Disentangling the galactic and intergalactic components in 313 observed Lyman-alpha line profiles between redshift 0 and 5

Lyman-Alpha (Ly$\alpha$) photons emitted in star-forming galaxies undergo complex radiative transfer through the interstellar (ISM), circumgalactic (CGM), and intergalactic medium (IGM), imprinting characteristic signatures on their observed line profiles. We use the open-source package $\tt{zELDA}$ (redshift Estimator for Line profiles of Distant Lyman-Alpha emitters) to disentangle the galactic and intergalactic contributions in 313 Ly$\alpha$ spectra observed with HST/COS and MUSE, spanning $0<z<6$. $\tt{zELDA}$ employs artificial neural networks trained on mock Ly$\alpha$ spectra generated with Monte Carlo radiative transfer through thin-shell models and IGM transmission curves from the TNG100 simulation. We find that sources at $z<0.5$ exhibit minimal IGM attenuation, whereas at $z>3$ the IGM significantly suppresses the blue peak of Ly$\alpha$. After correcting for IGM effects, the stacked intrinsic galactic Ly$\alpha$ line profiles display remarkably little evolution from $z=0$ to $z=6$. We measure the mean IGM Ly$\alpha$ escape fraction, finding $\langle f^{\mathrm{IGM}}_{\mathrm{esc}}\rangle > 90\%$ for $z<0.5$, decreasing from $\sim0.85$ at $z=3$ to $\sim0.55$ at $z=5$. Our measurement of the redshift evolution of the Ly$\alpha$ IGM escape fraction agrees with independent constraints on the IGM mean optical depth. After a comparison between our $\langle f^{\mathrm{IGM}}_{\mathrm{esc}}\rangle$ estimation and the global Ly$\alpha$ escape fraction from the literature, our findings indicate that the IGM might dominate Ly$\alpha$ observability at redshift $z \gtrsim 5.0$, after which ISM and CGM effects tend to dominate at lower $z$. Our results demonstrate that ${\tt zELDA}$ enables robust reconstruction of intrinsic Ly$\alpha$ spectra and provides a direct probe of the interplay between galactic outflows and IGM transmission across cosmic time.