The Lyman alpha (Lyα) line of Hydrogen is a prominent feature in the spectra of star-forming galaxies, usually redshifted by a few hundreds of km s −1 compared to the systemic redshift. This large offset hampers follow-up surveys, galaxy pair statistics and correlations with quasar absorption lines when only Lyα is available. We propose diagnostics that can be used to recover the systemic redshift directly from the properties of the Lyα 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 Lyα data from the literature spanning a wide redshift range (z ≈ 0 − 8). First, restricting our analysis to double-peaked Lyα spectra, we find a tight correlation between the velocity offset of the red peak with respect to the systemic redshift, V red peak , and the separation of the peaks. Secondly, we find a correlation between V red peak and the full width at half maximum of the Lyα line. Fitting formulas, to estimate systemic redshifts of galaxies with an accuracy of ≤ 100 km s −1 when only the Lyα emission line is available, are given for the two methods.

We have conducted a two-layered spectroscopic survey (1 × 1 ultra deep and 3 × 3 deep regions) in the Hubble Ultra Deep Field (HUDF) with the Multi Unit Spectroscopic Explorer (MUSE). The combination of a large field of view, high sensitivity, and wide wavelength coverage provides an order of magnitude improvement in spectroscopically confirmed redshifts in the HUDF; i.e., 1206 secure spectroscopic redshifts for HST continuum selected objects, which corresponds to 15% of the total (7904). The redshift distribution extends well beyond z > 3 and to HST/F775W magnitudes as faint as ≈ 30 mag (AB, 1σ). In addition, 132 secure redshifts were obtained for sources with no Hubble Space Telescope (HST) counterparts that were discovered in the MUSE data cubes by a blind search for emission-line features. In total, we present 1338 high quality redshifts, which is a factor of eight increase compared with the previously known spectroscopic redshifts in the same field. We assessed redshifts mainly with the spectral features [O ii] at z < 1.5 (473 objects) and Lyα at 2.9 < z < 6.7 (692 objects). With respect to F775W magnitude, a 50% completeness is reached at 26.5 mag for ultra deep and 25.5 mag for deep fields, and the completeness remains 20% up to 28 − 29 mag and ≈ 27 mag, respectively. We used the determined redshifts to test continuum color selection (dropout) diagrams of high-z galaxies. The selection condition for F336W dropouts successfully captures ≈ 80% of the targeted z ∼ 2.7 galaxies. However, for higher redshift selections (F435W, F606W, and F775W dropouts), the success rates decrease to ≈ 20 − 40%. We empirically redefine the selection boundaries to make an attempt to improve them to ≈ 60%. The revised boundaries allow bluer colors that capture Lyα emitters with high Lyα equivalent widths falling in the broadbands used for the color-color selection. Along with this paper, we release the redshift and line flux catalog.