We present the stellar mass - size relation for 49 galaxies within the z = 1.067 cluster SPT-CL J0546 - 5345 , with FWHM \sim 80-120 mas K _ { \mathrm { s } } -band data from the Gemini multi-conjugate adaptive optics system ( GeMS/GSAOI ) .
This is the first such measurement in a cluster environment , performed at sub-kpc resolution at rest-frame wavelengths dominated by the light of the underlying old stellar populations .
The observed stellar mass - size relation is offset from the local relation by 0.21 dex , corresponding to a size evolution proportional to ( 1 + z ) ^ { -1.25 } , consistent with the literature .
The slope of the stellar mass - size relation \beta = 0.74 \pm 0.06 , consistent with the local relation .
The absence of slope evolution indicates that the amount of size growth is constant with stellar mass .
This suggests that galaxies in massive clusters such as SPT-CL J0546 - 5345 grow via processes that increase the size without significant morphological interference , such as minor mergers and/or adiabatic expansion .
The slope of the cluster stellar mass - size relation is significantly shallower if measured in HST /ACS imaging at wavelengths blueward of the Balmer break , similar to rest-frame UV relations at z = 1 in the literature .
The stellar mass - size relation must be measured at redder wavelengths , which are more sensitive to the old stellar population that dominates the stellar mass of the galaxies .
The slope is unchanged when GeMS K _ { s } -band imaging is degraded to the resolution of K -band HST/NICMOS resolution but dramatically affected when degraded to K _ { s } -band Magellan/FourStar resolution .
Such measurements must be made with AO in order to accurately characterise the sizes of compact , z = 1 galaxies .