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We study the relationship between the morphology and star formation history(SFH) of 361 quiescent galaxies (QGs) at redshift $\langlez_{obs}\rangle\approx 2$, with stellar mass $\log M_*\ge10.3$, selected withthe UVJ technique. Taking advantage of panchromatic photometry covering therest-frame UV-to-NIR spectral range ($\approx40$ bands), we reconstruct thenon-parametric SFH of the galaxies with the fully Bayesian SED fitting codeProspector. We find that the half-light radius $R_e$, observed at $z_{obs}$,depends on the formation redshift of the galaxies, $z_{form}$, and that thisrelationship depends on stellar mass. At $\log M_*<11$, the relationship isconsistent with $R_e\propto(1+z_{form})^{-1}$, in line with the expectationthat the galaxies' central density depends on the cosmic density at the time oftheir formation, i.e. the "progenitor effect". At $\log M_*>11$, therelationship between $R_e$ and $z_{form}$ flattens, suggesting that mergersbecome increasingly important for the size growth of more massive galaxiesafter they quenched. We also find that the relationship between $z_{form}$ andgalaxy compactness similarly depends on stellar mass. While no clear trend isobserved for QGs with $\log M_*>11$, lower-mass QGs that formed earlier, i.e.with larger $z_{form}$, have larger central stellar mass surface densities,both within the $R_e$ ($\Sigma_e$) and central 1 kpc ($\Sigma_{1kpc}$), andalso larger $M_{1kpc}/M_*$, the fractional mass within the central 1 kpc. Thesetrends between $z_{form}$ and compactness, however, essentially disappear, ifthe progenitor effect is removed by normalizing the stellar density with thecosmic density at $z_{form}$. Our findings highlight the importance ofreconstructing the SFH of galaxies before attempting to infer their intrinsicstructural evolution.

astrophysical journal/the astrophysical journal

Reconstructing the Assembly of Massive Galaxies. I: The Importance of  the Progenitor Effect in the Observed Properties of Quiescent Galaxies at  $z\approx 2$