On the (Lack of) Evolution of the Stellar Mass Function of Massive Galaxies from $z$=1.5 to 0.4.

We study the evolution in the number density of the highest mass galaxies over $0.4 10.3$ using a forward-modeling method that fully accounts for statistical and systematic uncertainties on stellar mass. From $z$=0.4 to 1.5 the massive end of the SMF shows minimal evolution in its shape: the characteristic mass ($M^\ast$) evolves by less than 0.1 dex ($\pm$0.05 dex); the number density of galaxies with $\log (M_\ast/M_\odot) >11$ stays roughly constant at $\log (n/\mathrm{Mpc}^{-3})$ $\simeq$ $-$3.4 ($\pm$0.05), then declines to $\log (n/\mathrm{Mpc}^{-3})$=$-$3.7 ($\pm$0.05) at $z$=1.5. We discuss the uncertainties in the SMF, which are dominated by assumptions in the star formation history and details of stellar population synthesis models for stellar mass estimations. For quiescent galaxies, the data are consistent with no (or slight) evolution ($\lesssim0.1$ dex) in the characteristic mass nor number density from $z\sim 1.5$ to the present. This implies that any mass growth (presumably through "dry" mergers) of the quiescent massive galaxy population must balance the rate of mass losses from late-stage stellar evolution and the formation of quenching galaxies from the star-forming population. We provide a limit on this mass growth from $z=1.0$ to 0.4 of $\Delta M_\ast/M_\ast\leq$ 45% (i.e., $\simeq0.16$ dex) for quiescent galaxies more massive than $10^{11}$ $M_\odot$.