The VANDELS survey: A strong correlation between Ly$\alpha$ equivalent width and stellar metallicity at $\mathbf{3}\le \mathbf{z}\le \mathbf{5}$

We present the results of a new study investigating the relationship between observed Ly$\alpha$ equivalent width ($W_{\lambda }$(Ly$\alpha$)) and the metallicity of the ionizing stellar population ($Z_{\star }$) for a sample of $768$ star-forming galaxies at $3\le z\le 5$ drawn from the VANDELS survey. Dividing our sample into quartiles of rest-frame $W_{\lambda }$(Ly$\alpha$) across the range $-58\text{unicode}xC5\lesssim$ $W_{\lambda }$(Ly$\alpha$) $\lesssim 110\text{unicode}xC5$ we determine $Z_{\star }$ from full spectral fitting of composite far-ultraviolet (FUV) spectra and find a clear anti-correlation between $W_{\lambda }$(Ly$\alpha$) and $Z_{\star }$. Our results indicate that $Z_{\star }$ decreases by a factor $\gtrsim 3$ between the lowest $W_{\lambda }$(Ly$\alpha$) quartile ($⟨$$W_{\lambda }$(Ly$\alpha$)$⟩=-18\text{unicode}xC5$) and the highest $W_{\lambda }$(Ly$\alpha$) quartile ($⟨$$W_{\lambda }$(Ly$\alpha$)$⟩=24\text{unicode}xC5$). Similarly, galaxies typically defined as Lyman Alpha Emitters (LAEs; $W_{\lambda }$(Ly$\alpha$) $>20\text{unicode}xC5$) are, on average, metal poor with respect to the non-LAE galaxy population ($W_{\lambda }$(Ly$\alpha$) $\le 20\text{unicode}xC5$) with $Z_{\star }$${}_{\mathrm{n}\mathrm{o}\mathrm{n}-\mathrm{L}\mathrm{A}\mathrm{E}}\gtrsim 2\times$ $Z_{\star }$${}_{\mathrm{L}\mathrm{A}\mathrm{E}}$. Finally, based on the best-fitting stellar models, we estimate that the increasing strength of the stellar ionizing spectrum towards lower $Z_{\star }$ is responsible for $\simeq 15-25\mathrm{\%}$ of the observed variation in $W_{\lambda }$(Ly$\alpha$) across our sample, with the remaining contribution ($\simeq 75-85\mathrm{\%}$) being due to a decrease in the HI/dust covering fractions in low $Z_{\star }$ galaxies.