We present the results of the first, deep ALMA imaging covering the full 4.5 arcmin 2 of the HUDF imaged with WFC3/IR on HST. Using a 45-pointing mosaic, we have obtained a homogeneous 1.3-mm image reaching σ 1.335 µJy, at a resolution of 0.7 arcsec. From an initial list of 50 > 3.5σ peaks, a rigorous analysis confirms 16 sources with S 1.3 > 120 µJy. All of these have secure galaxy counterparts with robust redshifts ( z = 2.15). Due to the unparalleled supporting data, the physical properties of the ALMA sources are well constrained, including their stellar masses (M * ) and UV+FIR star-formation rates (SFR). Our results show that stellar mass is the best predictor of SFR in the high-redshift Universe; indeed at z ≥ 2 our ALMA sample contains 7 of the 9 galaxies in the HUDF with M * ≥ 2 × 10 10 M , and we detect only one galaxy at z > 3.5, reflecting the rapid drop-off of high-mass galaxies with increasing redshift. The detections, coupled with stacking, allow us to probe the redshift/mass distribution of the 1.3-mm background down to S 1.3 10 µJy. We find strong evidence for a steep star-forming 'main sequence' at z 2, with SFR ∝ M * and a mean specific SFR 2.2 Gyr −1 . Moreover, we find that 85% of total star formation at z 2 is enshrouded in dust, with 65% of all star formation at this epoch occurring in high-mass galaxies (M * > 2 × 10 10 M ), for which the average obscured:unobscured SF ratio is 200. Finally, we revisit the cosmic evolution of SFR density; we find this peaks at z 2.5, and that the star-forming Universe transits from primarily unobscured to primarily obscured at z 4.

Three billion years after the big bang (at redshift z = 2), half of the most massive galaxies were already old, quiescent systems with little to no residual star formation and extremely compact with stellar mass densities at least an order of magnitude larger than in low redshift ellipticals, their descendants. Little is known about how they formed, but their evolved, dense stellar populations suggest formation within intense, compact starbursts 1-2 Gyr earlier (at 3 < z < 6). Simulations show that gas-rich major mergers can give rise to such starbursts which produce dense remnants. Sub-millimeter selected galaxies (SMGs) are prime examples of intense, gas-rich, starbursts. With a new, representative spectroscopic sample of compact quiescent galaxies at z = 2 and a statistically wellunderstood sample of SMGs, we show that z = 3 − 6 SMGs are consistent with being the progenitors of z = 2 quiescent galaxies, matching their formation redshifts and their distributions of sizes, stellar masses and internal velocities. Assuming an evolutionary connection, their space densities also match if the mean duty cycle of SMG starbursts is 42 +40 −29 Myr (consistent with independent estimates), which indicates that the bulk of stars in these massive galaxies were formed in a major, early surge of star-formation. These results suggests a coherent picture of the formation history of the most massive galaxies in the universe, from their initial burst of violent star-formation through their appearance as high stellar-density galaxy cores and to their ultimate fate as giant ellipticals.