The evolution of compact massive quiescent and starforming galaxies derived from the $R_e-R_h$ and $M_{\rm star}-M_h$ relations

The mean size ( effective radius $R_e$) of Massive Galaxies (MGs, $M_{\rm star}>10^{11.2}M_\odot$) is observed to increase steadily with cosmic time. It is still unclear whether this trend originates from the size growth of individual galaxies (via, e.g., mergers and/or AGN feedback) or from the inclusion of larger galaxies entering the selection at later epochs (progenitor bias). We here build a data-driven, flexible theoretical framework to probe the structural evolution of MGs. We assign galaxies to dark matter haloes via stellar mass-halo mass (SMHM) relations with varying high-mass slopes and scatters $\sigma_{\rm SMHM}$ in stellar mass at fixed halo mass, and assign sizes to galaxies using an empirically-motivated, constant and linear relationship between $R_e$ and the host dark matter halo radius $R_h$. We find that: 1) the fast mean size growth of MGs is well reproduced independently of the shape of the input SMHM relation; 2) the numbers of compact MGs grow steadily until $z\gtrsim2$ and fall off at lower redshifts, suggesting a lesser role of progenitor bias at later epochs; 3) a time-independent scatter $\sigma_{\rm SMHM}$ is consistent with a scenario in which compact starforming MGs transition into quiescent MGs in a few $10^8$yr with a negligible structural evolution during the compact phase, while a scatter increasing at high redshift implies significant size growth during the starforming phase. A robust measurement of the size function of MGs at high redshift can set strong constraints on the scatter of the SMHM relation and, by extension, on models of galaxy evolution.
Comment: Accepted for publication in MNRAS. Comments still welcome