The NIKA2 cosmological legacy survey at 2 mm. Catalogs, colors, redshift distributions, and implications for deep surveys

Aims. Millimeter (mm) galaxy surveys are particularly effective in detecting dusty star-forming galaxies at high redshift. While such observations are typically conducted at similar to 1 mm, various authors have suggested over the last 20 years that 2 mm observations may be better suited for selecting sources at even higher redshifts. In this work, we use the unprecedented 2 mm data from the NIKA2 Cosmological Legacy Survey (N2CLS), together with the simulated infrared dusty extragalactic sky (SIDES), to study and interpret the statistical properties of galaxies selected at this wavelength. Methods. We used the N2CLS robust sample (95% purity) at 2 mm (similar to 18 arcsec resolution), which contains 25 sources in the deep GOODS-N field (159 arcmin(2), 0.047 mJy/beam RMS) and 90 sources in the wide COSMOS field (1130 arcmin(2), 0.09 mJy/beam RMS). The sources were matched with the N2CLS 1.2 mm sources, ancillary 850 mu m sources, and redshift catalogs to study the colors and redshift distributions. We also produced end-to-end simulations based on SIDES and the observed N2CLS detector timelines to interpret the data. Results. We found a mean S-2 mm/S-1.2 mm color of 0.222 +/- 0.008 with a standard deviation of 0.070 +/- 0.010, mainly caused by resolution and source extraction effects according to the SIDES simulation. We measured a mean redshift of 3.6 +/- 0.3 in GOODS-N, which is marginally higher than the expectations from SIDES (2.9 +/- 0.2) because of an overdensity at z similar to 5.2, and 3.2 +/- 0.2 in COSMOS, which is identical to that obtained in SIDES. We also show that the observed S-2 mm/S-1.2 mm colors exhibit a weak dependence with redshift but a large dispersion, which limits its efficiency with respect to selecting high-z sources. We compared the measured fluxes of 2 mm sources detected by both the N2CLS and the Ex-MORA surveys. The results only agree if we take into account the impact of the bandwidth, source blending, and source size. Finally, we studied the eight 2 mm sources that had not been detected at 1.2 mm and found that two of them are radiogalaxies and one is a z similar to 2 galaxy, while the remaining six (all in COSMOS) are compatible with the expected number of spurious detections. Consequently, the N2CLS survey shows no evidence of any exotic dusty galaxy population with either very cold dust or at very high redshift, which would only be detectable at 2 mm. Using SIDES, we show that 2 mm samples have a higher mean redshift compared to 1.2 mm because they miss dusty galaxies around cosmic noon (z similar to 2). Finally, we discuss the efficiency of single-dish and interferometric blind surveys to build samples of high-z dusty galaxies.