Predicting Lyα escape fractions with a simple observable: Lyα in emission as an empirically calibrated star formation rate indicator

Lyman-α (Lyα) is intrinsically the brightest line emitted from active galaxies. While it originates from many physical processes, for star-forming galaxies the intrinsic Lyα luminosity is a direct tracer of the Lyman-continuum (LyC) radiation produced by the most massive O- and early-type B-stars (M⋆ ≳ 10 M⊙) with lifetimes of a few Myrs. As such, Lyα luminosity should be an excellent instantaneous star formation rate (SFR) indicator. However, its resonant nature and susceptibility to dust as a rest-frame UV photon makes Lyα very hard to interpret due to the uncertain Lyα escape fraction, fesc, Lyα. Here we explore results from the CAlibrating LYMan-α with Hα (CALYMHA) survey at z = 2.2, follow-up of Lyα emitters (LAEs) at z = 2.2 − 2.6 and a z ∼ 0−0.3 compilation of LAEs to directly measure fesc, Lyα with Hα. We derive a simple empirical relation that robustly retrieves fesc, Lyα as a function of Lyα rest-frame EW (EW0): fesc,Lyα = 0.0048 EW0[Å] ± 0.05 and we show that it constrains a well-defined anti-correlation between ionisation efficiency (ξion) and dust extinction in LAEs. Observed Lyα luminosities and EW0 are easy measurable quantities at high redshift, thus making our relation a practical tool to estimate intrinsic Lyα and LyC luminosities under well controlled and simple assumptions. Our results allow observed Lyα luminosities to be used to compute SFRs for LAEs at z ∼ 0−2.6 within ±0.2 dex of the Hα dust corrected SFRs. We apply our empirical SFR(Lyα,EW0) calibration to several sources at z ≥ 2.6 to find that star-forming LAEs have SFRs typically ranging from 0.1 to 20 M⊙ yr−1 and that our calibration might be even applicable for the most luminous LAEs within the epoch of re-ionisation. Our results imply high ionisation efficiencies (log10[ξion/Hz erg−1] = 25.4−25.6) and low dust content in LAEs across cosmic time, and will be easily tested with future observations with JWST which can obtain Hα and Hβ measurements for high-redshift LAEs.