Constraining Lyman-alpha spatial offsets at $3<z<5.5$ from VANDELS slit spectroscopy

We constrain the distribution of spatially offset Lyman-alpha emission (Ly$\alpha$) relative to rest-frame ultraviolet emission in $\sim300$ high redshift ($3<z<5.5$) Lyman-break galaxies (LBGs) exhibiting Ly$\alpha$ emission from VANDELS, a VLT/VIMOS slit-spectroscopic survey of the CANDELS Ultra Deep Survey and Chandra Deep Field South fields (${\simeq0.2}~\mathrm{deg}^2$ total). Because slit spectroscopy compresses two-dimensional spatial information into one spatial dimension, we use Bayesian inference to recover the underlying Ly$\alpha$ spatial offset distribution. We model the distribution using a 2D circular Gaussian, defined by a single parameter $\sigma_{r,\mathrm{Ly}\alpha}$, the standard deviation expressed in polar coordinates. Over the entire redshift range of our sample ($3<z<5.5$), we find $\sigma_{r,\mathrm{Ly}\alpha}=1.70^{+0.09}_{-0.08}$ kpc ($68\%$ conf.), corresponding to $\sim0.25$ arcsec at $\langle z\rangle=4.5$. We also find that $\sigma_{r,\mathrm{Ly}\alpha}$ decreases significantly with redshift. Because Ly$\alpha$ spatial offsets can cause slit-losses, the decrease in $\sigma_{r,\mathrm{Ly}\alpha}$ with redshift can partially explain the increase in the fraction of Ly$\alpha$ emitters observed in the literature over this same interval, although uncertainties are still too large to reach a strong conclusion. If $\sigma_{r,\mathrm{Ly}\alpha}$ continues to decrease into the reionization epoch, then the decrease in Ly$\alpha$ transmission from galaxies observed during this epoch might require an even higher neutral hydrogen fraction than what is currently inferred. Conversely, if spatial offsets increase with the increasing opacity of the IGM, slit losses may explain some of the drop in Ly$\alpha$ transmission observed at $z>6$. Spatially resolved observations of Ly$\alpha$ and UV continuum at $6<z<8$ are needed to settle the issue.