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Lyman-$\alpha$ emitters (LAEs) are a promising probe of the large-scalestructure at high redshift, $z\gtrsim 2$. In particular, the Hobby-EberlyTelescope Dark Energy Experiment aims at observing LAEs at 1.9 $<z<$ 3.5 tomeasure the Baryon Acoustic Oscillation (BAO) scale and the Redshift-SpaceDistortion (RSD). However, Zheng et al. (2011) pointed out that the complicatedradiative transfer (RT) of the resonant Lyman-$\alpha$ emission line generatesan anisotropic selection bias in the LAE clustering on large scales, $s\gtrsim10$ Mpc. This effect could potentially induce a systematic error in the BAO andRSD measurements. Also, Croft et al. (2016) claims an observational evidence ofthe effect in the Lyman-$\alpha$ intensity map, albeit statisticallyinsignificant. We aim at quantifying the impact of the Lyman-$\alpha$ RT on thelarge-scale galaxy clustering in detail. For this purpose, we study thecorrelations between the large-scale environment and the ratio of an apparentLyman-$\alpha$ luminosity to an intrinsic one, which we call the `observedfraction', at $2<z<6$. We apply our Lyman-$\alpha$ RT code by post-processingthe full Illustris simulations. We simply assume that the intrinsic luminosityof the Lyman-$\alpha$ emission is proportional to the star formation rate ofgalaxies in Illustris, yielding a sufficiently large sample of LAEs to measurethe anisotropic selection bias. We find little correlations between large-scaleenvironment and the observed fraction induced by the RT, and hence a smalleranisotropic selection bias than what was claimed by Zheng et al. (2011). Weargue that the anisotropy was overestimated in the previous work due to theinsufficient spatial resolution: it is important to keep the resolution suchthat it resolves the high density region down to the scale of the interstellarmedium, $\sim1$ physical kpc. (abridged)

The impact of Lyman-$\alpha$ radiative transfer on large-scale clustering in the Illustris simulation