HST/WFC3 grism observations of $z~\mathtt{\sim}~1$ clusters: The cluster vs. field stellar mass-size relation and evidence for size growth of quiescent galaxies from minor mergers

Minor mergers are thought to be responsible for the size growth of quiescent field galaxies with decreasing redshift. We test this hypothesis using the cluster environment as a laboratory. Satellite galaxies in clusters move at high velocities, making mergers between them rare. The stellar mass-size relation in ten clusters and in the field is measured and compared at $z~\mathtt{\sim}~1$. Our cluster sample contains 344 spectroscopically-confirmed cluster members with Gemini/GMOS and 182 confirmed with HST WFC3 G141 grism spectroscopy. On average, quiescent and star-forming cluster galaxies are smaller than their field counterparts by ($0.08\pm0.04$) dex and ($0.07\pm0.01$) dex respectively. These size offsets are consistent with the average sizes of quiescent and star-forming field galaxies between $1.2\leqslant z\leqslant1.5$, implying the cluster environment has inhibited size growth between this period and $z~\mathtt{\sim}~1$. The negligible differences measured between the $z~\mathtt{\sim}~0$ field and cluster quiescent mass-size relations in other works imply that the average size of quiescent cluster galaxies must rise with decreasing redshift. Using a toy model, we show that the disappearance of the compact cluster galaxies might be explained if, on average, $\mathtt{\sim}40\%$ of them merge with their brightest cluster galaxies (BCGs) and $\mathtt{\sim}60\%$ are tidally destroyed into the intra-cluster light (ICL) between $0\leqslant z\leqslant1$. This is in agreement with the observed stellar mass growth of BCGs between $0\leqslant z\leqslant1$ and the observed ICL stellar mass fraction at $z~\mathtt{\sim}~0$. Our results support minor mergers as the cause for the size growth in quiescent field galaxies, with cluster-specific processes responsible for the similarity between the field and cluster quiescent mass-size relations at low redshift.