The connection between stellar mass, age and quenching timescale in massive quiescent galaxies at z simeq 1

We present a spectro-photometric study of a mass-complete sample of quiescent galaxies at $1.0 < z < 1.3$ with $\mathrm{log_{10}}(M_{\star}/\mathrm{M_{\odot}}) \geq 10.3$ drawn from the VANDELS survey, exploring the relationship between stellar mass, age and star-formation history. Within our sample of 114 galaxies, we derive a stellar-mass vs stellar-age relation with a slope of $1.20^{+0.28}_{-0.27}$ Gyr per decade in stellar mass. When combined with recent literature results, we find evidence that the slope of this relation remains consistent over the redshift interval $0<z<4$. The galaxies within the VANDELS quiescent display a wide range of star-formation histories, with a mean star-formation timescale of $1.5\pm{0.1}$ Gyr and a mean quenching timescale of $1.4\pm{0.1}$ Gyr. We also find a large scatter in the quenching timescales of the VANDELS quiescent galaxies, in agreement with previous evidence that galaxies at $z \sim 1$ cease star formation via multiple mechanisms. We then focus on the oldest galaxies in our sample, finding that the number density of galaxies that quenched before $z = 3$ with stellar masses $\mathrm{log_{10}}(M_{\star}/\mathrm{M_{\odot}}) \geq 10.6$ is $ 1.12_{-0.72}^{+1.47} \times 10^{-5} \ \mathrm{Mpc}^{-3}$. Although uncertain, this estimate is in good agreement with the latest observational results at $3<z<4$, tentatively suggesting that neither rejuvenation nor merger events are playing a major role in the evolution of the oldest massive quiescent galaxies within the redshift interval $1<z<3$.