Characterizing Protoclusters and Protogroups at z $\sim$ 2.5 Using Ly$\alpha$ Tomography

Ly-$\alpha$ tomography surveys have begun to produce three-dimensional (3D) maps of the intergalactic medium (IGM) opacity at $z \sim 2.5$ with Mpc resolution. These surveys provide an exciting new way to discover and characterize high-redshift overdensities, including the progenitors of today's massive groups and clusters of galaxies, known as protogroups and protoclusters. We use the IllustrisTNG-$300$ hydrodynamical simulation to build mock maps that realistically mimic those observed in the Ly-$\alpha$ Tomographic IMACS Survey (LATIS). We introduce a novel method for delineating the boundaries of structures detected in 3D Ly-$\alpha$ flux maps by applying the watershed algorithm. We provide estimators for the dark matter masses of these structures (at $z\sim2.5$), their descendant halo masses at $z=0$, and the corresponding uncertainties. We also investigate the completeness of this method for the detection of protogroups and protoclusters. Compared to earlier work, we apply and characterize our method over a wider mass range that extends to massive protogroups. We also assess the widely used fluctuating Gunn-Peterson approximation (FGPA) applied to dark-matter-only simulations; we conclude while it is adequate for estimating the Ly-$\alpha$ absorption signal from moderate-to-massive protoclusters ($\gtrsim 10^{14.2} M_{\odot}$), it artificially merges a minority of lower-mass structures with more massive neighbors. Our methods will be applied to current and future Ly-$\alpha$~tomography surveys to create catalogs of overdensities and study environment-dependent galaxy evolution in the Cosmic~Noon~era.