ALMACAL I: First dual-band number counts from a deep and wide ALMA submm survey, free from cosmic variance

We have exploited ALMA calibration observations to carry out a novel, wide and deep submm survey, ALMACAL. These calibration data comprise a large number of observations of calibrator fields in a variety of frequency bands and array configurations. Gathering together data acquired during multiple visits to many ALMA calibrators, it is possible to reach noise levels which allow the detection of faint dusty, star-forming galaxies (DSFGs) over a significant area. In this paper we outline our survey strategy and report the first results. We have analysed data for 69 calibrators, reaching depths of $\sim 25 \, {\rm \mu Jy \, beam^{-1}}$ at sub-arcsec resolution. Adopting a conservative approach based on $\geq 5 \sigma$ detections, we have found eight and 11 DSFGs in ALMA bands 6 and 7, respectively, with flux densities $S_{\rm 1.2 mm} \geq 0.2 \, {\rm mJy}$. The faintest galaxies would have been missed by even the deepest \emph{Herschel} surveys. Our cumulative number counts have been determined independently at 870 $\mu$m and 1.2 mm, from a sparse sampling of the astronomical sky, and are thus relatively free of cosmic variance. The counts are lower than reported previously by a factor of at least $2\times$. Future analyses will yield large, secure samples of DSFGs, with redshifts determined via detection of submm spectral lines. Uniquely, our strategy then allows morphological studies of very faint DSFGs - representative of more normal star-forming galaxies than conventional submm galaxies (SMGs) - in fields where self-calibration is feasible, yielding milliarcsecond spatial resolution.