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.
