We present the stellar mass-size relations for elliptical, lenticular, and spiral galaxies in the field and cluster environments using HST/ACS imaging and data from the Space Telescope A901/2 Galaxy Evolution Survey (STAGES). We use a large sample of ~1200 field and cluster galaxies, and a sub-sample of cluster core galaxies, and quantify the significance of any putative environmental dependence on the stellar mass-size relation. For elliptical, lenticular, and high-mass (log M*/M_sun > 10) spiral galaxies we find no evidence to suggest any such environmental dependence, implying that internal drivers are governing their size evolution. For intermediate/low-mass spirals (log M*/M_sun < 10) we find evidence, significant at the 2-sigma level, for a possible environmental dependence on galaxy sizes: the mean effective radius a_e for lower-mass spirals is ~15-20 per cent larger in the field than in the cluster. This is due to a population of low-mass large-a_e field spirals that are largely absent from the cluster environments. These large-a_e field spirals contain extended stellar discs not present in their cluster counterparts. This suggests the fragile extended stellar discs of these spiral galaxies may not survive the environmental conditions in the cluster. Our results suggest that internal physical processes are the main drivers governing the size evolution of galaxies, with the environment possibly playing a role affecting only the discs of intermediate/low-mass spirals.
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