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Lyman-alpha (Lya) is intrinsically the brightest line emitted from activegalaxies. While it originates from many physical processes, for star-forminggalaxies the intrinsic Lya luminosity is a direct tracer of the Lyman-continuum(LyC) radiation produced by the most massive O- and early-type B-stars withlifetimes of a few Myrs. As such, Lya luminosity should be an excellentinstantaneous star formation rate (SFR) indicator. However, its resonant natureand susceptibility to dust as a rest-frame UV photon makes Lya very hard tointerpret due to the uncertain Lya escape fraction, f$_{esc,Ly\alpha}$. Here weexplore results from the CALYMHA survey at z=2.2, follow-up of Lya emitters(LAEs) at z=2.2-2.6 and a z~0-0.3 compilation of LAEs to directly measuref$_{esc,Ly\alpha}$ with H-alpha (Ha). We derive a simple empirical relationthat robustly retrieves f$_{esc,Ly\alpha}$ as a function of Lya rest-frame EW(EW$_0$): f$_{esc,Ly\alpha}$= 0.0048 EW$_0$[A]$\pm0.05$ and we show that itconstrains a well-defined anti-correlation between ionisation efficiency anddust extinction in LAEs. Observed Lya luminosities and EW$_0$ are easymeasurable quantities at high redshift, thus making our relation a practicaltool to estimate intrinsic Lya and LyC luminosities under well controlled andsimple assumptions. Our results allow observed Lya luminosities to be used tocompute SFRs for LAEs at z~0-2.6 within 0.2 dex of the Ha dust corrected SFRs.We apply our empirical SFR(Lya,EW$_0$) calibration to several sources at z>2.6to find that star-forming LAEs have SFRs typically ranging from 0.1 to 20M$_{\odot}$/yr and that our calibration might be even applicable for the mostluminous LAEs within the epoch of re-ionisation. Our results imply highionisation efficiencies and low dust content in LAEs across cosmic time, andwill be easily tested with future observations with JWST.

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