANDELS WFC3 catalog .
We detect a stacked flux of \sim 0.03 –0.05 mJy , corresponding to L _ { IR } < 10 ^ { 11 } ~ { } L _ { \sun } and a star formation rate ( SFR ) of \sim 15 ~ { } M _ { \sun } yr ^ { -1 } at z = 2 .
We find that galaxies brighter in the rest-frame near-infrared tend to be also brighter at 1.1 mm , and galaxies fainter than m _ { 3.6 \mu m } = 23 do not produce detectable 1.1 mm emission .
This suggests a correlation between stellar mass and SFR , but outliers to this correlation are also observed , suggesting strongly boosted star formation or extremely large extinction .
We also find tendencies that redder galaxies and galaxies at higher redshifts are brighter at 1.1 mm .
Our field contains z \sim 2.5 H \alpha emitters and a bright single-dish source .
However , we do not find evidence of bias in our results caused by the bright source .
By combining the fluxes of sources detected by ALMA and fluxes of faint sources detected with stacking , we recover a 1.1 mm surface brightness of up to 20.3 \pm 1.2 Jy deg ^ { -2 } , comparable to the extragalactic background light measured by COBE .
Based on the fractions of optically faint sources in our and previous ALMA studies and the COBE measurements , we find that approximately half of the cosmic star formation may be obscured by dust and missed by deep optical surveys , Much deeper and wider ALMA imaging is therefore needed to better constrain the obscured cosmic star formation history .