No evidence for a dependence of the mass size relation of early-type galaxies on environment in the local Universe

The early--type galaxy (ETG) mass--size relation has been largely studied to understand how these galaxies have assembled their mass. One key observational result of the last years is that massive galaxies increased their size by a factor of a few at fixed stellar mass from $z\sim2$. Hierarchical models favor minor mergers as a plausible driver of this size growth. Some of these models, predict a significant environmental dependence in the sense that galaxies residing in more massive halos tend to be larger than galaxies in lower mass halos, at fixed stellar mass and redshift. At present, observational results of this environmental dependence have been contradictory. In this paper we revisit this issue in the local Universe, by investigating how the sizes of massive ETGs depend on large-scale environment using an updated and accurate sample of ETGs in different environments - field, group, clusters - from the Sloan Digital Sky Survey DR7. Our analysis does not show any significant environmental dependence of the sizes of central and satellites ETGs at fixed stellar mass at $z\sim0$. The size-mass relation of early-type galaxies at $z\sim0$ seems to be universal, i.e., independent of the mass of the host halo and of the position of the galaxy in that halo (central or satellite). The result is robust to different galaxy selections based on star formation, morphology or central density. In fact, considering our observational errors and the size of the sample, any size ratio larger than $30-40%$ between massive galaxies ($log(M_*/M_\odot)>11$) living in clusters and in the field can be ruled out at $3σ$ level.