Across the green valley with HST grisms: colour evolution, crossing time-scales, and the growth of the red sequence at z=1.0-1.8

We measure the colour evolution and quenching time-scales of z = 1.0-1.8 galaxies across the green valley. We derive rest-frame NUVrK colours and select blue-cloud, green-valley, and red-sequence galaxies from the spectral energy distribution modelling of CANDELS GOODS-South and UDS multiband photometry. Separately, we constrain the star-formation history (SFH) parameters (ages, tau) of these galaxies by fitting their deep archival HST grism spectroscopy. We derive the galaxy colour-age relation and show that only rapidly evolving galaxies with characteristic delayed-tau SFH time-scales of <0.5 Gyr reach the red sequence at these redshifts, after a period of accelerated colour evolution across the green valley. These results indicate that the stellar mass build-up of these galaxies stays minimal after leaving the blue cloud and entering the green valley (i.e. it may represent less than or similar to 5 per cent of the galaxies' final, quiescent masses). Visual inspection of age-sensitive features in the stacked spectra also supports the view that these galaxies follow a quenching sequence along the blue-cloud -> green-valley -> red-sequence track. For this rapidly evolving population, we measure a green-valley crossing time-scale of 0.99(-0.25)(+0.42) Gyr and a crossing rate at the bottom of the green valley of 0.82(-0.25)(+0.27) mag Gyr(-1). Based on these time-scales, we estimate that the number density of massive (M-* > 10(10)M(circle dot)) red-sequence galaxies doubles every Gyr at these redshifts, in remarkable agreement with the evolution of the quiescent galaxy stellar mass function. These results offer a new approach to measuring galaxy quenching over time and represent a pathfinder study for future JWST, Euclid, and Roman Space Telescope programs.