Connecting the escape fraction of Lyman-alpha and Lyman-continuum photons in star-forming galaxies at $\mathbf{z\simeq 4-5}$

Abstract: We present a study of the connection between the escape fraction of Lyman-alpha (Ly$\alpha$) and Lyman-continuum (LyC) photons within a sample of N=152 star-forming galaxies selected from the VANDELS survey at $3.85<z_{spec}<4.95$. By combining measurements of H$\alpha$ equivalent width $(W_\lambda(\rm{H\alpha}))$ derived from broad-band photometry with Ly$\alpha$ equivalent width $(W_\lambda(Ly\alpha))$ measurements from VANDELS spectra, we individually estimate $f_{\rm{esc}}^{Ly\alpha}$ for our full sample. In agreement with previous studies, we find a positive correlation between $W_\lambda(Ly\alpha)$ and $f_{\rm{esc}}^{Ly\alpha}$, increasing from $f_{\rm{esc}}^{Ly\alpha}\simeq0.04$ at $W_\lambda(Ly\alpha)=10$\r{A} to $f_{\rm{esc}}^{Ly\alpha}\simeq0.1$ at $W_\lambda(Ly\alpha)=25$\r{A}. For the first time at $z\sim4-5$, we investigate the relationship between $f_{\rm{esc}}^{Ly\alpha}$ and $f_{\rm{esc}}^{\rm{LyC}}$ using $f_{\rm{esc}}^{\rm{LyC}}$ estimates derived using the equivalent widths of low-ionization, FUV absorption lines in composite VANDELS spectra. Our results indicate that $f_{\rm{esc}}^{\rm{LyC}}$ rises monotonically with $f_{\rm{esc}}^{Ly\alpha}$, following the relation $f_{\rm{esc}}^{\rm{LyC}}\simeq 0.15^{+0.06}{-0.04}f{\rm{esc}}^{Ly\alpha}$. Based on composite spectra of sub-samples with roughly constant $W_\lambda(Ly\alpha)$, but very different $f_{\rm{esc}}^{Ly\alpha}$, we show that the $f_{\rm{esc}}^{\rm{LyC}}-f_{\rm{esc}}^{Ly\alpha}$ correlation is not driven by a secondary correlation between $f_{\rm{esc}}^{Ly\alpha}$and $W_\lambda(Ly\alpha)$. The $f_{\rm{esc}}^{\rm{LyC}}-f_{\rm{esc}}^{Ly\alpha}$ correlation is in good qualitative agreement with theoretical predictions and provides further evidence that estimates of $f_{\rm{esc}}^{\rm{LyC}}$ within the Epoch of Reionization should be based on proxies sensitive to neutral gas density/geometry and dust attenuation.