Ly$\alpha$ with SPICE: Interpreting Ly$\alpha$ emission at $z>5$

Ly$\alpha$ emission is key to understanding the process of cosmic reionisation. JWST is finally enabling us to measure Ly$\alpha$ emission deep into the epoch of reionisation for an increasing number of galaxies. However, discrepancies between measurements of Ly$\alpha$ equivalent widths (EW$_0$) of Ly$\alpha$ emitters (LAEs) have been noted between JWST and ground-based facilities. We employ SPICE, a suite of radiation-hydrodynamical simulations featuring different stellar feedback models, and investigate the impact of radiative transfer effects and observational systematics on the measured Ly$\alpha$ EW$_0$. We perform radiative transfer of Ly$\alpha$ and UV photons for SPICE galaxies to mimic slit spectroscopy for ground-based slits and JWST-MSA pseudo-slits. Spatial Ly$\alpha$-UV offsets exist independently of feedback model, and are common ($>70$% galaxies) with median values of $\approx0.07-0.11''$ and these predictions are consistent with the observed spatial offsets. Spatial Ly$\alpha$-UV offsets are a major cause of loss of flux for JWST-MSA observations, with median pseudo-slit losses of $\approx65$%, and $\approx30$% cases suffering from $>95$% pseudo-slit losses. Even in the absence of such spatial offsets, the presence of extended emission can cause median pseudo-slit losses of $40$%, with $4$% cases suffering from $>95$% pseudo-slit losses. Complex galaxy morphologies or misplaced JWST-MSA pseudo-slit can lead to under-estimated UV continuum, resulting in spuriously high estimates of EW$_0$ from JWST in $6-8$% of galaxies. We compare the predictions from {\tt SPICE} to 25 galaxies with Ly$\alpha$ emission observations from both the ground and JWST. The EW$_0^{\tt JWST}$ and the EW$_0^{\tt Ground}$ exhibit scatter in line with predictions, indicating that both physical and systematic effects are likely at play.