Modeling $237$ Lyman-$\alpha$ spectra of the MUSE-Wide survey

We compare $237$ Lyman-$\alpha$ (Ly$\alpha$) spectra of the "MUSE-Wide survey" (Herenz et al. 2017) to a suite of radiative transfer simulations consisting of a central luminous source within a concentric, moving shell of neutral gas, and dust. This six parameter shell-model has been used numerously in previous studies, however, on significantly smaller data-sets. We find that the shell-model can reproduce the observed spectral shape very well - better than the also common `Gaussian-minus-Gaussian' model which we also fitted to the dataset. Specifically, we find that $\sim 94\%$ of the fits possess a goodness-of-fit value of $p(\chi^2)>0.1$. The large number of spectra allows us to robustly characterize the shell-model parameter range, and consequently, the spectral shapes typical for realistic spectra. We find that the vast majority of the Ly$\alpha$ spectral shapes require an outflow and only $\sim 5\%$ are well-fitted through an inflowing shell. In addition, we find $\sim 46\%$ of the spectra to be consistent with a neutral hydrogen column density $<10^{17}\,\mathrm{cm}^{-2}$ - suggestive of a non-negligible fraction of continuum leakers in the MUSE-Wide sample. Furthermore, we correlate the spectral against the Ly$\alpha$ halo properties against each other but do not find any strong correlation.