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.
