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

Lyman-alpha (Ly alpha) is intrinsically the brightest line emitted from active galaxies. While it originates from many physical processes, for star-forming galaxies the intrinsic Ly alpha luminosity is a direct tracer of the Lyman-continuum (LyC) radiation produced by the most massive O- and early-type B-stars (M-* greater than or similar to 10 M-circle dot) with lifetimes of a few Myrs. As such, Ly alpha 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 Ly alpha very hard to interpret due to the uncertain Ly alpha escape fraction, f(esc,Ly alpha). Here we explore results from the CAlibrating cs LYMan-a with Ha (CALYMHA) survey at z = 2.2, follow-up of Ly alpha emitters (LAEs) at z = 2.2 - 2.6 and a z similar to 0-0.3 compilation of LAEs to directly measure f(escLy alpha) with H alpha. We derive a simple empirical relation that robustly retrieves f(esc,Ly alpha) as a function of Ly alpha rest-frame EW (EW0):f(esc,Ly alpha)= 0.0048 EW0[angstrom] +/- 0.05 and we show that it constrains a well-defined anti-correlation between ionisation efficiency (xi ion) and dust extinction in LAEs. Observed Ly alpha luminosities and EW0 are easy measurable quantities at high redshift, thus making our relation a practical tool to estimate intrinsic Ly alpha and LyC luminosities under well controlled and simple assumptions. Our results allow observed Ly alpha luminosities to be used to compute SFRs for LAEs at z similar to 0-2.6 within +/- 0.2 dex of the H alpha dust corrected SFRs. We apply our empirical SFR(Ly alpha ,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(circle dot)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 (log(10)[xi ion/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 H alpha and H beta measurements for high-redshift LAEs.