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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 $K_{\mathrms}$-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 thelight of the underlying old stellar populations. The observed stellar mass -size relation is offset from the local relation by 0.21 dex, corresponding to asize 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 indicatesthat the amount of size growth is constant with stellar mass. This suggeststhat galaxies in massive clusters such as SPT-CL J0546$-$5345 grow viaprocesses that increase the size without significant morphologicalinterference, such as minor mergers and/or adiabatic expansion. The slope ofthe cluster stellar mass - size relation is significantly shallower if measuredin $HST$/ACS imaging at wavelengths blueward of the Balmer break, similar torest-frame UV relations at $z$ = 1 in the literature. The stellar mass - sizerelation must be measured at redder wavelengths, which are more sensitive tothe old stellar population that dominates the stellar mass of the galaxies. Theslope is unchanged when GeMS $K_s$-band imaging is degraded to the resolutionof $K$-band HST/NICMOS resolution but dramatically affected when degraded to$K_s$-band Magellan/FourStar resolution. Such measurements must be made with AOin order to accurately characterise the sizes of compact, $z$ = 1 galaxies.

monthly notices of the royal astronomical society

The stellar mass - size relation for cluster galaxies at z=1 with high  angular resolution from the Gemini/GeMS multi-conjugate adaptive optics  system