  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.
