Effect of local environment on Ly$\alpha$ line profile in DESI/ODIN LAEs

Lyman-Alpha Emitters (LAEs) are star-forming galaxies with significant Ly$\alpha$ emission and are often used as tracers of large-scale structure at high redshift. We explore the relationship between the Ly$\alpha$ line profile and environmental density with spectroscopy from the Dark Energy Spectroscopic Instrument (DESI) of LAEs selected with narrow-band photometry through the One-hundred-deg$^2$ DECam Imaging in Narrowbands (ODIN) survey. We use LAE surface density maps in the N419 (z $\sim$ 2.45) and N501 (z $\sim$ 3.12) narrow bands to probe the relationship between local environmental density and the Ly$\alpha$ line profile. In both narrow bands, we stack the LAE spectra in bins of environmental density and inside and outside of protocluster regions. The N501 data shows $\sim$15% higher Ly$\alpha$ line luminosity for galaxies in protoclusters, suggesting increased star formation in these regions. However, the line luminosity is not appreciably greater in protocluster galaxies in the N419 band, suggesting a potential redshift evolution of this effect. The shape of the line profile itself does not vary with environmental density, suggesting that line shape changes are caused by local effects independent of a galaxy's environment. These data indicate a potential relationship between LAE local environmental density, ionized gas distribution, and Ly$\alpha$ line luminosity.