Recovering the systemic redshift of galaxies from their Lyman alpha line profile

The Lyman alpha (lya) line of Hydrogen is a prominent feature in the spectra of star-forming galaxies, usually redshifted by a few hundreds of km/s compared to the systemic redshift. This large offset hampers follow-up surveys, galaxy pair statistics and correlations with quasar absorption lines when only lya is available. We propose diagnostics that can be used to recover the systemic redshift directly from the properties of the lya line profile. We use spectroscopic observations of Lyman-Alpha Emitters (LAEs) for which a precise measurement of the systemic redshift is available. Our sample contains 13 sources detected between z~3 and z~6 as part of various Multi Unit Spectroscopic Explorer (MUSE) Guaranteed Time Observations (GTO). We also include a compilation of spectroscopic lya data from the literature spanning a wide redshift range (z~0-8). First, restricting our analysis to double-peaked lya spectra, we find a tight correlation between the velocity offset of the red peak with respect to the systemic redshift, Vpeak, and the separation of the peaks. Secondly, we find a correlation between Vpeak and the full width at half maximum of the lya line. Fitting formulas, to estimate systemic redshifts of galaxies with an accuracy of +-100 km/s when only the lya emission line is available, are given for the two methods.