Quantifying the impact of baryon-CDM perturbations on halo clustering and baryon fraction

Baryons and cold dark matter (CDM) did not comove prior to recombination. This leads to differences in the local baryon and CDM densities, the so-called baryon-CDM isocurvature perturbations $\delta_{bc}$. These perturbations are usually neglected in the analysis of Large-Scale Structure data but taking them into account might become important in the era of high precision cosmology. Using gravity-only 2-fluid simulations we assess the impact of such perturbations on the dark matter halos distribution. In particular, we focus on the baryon fraction in halos as a function of mass and large-scale $\delta_{bc}$, which also allows us to study details of the nontrivial numerical setup required for such simulations. We further measure the cross-power spectrum between the halo field and $\delta_{bc}$ over a wide range of mass. This cross-correlation is nonzero and negative which shows that halo formation is impacted by $\delta_{bc}$. We measure the associated bias parameter $b_{\delta_{bc}}$ and compare it to recent results, finding good agreement. Finally we quantify the impact of such perturbations on the halo-halo power spectrum and show that this effect can be degenerate with the one of massive neutrinos for surveys like DESI.