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.
