The KMOS Cluster Survey (KCS) I: The fundamental plane and the formation ages of cluster galaxies at redshift $1.4<z<1.6$

We present the analysis of the fundamental plane (FP) for a sample of 19 massive red-sequence galaxies ($M_{\star }>4\times {10}^{10}{M}_{\odot }$) in 3 known overdensities at $1.39<z<1.61$ from the KMOS Cluster Survey, a guaranteed time program with spectroscopy from the K-band Multi-Object Spectrograph (KMOS) at the VLT and imaging from the Hubble Space Telescope. As expected, we find that the FP zero-point in $B$ band evolves with redshift, from the value 0.443 of Coma to $-0.10\pm 0.09$, $-0.19\pm 0.05$, $-0.29\pm 0.12$ for our clusters at $z=1.39$, $z=1.46$, and $z=1.61$, respectively. For the most massive galaxies ($\log M_{\star }\mathrm{/}{M}_{\odot }>11$) in our sample, we translate the FP zero-point evolution into a mass-to-light-ratio $M\mathrm{/}L$ evolution finding $\Delta \log M/L_{B}=(-0.46\pm0.10)z$,$\Delta \log M/L_{B}=(-0.52\pm0.07)z$,to$\Delta \log M/L_{B}=(-0.55\pm0.10)z$, respectively. We assess the potential contribution of the galaxies structural and stellar velocity dispersion evolution to the evolution of the FP zero-point and find it to be $\sim$6-35 % of the FP zero-point evolution. The rate of $M\mathrm{/}L$ evolution is consistent with galaxies evolving passively. By using single stellar population models, we find an average age of $2.33_{-0.51}^{+0.86}$ Gyr for the $\log M_{\star}/M_{\odot}>11$galaxiesinourmassiveandvirializedclusterat$z=1.39$,$1.59^{+1.40}{-0.62}$Gyrinamassivebutnotvirializedclusterat$z=1.46$,and$1.20^{+1.03}{-0.47}$Gyrinaprotoclusterat$z=1.61$. After accounting for the difference in the age of the Universe between redshifts, the ages of the galaxies in the three overdensities are consistent within the errors, with possibly a weak suggestion that galaxies in the most evolved structure are older.