An optimal ALMA image of the Hubble Ultra Deep Field in the era of JWST: obscured star formation and the cosmic far-infrared background

We combine archival ALMA data targeting the Hubble Ultra Deep Field (HUDF) to produce the deepest currently attainable 1-mm maps of this key region. Our deepest map covers 4.2 arcmin(2), with a beamsize of 1.49 arcsec x1.07 arcsec at an effective frequency of 243 GHz (1.23 mm). It reaches an rms of 4.6 mu Jy beam-1, with 1.5 arcmin(2) below 9.0 mu Jy beam(-1), an improvement of >5 per cent (and up to 50 per cent in some regions) over the best previous map. We also make a wider, shallower map, covering 25.4 arcmin(2). We detect 45 galaxies in the deep map down to 3.6 sigma, 10 more than previously detected, and 39 of these galaxies have JWST counterparts. A stacking analysis on the positions of ALMA-undetected JWST galaxies yields 10 per cent more signal compared to previous stacking analyses, and we find that detected sources plus stacking contribute (10.0 +/- 0.5) Jy deg(-2) to the cosmic infrared background (CIB) at 1.23 mm. Although this is short of the (uncertain) background level of about 20 Jy deg(-2), we show that our measurement is consistent with the background if the HUDF is a mild (similar to 2 sigma) negative CIB fluctuation, and that the contribution from faint undetected objects is small and converging. This suggests that JWST has detected essentially all of the galaxies that contribute to the CIB, as anticipated from the strong correlation between galaxy stellar mass and obscured star formation.