Abstract
To understand the mechanism behind high-$z$ Ly$\alpha$ nebulae, we simulate
the scattering of Ly$\alpha$ in a $H\,I$ halo about a central
Ly$\alpha$ source. For the first time, we consider both smooth and clumpy
distributions of halo gas, as well as a range of outflow speeds, total $\rm
H\,I$ column densities, $H\,I$ spatial concentrations, and central source
galaxies (e.g., with Ly$\alpha$ line widths corresponding to those typical of
AGN or star-forming galaxies). We compute the spatial-frequency diffusion and
the polarization of the Ly$\alpha$ photons scattered by atomic hydrogen. Our
scattering-only model reproduces the typical size of Ly$\alpha$ nebulae
($100\,$kpc) at total column densities $N_HI 10^20 \rm
cm^-2$ and predicts a range of positive, flat, and negative polarization
radial gradients. We also find two general classes of Ly$\alpha$ nebula
morphologies: with and without bright cores. Cores are seen when $N_HI$
is low, i.e., when the central source is directly visible, and are associated
with a polarization jump, a steep increase in the polarization radial profile
just outside the halo center. Of all the parameters tested in our smooth or
clumpy medium model, $N_HI$ dominates the trends. The radial behaviors of
the Ly$\alpha$ surface brightness, spectral line shape, and polarization in
the clumpy model with covering factor $f_c 5$ approach those of the
smooth model at the same $N_HI$. A clumpy medium with high $N_HI$
and low $f_c 2$ generates Ly$\alpha$ features via scattering that
the smooth model cannot: a bright core, symmetric line profile, and
polarization jump.
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