ODIN: Rest-frame Optical Morphologies and Star Formation Activity of Ly{α} Emitters at z=2.4, 3.1, and 4.5

We analyze the rest-frame optical (~8000 {\AA}) morphologies and star formation activity of Ly{\alpha} emitters (LAEs) at redshifts $2.4$, $3.1$, and $4.5$, identified in the ODIN survey. To compare their physical properties with those of other galaxies, we construct a comparison sample of typical star-forming galaxies (SFGs) at similar redshifts from the COSMOS2025 catalog. Using the \textit{JWST}/NIRCam images from the COSMOS-Web survey, we measure the rest-frame optical sizes and S\'ersic indices. We first examine their size-mass relations and find that LAEs at all three redshifts have smaller sizes than typical SFGs, with the size difference decreasing at higher redshifts. We also find that LAEs tend to have larger S\'ersic indices at $z=2.4$ and $3.1$ than typical SFGs, but the difference becomes weaker at $z=4.5$. These trends are qualitatively reproduced in the Horizon Run 5 cosmological hydrodynamical simulation. We then investigate star formation activity and find that LAEs exhibit higher star formation rates than typical SFGs at all redshifts considered. Finally, we examine the connection between Ly{\alpha} emission and galaxy structure, finding that the rest-frame equivalent width (REW) of the Ly{\alpha} emission line has negative and positive correlations with size and S\'ersic index, respectively. In addition, we find a strong positive correlation between the Ly{\alpha} REW and the ratio of the instantaneous star formation rate to that averaged over the last $100\;\mathrm{Myr}$ (i.e., $\mathrm{SFR_{inst}}/\mathrm{SFR_{100 Myr}}$). These results suggest the compact and starbursting nature of LAEs, and provide important constraints on the physical mechanism for the Ly{\alpha} photon escape from galaxies.