Abstract
We use the astraeus framework to investigate how the visibility and
spatial distribution of Lyman-$\alpha$ (Ly$\alpha$) emitters (LAEs) during
reionisation is sensitive to a halo mass-dependent fraction of ionising
radiation escaping from the galactic environment ($f_esc$) and the
ionisation topology. To this end, we consider the two physically plausible
bracketing scenarios of $f_esc$ increasing and decreasing with rising
halo mass. We derive the corresponding observed Ly$\alpha$ luminosities of
galaxies for three different analytic Ly$\alpha$ line profiles and associated
Ly$\alpha$ escape fraction ($f_esc^Ly\alpha$) models:
importantly, we introduce two novel analytic Ly$\alpha$ line profile models
that describe the surrounding interstellar medium (ISM) as outflowing dusty gas
clumps. They are based on parameterising results from radiative transfer
simulations, with one of them relating $f_esc^Ly\alpha$ to
$f_esc$ by assuming the ISM of being interspersed with low-density
tunnels. Our key findings are: (i) for outflowing clumps, the Ly$\alpha$ line
profile develops from a central to double peak profile as a galaxy's halo mass
increases; (ii) LAEs are galaxies with $M_h\gtrsim10^10M_ødot$ located in
overdense and highly ionised regions; (iii) for this reason, the spatial
distribution of LAEs is primarily sensitive to the global ionisation fraction
and only weakly in second-order to the ionisation topology or a halo
mass-dependent $f_esc$; (iv) furthermore, as the observed Ly$\alpha$
luminosity functions reflect the Ly$\alpha$ emission from more massive
galaxies, there is a degeneracy between the $f_esc$-dependent
intrinsic Ly$\alpha$ luminosity and the Ly$\alpha$ attenuation by dust in the
ISM if $f_esc$ does not exceed $\sim50\%$.
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