ODIN: Identifying Protoclusters and Cosmic Filaments Traced by Ly$\alpha$-emitting Galaxies

To understand the formation and evolution of massive cosmic structures, studying them at high redshift, in the epoch when they formed the majority of their mass is essential. The One-hundred-deg$^2$ DECam Imaging in Narrowbands (ODIN) survey is undertaking the widest-area narrowband program to date, to use Ly$\alpha$-emitting galaxies (LAEs) to trace the large-scale structure (LSS) of the Universe on the scale of 10 - 100 cMpc at three cosmic epochs. In this work, we present results at $z$ = 3.1 based on early ODIN data in the COSMOS field. We identify and characterize protoclusters and cosmic filaments using multiple methods and discuss their strengths and weaknesses. We then compare our observations against the IllustrisTNG suite of cosmological hydrodynamical simulations. The two are in excellent agreement, with a similar number and angular size of structures identified above a specified density threshold. We are able to recover the simulated protoclusters with $\log$(M$_{z=0}$/$M_\odot$) $\gtrsim$ 14.4 in $\sim$ 60% of the cases. With these objects we show that the descendant masses of the protoclusters in our sample can be estimated purely based on our 2D measurements, finding a median $z$ = 0 mass of $\sim10^{14.5}$M$_\odot$. The lack of information on the radial extent of each protocluster introduces a $\sim$0.4 dex uncertainty in its descendant mass. Finally, we show that the recovery of the cosmic web in the vicinity of protoclusters is both efficient and accurate. The similarity of our observations and the simulations imply that our structure selection is likewise robust and efficient, demonstrating that LAEs are reliable tracers of the LSS.