The bending of the star-forming main sequence traces the cold- to hot-accretion transition mass over 0

We analyse measurements of the evolving stellar mass ( M 0 ) at which the bending of the star-forming main sequence (MS) occurs over 0 < z < 4. We find M 0 ≈ 10 10 M (cid:12) over 0 < z < 1 before M 0 rises up to ∼ 10 11 M (cid:12) at z = 2 and then stays flat or slowly increases towards higher redshifts. When converting M 0 values into hosting dark matter halo masses, we show that this behaviour is remarkably consistent with the evolving cold- to hot-accretion transition mass, as predicted by theory and defined by the redshift-independent M shock at z < 1 . 4 and by the rising M stream at z (cid:38) 1 . 4 (for which we propose a revision in agreement with the latest simulations). We therefore argue that the MS bending is primarily due to a drop in cold accretion, causing a reduction in available cold gas in galaxies, which supports predictions of gas feeding theory. In particular, the rapidly rising M 0 with redshift at z > 1 is evidence in favour of the cold-streams scenario. In this picture, a progressive fuelling reduction rather than its sudden suppression in halos more massive than M shock / M stream produces a nearly constant star-formation rate in galaxies with stellar masses larger than M 0 , and not their quenching, which therefore requires other physical processes. Compared to the knee M ∗ in the stellar mass function of galaxies, M 0 is significantly lower at z < 1 . 5, and higher at z > 2, suggesting that the imprint of gas deprivation on the distribution of galaxy masses happened at early times ( z > 1 . 5–2). The typical mass at which galaxies inside the MS become bulge-dominated evolves di ff erently from M 0 , which is consistent with the idea that bulge formation is a distinct process from the phasing out of cold accretion.