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 $\mathrm{l}\mathrm{o}{\mathrm{g}}_{10}(M_{\star }\mathrm{/}{\mathrm{M}}_{\odot })\ge 10.3$ 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 $1.20_{-0.27}^{+0.28}$ 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 $\mathrm{l}\mathrm{o}{\mathrm{g}}_{10}(M_{\star }\mathrm{/}{\mathrm{M}}_{\odot })\ge 10.6$ is $1.12_{-0.72}^{+1.47}\times {10}^{-5}{\mathrm{M}\mathrm{p}\mathrm{c}}^{-3}$. 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 $1<z<3$.