Quantifying the escape of Lyα at z≈ 5-6: a census of Lyα escape fraction with Hα emitting galaxies spectroscopically confirmed by JWST and VLT/MUSE

JWST provides an unprecedented opportunity for unbiased surveys of Hα-emitting galaxies at z>4 with the NIRCam wide-field slitless spectroscopy (WFSS). In this work, we present a census of Lyα escape fraction (f_esc, Lyα) of 165 star-forming galaxies at z=4.9-6.3 using their Hα emission directly measured from FRESCO NIRCam/WFSS data. We search for Lyα emission of each Hα-emitting galaxy in VLT/MUSE data. The overall f_esc, Lyα measured by stacking is f_esc, Lyα is 0.090±0.006. We find that f_esc, Lyα displays a strong dependence on the observed UV slope (β_ obs) and E(B-V), such that the bluest galaxies (β_ obs∼-2.5) have the largest escape fractions (f_ esc, Lyα≈0.6), indicative of the crucial role of dust and gas in modulating the escape of Lyα photons. f_esc, Lyα is less well related to other parameters, including the UV luminosity and stellar mass, and the variation in f_esc, Lyα with them can be explained by their underlying coupling with E(B-V) or β_ obs. Our results suggest a tentative decline in f_esc, Lyα at z≳ 5, implying increasing intergalactic medium attenuation towards higher redshift. Furthermore, the dependence of f_esc, Lyα on β_ obs is proportional to that of the ionizing photon escape fraction (f_ esc, LyC), indicating the escape of Lyα and ionizing photon may be regulated by similar physical processes. With f_esc, Lyα as a proxy to f_ esc, LyC, we infer that UV-faint (M_ UV>-16) galaxies contribute >70% of the total ionizing emissivity at z=5-6. If these relations hold during the epoch of reionization, UV-faint galaxies can contribute the majority of UV photon budget to reionize the Universe.