Reionization morphology and intrinsic velocity offsets allow transmission of Lyman-α emission from JADES-GS-z13-1-LA

We investigate the detectability of Lyman-$\alpha$ (Ly$\alpha$) emission from galaxies at the onset of cosmic reionization, aiming to understand the conditions necessary for detecting high-redshift sources like JADES-GS-z13-1-LA at $z=13$. By integrating galaxy formation models with detailed intergalactic medium (IGM) reionization simulations, we construct high-redshift galaxy catalogs to model intrinsic Ly$\alpha$ profiles and assess their transmission through the IGM. For a galaxy with $M_{\rm UV}\sim -18.5$ like JADES-GS-z13-1-LA, our fiducial model predicts a Ly$\alpha$ transmission of ${\sim}13$% and there is a probability of observing Ly$\alpha$ emission with an equivalent width >40A of up to 10%. We also explore how variations in the UV ionizing escape fraction, dependent on host halo mass, impact Ly$\alpha$ detectability. Our findings reveal that reionization morphology significantly influences detection chances -- models where reionization is driven by low-mass galaxies can boost the detection probability to as much as 12%, while those driven by massive galaxies tend to reduce ionized regions around faint emitters, limiting their detectability. This study underscores the importance of reionization morphology in interpreting high-redshift Ly$\alpha$ observations.