Relative velocity of dark matter and baryonic fluids and the formation of the first structures

TL;DR

The paper shows that a supersonic relative velocity between baryons and dark matter, ${\bf v}_{bc}$, after recombination nonlinearly couples large- and small-scale modes and suppresses early small-scale power near the baryon Jeans scale. It develops moving-background perturbation theory (MBPT) to compute local transfer functions $P_{\rm loc,m}(k;v_{bc})$ and then averages over the $v_{bc}$ distribution to obtain the global matter power spectrum, finding a typical suppression of $\sim 10$–$15\%$ around $k_J$. Using a peak-background-split and a conditional Press-Schechter approach in coherence patches, the study predicts a substantial reduction in the abundance of the first haloes (e.g., $\Delta_N \gtrsim -0.6$ at $M\sim 10^6 M_\odot$) and reveals that halo clustering becomes scale-dependent with enhanced bias and stochasticity, particularly for low-mass halos. These results have important implications for the timing and topology of reionization and the interpretation of high-redshift galaxy clustering and 21 cm signals, motivating more detailed simulations and observational diagnostics of the relative-velocity effect.

Abstract

At the time of recombination, baryons and photons decoupled and the sound speed in the baryonic fluid dropped from relativistic to the thermal velocities of the hydrogen atoms. This is less than the relative velocities of baryons and dark matter computed via linear perturbation theory, so we infer that there are supersonic coherent flows of the baryons relative to the underlying potential wells created by the dark matter. As a result, the advection of small-scale perturbations (near the baryonic Jeans scale) by large-scale velocity flows is important for the formation of the first baryonic structures. This effect involves a quadratic term in the cosmological perturbation theory equations and hence has not been included in studies based on linear perturbation theory. We show that the relative motion suppresses the abundance of the first bound objects, even if one only investigates dark matter haloes, and leads to qualitative changes in their spatial distribution, such as introducing scale-dependent bias and stochasticity. We discuss the possible observable implications for high-redshift galaxy clustering and reionization.

Figures (6)

• Figure 1: The coherence scale of ${\bf v}_{\rm bc}$ is determined by the range of scales over which $\Delta^2_{\rm vbc}(k)$ is non-zero. Here we plot $\Delta^2_{\rm vbc}(k)$, the variance of the relative velocity perturbation per $\ln k$, as a function of wavenumber $k$. The power spectrum drops rapidly at $k>0.5\,$Mpc$^{-1}$, indicating that the relative velocity is coherent over scales smaller than a few Mpc comoving.
• Figure 2: Power spectrum of matter distribution in the first order CDM model (solid line) and with the $v_{\rm bc}$ effect included (dashed line) at the redshift of $z = 40$.
• Figure 3: Top panel: The matter density contrast $\delta_m$ on a 2D slice of the 3D simulation box. The halo density contrast $\delta_n$ for $M_{\rm halo}=10^6\,M_\odot$ on the same slice with $V_{bc} = 0$ (Middle panel) and with $V_{bc} \neq 0$ (Bottom panel). All panels are at $z = 40$.
• Figure 4: Top panel: The number density of dark matter haloes produced in our simulation box without the effect of relative velocity (solid line) and with the effect (dashed line). Bottom panel: The relative decrease in the number density of haloes as a function of the halo mass. Number densities in our simulation correspond to the redshift of $z = 40$.
• Figure 5: The correction to the bias parameter $\Delta b$ (top panel) and the stochasticity $\chi=r_{\rm hm}^2$ (bottom panel) for various halo masses at $z=40$. The solid curve corresponds to $M_h = 10^4 M_{\odot}$; the thick-solid to $M_h = 10^5 M_{\odot}$; the dashed to $M_h = 10^6 M_{\odot}$; the dot-dashed to $M_h = 10^7 M_{\odot}$; and the dotted to $M_h = 10^8 M_{\odot}$. In the first order CDM model $\Delta b = 0$ and $\chi=1$ on large scales. The enhancement of bias on small scales $k>0.3\,$Mpc$^{-1}$ is due to the nonlinear dependence of halo abundance on $\delta_{\rm l}$.