The Scaling Relation between Galaxy Luminosity and WHIM Density from
  EAGLE Simulations with application to SDSS data
  This paper presents an updated scaling relation between the optical
luminosity density (LD) of galaxies in the $r$ band and the density of the
warm-hot intergalactic medium (WHIM) in cosmic filaments, using the
high-resolution EAGLE simulations. We find a strong degree of correlation
between the WHIM density and the galaxy luminosity density, resulting in a
scaling relation between the two quantities that permits to predict the WHIM
density of filaments with a scatter of less than $\frac{1}{2}$ dex in a broad
range of smoothed filament luminosity densities. In order to estimate the
performance of the simulation-based calibration of the LD-WHIM density
relation, we applied it to a sample of low-redshift filaments detected with the
\emph{Bisous} method in the Legacy Survey SDSS~DR12 data. In the volume covered
by the SDSS data, our relation predicts a WHIM density amounting to
$31\pm7\pm12$ % (statistical errors followed by systematic) of cosmic baryon
density. This agrees, albeit within the large uncertainties, with the current
estimates of the cosmological missing baryon fraction, implying that our
LD-WHIM density relation may be a useful tool in the search for the missing
baryons. This method of analysis provides a new promising avenue to study the
physical properties of the missing baryons, using an observable that is
available for large volumes of the sky, complementary and independent from WHIM
searches with absorption-line systems in the FUV or X-rays.
