Modeling spatially-resolved galactic H$\alpha$ emission for galaxy clustering

Near-infrared spectroscopic surveys target high-redshift emission-line galaxies (ELGs) to probe cosmological scenarios. Understanding the clustering properties of ELGs is essential to derive optimal constraints. We present a simple radiative transfer model for spatially resolved galactic H$\alpha$ emission, which includes emission from the warm-hot diffuse interstellar medium. The atomic level populations are in steady-state and computed in the coronal approximation. The model is applied to multiple IllustrisTNG simulations in the redshift range $1\leq z \leq 2$ to produce the luminosity function (LF) and the halo occupation distribution (HOD). Collisional processes account for a significant fraction of $\approx 40\%$ of the total ${\rm H}\alpha$ luminosity ($L_{{\rm H}\alpha}$). Our LFs are in reasonable agreement with measurements from H$\alpha$ surveys if a uniform extinction of $0.3<A_{{\rm H}\alpha}<0.85$ mag is assumed. Our HOD is consistent with that of the ${\it Euclid}$ Flagship galaxy mock up to differences that can be attributed to baryonic feedback, which is absent from the latter. When H$\alpha$ luminosities are computed from an empirical relation between $L_{{\rm H}\alpha}$ and the total star formation rate (SFR) the resulting LFs are in tension with previous observations. Our approach can be extended to other atomic lines, which should be helpful for the mining of high-redshift galaxy spectra in forthcoming surveys.