Directional Lya equivalent boosting I. Spherically symmetric
  distributions of clumps
  We quantify the directional dependence of the escape fraction of
Lyman-$\alpha$ (Ly$\alpha$) and non-ionising UV-continuum photons from a
multiphase medium, and investigate whether there exist directional enhancements
in the Ly$\alpha$ equivalent width (EW). Our multiphase medium consists of
spherically symmetric distributions of cold, dusty clumps embedded within a hot
dust-free medium. We focus on three models from the analysis presented by
Laursen et al. (2013). We find that for a Ly$\alpha$ and UV-continuum point
source, it is possible to find an EW boost $b(\theta,\phi) > 5 \bar{b}$ in a
few per cent of sight lines, where $\bar{b}$ denotes the boost averaged over
all photons. For spatially extended sources this directional dependence
vanishes quickly when the size of the UV emitting region exceeds the mean
distance between cold dusty clumps. Our analysis suggests that directional EW
boosting can occur, and that this is mostly driven by reduced escape fractions
of UV photons (which gives rise to UV-continuum `shadows'), and less due to an
enhanced Ly$\alpha$ escape fraction (or beaming), in certain directions.
