The MUSE Deep Lensed Field on the Hubble Frontier Field MACS~J0416

Context. A census of faint and tiny star forming complexes at high redshift is key to improving our understanding of reionizing sources, galaxy growth, and the formation of globular clusters. Aims: We present the MUSE Deep Lensed Field (MDLF) program, which is aimed at unveiling the very faint population of high redshift sources that are magnified by strong gravitational lensing and to significantly increase the number of constraints for the lens model. Methods: We describe Deep MUSE observations of 17.1 h of integration on a single pointing over the Hubble Frontier Field galaxy cluster MACS J0416, providing line flux limits down to 2 × 10-19 erg s-1 cm-2 within 300 km s-1 and continuum detection down to magnitude 26, both at the three sigma level at λ = 7000 A. For point sources with a magnification (μ) greater than 2.5 (7.7), the MLDF depth is equivalent to integrating more than 100 (1000) h in blank fields, as well as complementing non-lensed studies of very faint high-z sources. The source-plane effective area of the MDLF with μ > 6.3 is 10 for individual objects down to de-lensed magnitudes between 28 and 30. The median stacked spectrum of 33 sources with a median MUV ≃ -17 and ⟨z⟩ = 3.2 (1.7 < z < 3.9) shows high-ionization lines, suggesting that they are common in such faint sources. Conclusions: Deep MUSE observations, in combination with existing HST imaging, allowed us to: (1) confirm redshifts for extremely faint high-z sources; (2) peer into their internal structure to unveil clumps down to 100 - 200 pc scale; (3) in some cases, break down such clumps into star-forming complexes matching the scales of bound star clusters (< 20 pc effective radius); (4) double the number of constraints for the lens model, reaching an unprecedented set of 182 bona-fide multiple images and confirming up to 213 galaxy cluster members. These results demonstrate the power of JWST and future adaptive optics facilities mounted on the Extremely Large Telescopes (e.g., European-ELT Multi-conjugate Adaptive Optics RelaY, MAORY, coupled with the Multi-AO Imaging CamerA for Deep Observations, MICADO) or Very Large Telescope (e.g., MCAO Assisted Visible Imager and Spectrograph, MAVIS) when combined in studies with gravitational telescopes. Full Table A.2 is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/646/A57 Based on observations collected at the European Southern Observatory for Astronomical research in the Southern Hemisphere under ESO programmes ID 0100.A-0763(A) (PI E. Vanzella), 094.A-0115B (PI J. Richard), 094.A-0525(A) (PI F.E. Bauer).