The effects of projection on measuring the splashback feature

The splashback radius $R_{\rm sp}$ is a boundary of a halo that separates infalling and accreted matter. This results in a steep drop in the density profile at $R_{\rm st}$, which is a commonly adopted proxy for $R_{\rm sp}$. Observationally, $R_{\rm st}$ can be measured through fitting the projected galaxy number density profile of the halo, but there has been some discrepancy between the observed and expected $R_{\rm st}$. Therefore, we investigate whether the projection of the density profile onto the plane of the sky could lead to any systematic bias in determining $R_{\rm st}$, by studying the true 3-dimensional and projected halo density profiles from the IllustrisTNG simulation. We investigate a range of projection lengths, and find that $R^p_{\rm st}$ obtained from projected profiles is close to the true $R^*_{\rm st}$, but has a slight decreasing trend with increasing projection length. We also quantify the prominence of the splashback feature and find how the feature shape changes with projection length.