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 multi-band
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 $\lesssim
5\%$ 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 $\rightarrow$
green-valley $\rightarrow$ red-sequence track. For this rapidly evolving
population, we measure a green-valley crossing time-scale of
$0.99^{+0.42}_{-0.25}$ Gyr and a crossing rate at the bottom of the green
valley of $0.82^{+0.27}_{-0.25}$ mag/Gyr. Based on these time-scales, we
estimate that the number density of massive ($M_\star>10^{10} M_\odot$)
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.
