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We present the results of a new study investigating the relationship betweenobserved Ly$\alpha$ equivalent width ($W_{\lambda}$(Ly$\alpha$)) and themetallicity of the ionizing stellar population ($Z_{\star}$) for a sample of$768$ star-forming galaxies at $3 \leq z \leq 5$ drawn from the VANDELS survey.Dividing our sample into quartiles of rest-frame $W_{\lambda}$(Ly$\alpha$)across the range $-58 \unicode{xC5} \lesssim$ $W_{\lambda}$(Ly$\alpha$)$\lesssim 110 \unicode{xC5}$ we determine $Z_{\star}$ from full spectralfitting of composite far-ultraviolet (FUV) spectra and find a clearanti-correlation between $W_{\lambda}$(Ly$\alpha$) and $Z_{\star}$. Our resultsindicate that $Z_{\star}$ decreases by a factor $\gtrsim 3$ between the lowest$W_{\lambda}$(Ly$\alpha$) quartile($\langle$$W_{\lambda}$(Ly$\alpha$)$\rangle=-18\unicode{xC5}$) and the highest$W_{\lambda}$(Ly$\alpha$) quartile($\langle$$W_{\lambda}$(Ly$\alpha$)$\rangle=24\unicode{xC5}$). Similarly,galaxies typically defined as Lyman Alpha Emitters (LAEs;$W_{\lambda}$(Ly$\alpha$) $>20\unicode{xC5}$) are, on average, metal poor withrespect to the non-LAE galaxy population ($W_{\lambda}$(Ly$\alpha$)$\leq20\unicode{xC5}$) with $Z_{\star}$$_{\rm{non-LAE}}\gtrsim 2 \times$$Z_{\star}$$_{\rm{LAE}}$. Finally, based on the best-fitting stellar models, weestimate that the increasing strength of the stellar ionizing spectrum towardslower $Z_{\star}$ is responsible for $\simeq 15-25\%$ of the observed variationin $W_{\lambda}$(Ly$\alpha$) across our sample, with the remaining contribution($\simeq 75-85\%$) being due to a decrease in the HI/dust covering fractions inlow $Z_{\star}$ galaxies.

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