demonstrating that the model fits the observations superbly and our observations are noise-limited.

also outputs the ‘best’ parameter values from the maximum posterior model, alongside their errors. These values for the companion galaxy fits are given in Table \[tab:galaxy\_properties\].

Results
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Quasar Host Galaxies
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### Magnitude Limits

![image](figures/quasar_host_photometry_J.pdf) ![image](figures/quasar_host_photometry_H.pdf)

The formal signal-to-noise ratio ($S/N$) of the residual flux in the core of each quasar after PSF-subtraction is presented in Figure \[fig:quasar\_photometry\]. This central region includes residual flux from the core of the quasar PSF, caused by an imperfect match of profiles of the quasar and empirical PSF used for subtraction, alongside any potential host galaxy flux. While the total flux is subtracted correctly, with a median residual consistent with zero, the pixel-to-pixel variation of the PSFs results in pixels with residual flux that is significantly larger than expected by the noise map, with formal signal-to-noise ratios of up to $\left|S/N\right|\simeq30$. In other words, the subtraction technique produces considerable residuals in the inner region. We note that significant quasar over- or under-subtraction is unlikely as this would produce negative or positive residuals in the diffraction spikes, respectively, which are not visible.

To estimate the flux of the host without including 