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

Lyman-$\alpha$ emitters (LAEs) are a promising probe of the large-scale structure at high redshift, \gtrsim 2$. In particular, the Hobby-Eberly Telescope Dark Energy Experiment aims at observing LAEs at 1.9 $<z<$ 3.5 to measure the Baryon Acoustic Oscillation (BAO) scale and the Redshift-Space Distortion (RSD). However, Zheng et al. (2011) pointed out that the complicated radiative transfer (RT) of the resonant Lyman-$\alpha$ emission line generates an anisotropic selection bias in the LAE clustering on large scales, \gtrsim 10$ Mpc. This effect could potentially induce a systematic error in the BAO and RSD measurements. Also, Croft et al. (2016) claims an observational evidence of the effect in the Lyman-$\alpha$ intensity map, albeit statistically insignificant. We aim at quantifying the impact of the Lyman-$\alpha$ RT on the large-scale galaxy clustering in detail. For this purpose, we study the correlations between the large-scale environment and the ratio of an apparent Lyman-$\alpha$ luminosity to an intrinsic one, which we call the 'observed fraction', at <z<6$. We apply our Lyman-$\alpha$ RT code by post-processing the full Illustris simulations. We simply assume that the intrinsic luminosity of the Lyman-$\alpha$ emission is proportional to the star formation rate of galaxies in Illustris, yielding a sufficiently large sample of LAEs to measure the anisotropic selection bias. We find little correlations between large-scale environment and the observed fraction induced by the RT, and hence a smaller anisotropic selection bias than what was claimed by Zheng et al. (2011). We argue that the anisotropy was overestimated in the previous work due to the insufficient spatial resolution: it is important to keep the resolution such that it resolves the high density region down to the scale of the interstellar medium, $\sim1$ physical kpc. (abridged)