C III] λ1909 emission as an alternative to Ly α in the reionization era: the dependence of C III] and Ly α at 3 < z < 4 from the VANDELS survey

The velocity offset of Ly α emission from a galaxy's systemic redshift is an excellent tracer of conditions that enable the escape of Ly α photons from the galaxy, and potentially the all-important hydrogen ionizing Lyman continuum photons. However at z ≥ 6, Ly α is often heavily attenuated by the neutral intergalactic medium. Here we investigate the utility of C III] λλ1907, 1909 emission, usually the brightest ultraviolet (UV) line after Ly α, as a proxy estimating the Ly α velocity offset (Δv_{Ly α}). To do so, we use analogues of reionization era galaxies based upon 52 star-forming galaxies with robust C III] detections drawn from the VANDELS survey. Our sample spans a broad UV magnitude range of -18.5 < M_UV < -22.0, with a sample average value of EW(C III]) = 5.3 Å. We find a slight increase of EW(C III]) with increasing EW(Ly α), but find a large range of EW(C III]) ~ 1-13 Å particularly at EW(Ly α) < 10 Å. Using the C III] line peak as the systemic redshift, we calculate Δv_{Ly α} and recover the previously reported trend of decreasing Δv_{Ly α} with increasing EW(Ly α). Interestingly, we find an anticorrelation between Δv_{Ly α} and EW(C III]), which also displays a dependence on the UV absolute magnitude. We derive a multivariate fit to obtain Δv_{Ly α} using both EW(C III]) and M_UV, finding that Δv_{Ly α} is more strongly dependent on EW(C III]), with a weaker but non-negligible dependence on M_UV. We find that for a fixed EW(C III]), UV-bright Ly α emitting galaxies show smaller values of Δv_{Ly α},which suggests that such galaxies may be undergoing more bursty star-formation compared to the UV-fainter ones, akin to a population of extremely UV-bright galaxies identified at z > 10.