ODIN: Using multiplicity of Lyman-Alpha Emitters to assess star formation activity in dark matter halos

Abstract: We investigate if systems of multiple Lyman-alpha emitters (LAEs) can serve as a proxy for dark matter halo mass, assess how their radiative properties relate to the underlying halo conditions, and explore the physics of star formation activity in LAEs and its relation to possible physically related companions. We use data from the One-hundred-deg$<sup>2$ DECam Imaging in Narrowbands (ODIN) survey, which targets LAEs in three narrow redshift slices. We identify physically associated LAE multiples in the COSMOS field at $z = 2.4$, $z = 3.1$, and $z=4.5$, and use a mock catalog from the IllustrisTNG100 simulation to assess the completeness and contamination affecting the resulting sample of LAE multiples. We then study their statistical and radiative properties as a function of multiplicity, where we adopt the term multiplicity to refer to the number of physically associated LAEs. We find a strong correlation between LAE multiplicity and host halo mass in the mocks, with higher multiplicity systems preferentially occupying more massive halos. In both ODIN and the mock sample, we find indications that the mean Ly$\alpha$ luminosity and UV magnitude of LAEs in multiples increase with multiplicity. The halo-wide LAE surface brightness densities in Ly$\alpha$ and UV increase with multiplicity, reflecting more compact and actively star-forming environments. The close agreement between the model and ODIN observations supports the validity of the Ly$\alpha$ emission model in capturing key physical processes in LAE environments. Finally, a subhalo-based perturbation induced star formation model reproduces the minimum subhalo mass distribution in simulations at $z=2.4$, suggesting that local perturbations, rather than the presence of LAE companions, drive star formation in these systems. For the higher redshifts, neighbor perturbations do not seem to be the main driver that triggers star formation.