MApping the Most Massive Overdensities Through Hydrogen (MAMMOTH) I:
  Methodology
  Modern cosmology predicts that a galaxy overdensity is associated to a large
reservoir of the intergalactic gas, which can be traced by the Ly$\alpha$
forest absorption. We have undertaken a systematic study of the relation
between Coherently Strong intergalactic Ly$\alpha$ Absorption systems (CoSLAs),
which have highest optical depth ($\tau$) in $\tau$ distribution, and mass
overdensities on the scales of $\sim$ 10 - 20 $h^{-1}$ comoving Mpc. On such
large scales, our cosmological simulations show a strong correlation between
the effective optical depth ($\tau_{\rm{eff}}$) of the CoSLAs and the 3-D mass
overdensities. In moderate signal-to-noise spectra, however, the profiles of
CoSLAs can be confused with high column density absorbers. For $z>2.6$, where
the corresponding Ly$\beta$ is redshifted to the optical, we have developed the
technique to differentiate between these two alternatives. We have applied this
technique to SDSS-III quasar survey at $z = 2.6$ - 3.3, and we present a sample
of five CoSLA candidates with $\tau_{\rm{eff}}$ on 15 $h^{-1}$ Mpc greater than
$4.5\times$ the mean optical depth. At lower redshifts of $z < 2.6$, where the
background quasar density is higher, the overdensity can be traced by
intergalactic absorption groups using multiple sight lines. Our overdensity
searches fully utilize the current and next generation of Ly$\alpha$ forest
surveys which cover a survey volume of $> (1\ h^{-1}$ Gpc)$^3$. In addition,
systems traced by CoSLAs will build a uniform sample of the most massive
overdensities at $z > 2$ to constrain the models of structure formation, and
offer a unique laboratory to study the interactions between galaxy
overdensities and the intergalactic medium.
