Lopsided and Bulging Distribution of Satellites around Paired Halos. II. 3D Analysis and Dependence on Projection and Selection Effects

Abstract

We use the Illustris-TNG simulation to investigate the anisotropic distribution of subhalos in/around dark matter halo pairs. We measure the position angle ($\theta$) of each subhalo by the angle between the line connecting it to the nearest host halo and the line connecting the paired halos, and examine $P(\cos\theta)$ (the distribution of $\cos\theta$ of all subhalos) for halo pairs with various separations ($d_{\text{sep}}$), primary halo masses ($M_p$) and secondary-to-primary halo mass ratios ($M_s/M_p$). We find that $P(\cos\theta)$ generally exhibits a combined result of two distinct features: the `bulging' distribution characterized by an overabundance along the pairwise direction, and the `lopsided' distribution showing an overabundance in the region between the paired halos. The bulging signal is stronger for halo pairs with larger $d_{\text{sep}}$ and smaller $M_p$, while the lopsidedness strengthens as $M_p$ increases. Both signals depend weakly on $M_s/M_p$, and are primarily contributed by subhalos that are relatively distant from host halos. Remarkably, these measurements can be broadly reproduced by the overlap effect, provided the spatial alignment of halos is properly taken into account. Our findings suggest distinct origins: lopsidedness arises from simple halo overlap, while bulging reflects alignment with large-scale filaments. We examine the impact of projection and selection effects by conducting the same analysis in two dimensions and in a mock catalog that replicates the selection effects of the SDSS galaxy sample. We find that the 3D-to-2D projection significantly suppresses the bulging distribution, with particularly strong effects at large $d_{\text{sep}}$, small $M_p$, and large $M_s/M_p$.