with emissivity estimates from the [Ly$\alpha$]{} forest [e.g. @Bolton:2007p3273; @McQuinn:2011p3293]. We allow $\zeta$ to vary within the range $\zeta\in[5,100]$. Since, $\zeta$ is empirically defined unlike $f_{\rm esc}$ which can be observationally constrained at lower redshift, we will often provide both when recovering our parameter constraints. For our range of $\zeta$, this corresponds to $f_{\rm esc}\in[0.05,1]$ using our fiducial values adopted in equation (\[eq:Zeta\]). In this work, we will first consider a constant $\zeta$ (Section \[sec:SGP\]) before considering a more generalized halo mass-dependent model in Section \[sec:DPL\].

### Mean free path of ionizing photons within ionized regions, $R_{\rm mfp}$

The propagation of ionizing photons through the [IGM]{} strongly depends on the abundances and properties of absorption systems (Lyman limit as well as more diffuse systems), which are below the resolution limits of EoR simulations. These systems act as photon sinks, roughly dictating the maximum scales to which [H[II]{}]{} bubbles can grow around ionizing galaxies. In EoR modelling this effect is usually parametrized with an implicit maximum horizon for ionizing photons (corresponding to the maximum filtering scale in excursion-set EoR models). Physically, this maximum horizon is taken to correspond to the mean free path of ionizing photons within ionized regions, $R_{\rm mfp}$ 