Determining the systemic redshift of Lyman-alpha emitters with neural networks and improving the measured large-scale clustering

We explore how to mitigate the clustering distortions in Lyman-$\alpha$ emitters (LAEs) samples caused by the miss-identification of the Lyman-$\alpha$ (Ly$\alpha$) wavelength in their Ly$\alpha$ line profiles. We use the Ly$\alpha$ line profiles from our previous LAE theoretical model that includes radiative transfer in the interstellar and intergalactic mediums. We introduce a novel approach to measure the systemic redshift of LAEs from their Ly$\alpha$ line using neural networks. In detail, we assume that, for a fraction of the whole LAE population their systemic redshift is determined precisely through other spectral features. We then use this subset to train a neural network that predicts the Ly$\alpha$ wavelength given a Ly$\alpha$ line profile. We test two different training sets: i) the LAEs are selected homogeneously and ii) only the brightest LAEs are selected. In comparison with previous approaches in the literature, our methodology improves significantly both accuracy and precision in determining the Ly$\alpha$ wavelength. In fact, after applying our algorithm in ideal Ly$\alpha$ line profiles, we recover the clustering unperturbed down to 1cMpc/h. Then, we test the performance of our methodology in realistic Ly$\alpha$ line profiles by downgrading their quality. The machine learning techniques work well even if the Ly$\alpha$ line profile quality is decreased considerably. We conclude that LAE surveys such as HETDEX would benefit from determining with high accuracy the systemic redshift of a subpopulation and applying our methodology to estimate the systemic redshift of the rest of the galaxy sample.