Evolution of massive quiescent galaxies via envelope accretion

Massive quiescent galaxies at high redshift are significantly more compact than their present-day counterparts. We investigate the roles, in determining this evolution, of major and minor mergers, and of the accretion of diffuse envelopes of stars and dark matter. We model the evolution in stellar mass ($M_\star$), effective radius ($R_{\rm e}$), and effective stellar velocity dispersion ($\sigma_{\rm e}$) of a representative massive quiescent galaxy from $z\approx 3$ to $z\approx 0$, and compare the model with the observed redshift-dependent $R_{\rm e}$-$M_\star$ and $\sigma_{\rm e}$-$M_\star$ relations. In the model we account for the effects of collisionless (dry) major (satellite-to-main galaxy mass ratio $\xi>1/4$) and minor ($1/10<\xi<1/4$) mergers, using analytic recipes consistent with the results of $N$-body simulations of binary mergers. For the poorly constrained mini mergers ($\xi<1/10$) we explore both a 'standard' model (based on the same assumptions used in the case of higher-$\xi$ mergers), and a heuristic 'envelope accretion' model, aimed at describing the case in which diffuse satellites are completely disrupted in the galaxy outskirts. Major and minor dry mergers, at rates estimated observationally from galaxy-pair counts, induce relatively small variations in $R_{\rm e}$ and $\sigma_{\rm e}$, accounting only for $\approx 6\% $ of the size evolution and $\approx 40\%$ of the velocity-dispersion evolution observed from $z\approx 3$ to $z\approx 0$. As an addition to major and minor dry mergers, envelope accretion performs better than standard mini mergers at reproducing the redshift-dependence of the $R_{\rm e}$-$M_\star$ and $\sigma_{\rm e}$-$M_\star$ relations, being also consistent with plausible evolutionary scenarios of scaling relations involving the mass of the central supermassive black hole.