at the same redshift as the quasar. Our objects that have UV magnitudes and slopes consistent with $z\simeq6$ galaxies lie on a relatively tight size-luminosity relation. This relation is fairly consistent with, but somewhat higher than, that of $z\simeq6$ Lyman-break galaxies measured by @Shibuya2015 (for galaxies with $-22\lesssim M_{\textrm{UV}} \lesssim -18$ mag) and @Kawamata2018 (for galaxies with $-21.5\lesssim M_{\textrm{UV}} \lesssim -12$ mag), with our objects having larger sizes at the same luminosities.

We note that the measured sizes of galaxies may be affected by systematic differences between these studies. For example, the treatment of the sky background in the fitting can have a significant impact on the resulting Sérsic fit parameters [see, e.g., @Guo2009; @Bruce2012]. We include the background level as a free parameter in the MCMC-fitting, which can result in larger values of $R_e$ and Sérsic index $n$ than if the background level is fixed [@Bruce2012], potentially contributing to some of the discrepancy between our results and those of @Shibuya2015, who assume a fixed background level. @Bruce2012 show that there is a positive correlation between measured $R_e$ and Sérsic index $n$. @Shibuya2015 assume $n=1.5$ for Lyman-break galaxies, and @Kawamata2018 fix $n=1$. As our fitting method finds larger Sérsic indices 