Radiative Transfer in Ly{\alpha} Nebulae: I. Modeling a Continuous or Clumpy Spherical Halo with a Central Source

To understand the mechanism behind high-$z$ Ly${\alpha}$ nebulae, we simulate the scattering of Ly${\alpha}$ in a $\rm H\,I$ 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, $\rm H\,I$ 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 ($\sim 100\,$kpc) at total column densities $N_{\rm HI} \geq 10^{20} \rm cm^{-2}$ 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 $N_{\rm HI}$ 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, $N_{\rm HI}$ dominates the trends. The radial behaviors of the Ly${\alpha}$ surface brightness, spectral line shape, and polarization in the clumpy model with covering factor $f_c \gtrsim 5$ approach those of the smooth model at the same $N_{\rm HI}$. A clumpy medium with high $N_{\rm HI}$ and low $f_c \lesssim 2$ generates Ly${\alpha}$ features via scattering that the smooth model cannot: a bright core, symmetric line profile, and polarization jump.