This shows that our companion galaxy sizes are as large as the largest $z\simeq6$ CANDELS field galaxies, but are larger than the median size of $z\simeq6$ field galaxies by an average of $0\farcs1$. Their Sérsic profiles are as steep as the steepest Sérsic indexes of CANDELS $z\simeq6$ field galaxies, but are larger than the median Sérsic index of $z\simeq6$ field galaxies by an average of 2. Thus, our potential quasar companion galaxies have morphological parameters that are consistent with the larger and steeper-Sérsic CANDELS $z\simeq6$ field galaxies. Similar conclusions are made when comparing our potential companion galaxies to neighbors within $3''$ of $z\simeq6$ galaxies in the CANDELS GOODS-South sample [Figure \[fig:3DHST\], @VanDerWel2012], of which the majority (95%) are foreground objects at $z<5.5$. Our potential companions have sizes and Sérsic indices that are larger than the median of the neighbors of $z\simeq6$ CANDELS galaxies, although their properties are reasonably consistent with the more massive neighbors. Hence, based on their size and Sérsic distributions we cannot determine whether our observed neighbors are more likely to be $z\simeq6$ galaxies than foreground interlopers.

We show the relationship between size and UV absolute magnitude for these potential companion galaxies in Figure \[fig:size\_mag\], assuming they are 