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Lyman-$α$ emission from a WISE-selected optically faint powerful radio galaxy M151304.72-252439.7 at $z$ = 3.132

We report the detection of a large ($\sim90$ kpc) and luminous $\mathrm{Lyα}$ nebula [$L\mathrm{_{Lyα}}$ = $(6.80\pm0.08)\times 10^{44}$] $\rm{\,erg\,s^{-1}}$ around an optically faint (r$>23$ mag) radio galaxy M1513-2524 at $z\mathrm{_{em}}$=3.132. The double-lobed radio emission has an extent of 184 kpc, but the radio core, i.e., emission associated with the active galactic nucleus (AGN) itself, is barely detected. This object was found as part of our survey to identify high-$z$ quasars based on Wide-field Infrared Survey Explorer (WISE) colors. The optical spectrum has revealed $\mathrm{Lyα}$, NV, CIV and HeII emission lines with a very weak continuum. Based on long-slit spectroscopy and narrow band imaging centered on the $\mathrm{Lyα}$ emission, we identify two spatial components: a "compact component" with high velocity dispersion ($\sim 1500$$\rm{\,km\,s^{-1}}$) seen in all three lines, and an "extended component", having low velocity dispersion (i.e., 700-1000$\rm{\,km\,s^{-1}}$). The emission line ratios are consistent with the compact component being in photoionization equilibrium with an AGN. We also detect spatially extended associated $\mathrm{Lyα}$ absorption, which is blue-shifted within 250-400$\rm{\,km\,s^{-1}}$ of the $\mathrm{Lyα}$ peak. The probability of $\mathrm{Lyα}$ absorption detection in such large radio sources is found to be low ($\sim$10%) in the literature. M1513-2524 belongs to the top few percent of the population in terms of $\mathrm{Lyα}$ and radio luminosities. Deep integral field spectroscopy is essential for probing this interesting source and its surroundings in more detail.