Lyman-$\alpha$ 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
$\mathrm{Ly\alpha}$ nebula [$L\mathrm{_{Ly\alpha}}$ = $(6.80\pm0.08)\times
10^{44}$] $\rm{\,erg\,s^{-1}}$ 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
$\mathrm{Ly\alpha}$, NV, CIV and HeII emission lines with a very weak
continuum. Based on long-slit spectroscopy and narrow band imaging centered on
the $\mathrm{Ly\alpha}$ 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 $\mathrm{Ly\alpha}$ absorption, which is blue-shifted within
250-400$\rm{\,km\,s^{-1}}$ of the $\mathrm{Ly\alpha}$ peak. The probability of
$\mathrm{Ly\alpha}$ 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 $\mathrm{Ly\alpha}$ and radio
luminosities. Deep integral field spectroscopy is essential for probing this
interesting source and its surroundings in more detail.
