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.