Large-scale halo velocity correlations and the impact of finite simulation volumes

Abstract

The velocity correlation functions directly measured from the peculiar velocity field of dark matter in numerical simulations are known to have an amplitude lower than that predicted by theoretical models at large scales. The trend persists for dark-matter halos or galaxies that are more closely related to the observables. We investigate the impact of the finite simulation box sizes on the measured velocity correlation functions of halos, utilizing N-body simulations with different box sizes. We measure the halo velocity correlations from N-body simulations with side lengths of $1{\rm Gpc}/h$ and $2{\rm Gpc}/h$, confirming the former is more suppressed compared to the linear theory prediction on large scales due to the lack of large-scale modes beyond the box size. In contrast, even though we subdivide the larger-box simulations into those with side lengths of $1{\rm Gpc}/h$, the amount of the suppression is the same as that from the original boxes, as the large-scale modes are already imprinted. Introducing the lower limit of the integral in the Hankel transform, $k_{\rm min}$, as a free parameter and marginalizing it over, we find that the constrained growth rate parameter, $f(z)σ_8(z)$, returns the correct value assumed in the simulations. However, when we ignore the effect and set $k_{\rm min}=0$, the constraint on $fσ_8$ is significantly biased if the correlation between different separation bins is also ignored. Furthermore, we find that the suppression of the velocity correlation amplitude on large scales depends on halo mass, with more massive halos exhibiting a systematically stronger suppression. These results highlight the importance of accounting for missing long-wavelength modes when developing simulation-based modeling of velocity statistics, such as emulators.

Figures (4)

• Figure 1: Upper panel: angularly-averaged velocity correlation functions of halos, $\xi_{\rm{v}}$. The filled orange squares and blue circles are the measurements from the cubic boxes with side length of $1\,h^{-1}\,{\rm Gpc}$ ($L_{1\rm G}$) and $2\,h^{-1}\,{\rm Gpc}$ ($L_{2\rm G}$), respectively. The open squares and triangles are the results from the subdivided simulation boxes, $L_{2\rm G}$, to the side lengths of $1\,h^{-1}\,{\rm Gpc}$ ($L_{2{\rm G}}^{\times 0.5}$) and $0.3\,h^{-1}\,{\rm Gpc}$ ($L_{2{\rm G}}^{\times 0.15}$), respectively. The black curves are the nonlinear model with the true parameter of $f\sigma_{8}$ with $k_{\rm min}\to 0$. The orange and blue curves are the best-fitting model with $(f\sigma_{8},k_{\rm min})$ at $36\leq r\leq 400\,h^{-1}\,{\rm Mpc}$ for $L_{1\rm G}$ and $L_{2\rm G}$ simulations, respectively (see Table \ref{['tab:table']}). Lower panel: ratios of the above results to the linear-theory prediction with the true parameter of $f\sigma_{8}$ with $k_{\rm min}\to 0$.
• Figure 2: Top: joint constraints on the growth rate $f\sigma_{8}$ and the minimum wavenumber $k_{\rm min}$ in the $L_{1\rm G}$ simulation box. The contours show the $1\sigma$, $2\sigma$, and $3\sigma$ confidence levels from inward. The blue and red contours correspond to the results using the full and diagonal covariance matrices, respectively. Bottom: One-dimensional posterior distributions for $f\sigma_{8}$. The solid curves show the result when $k_{\rm min}$ is marginalized over, while the dashed curves show that where $k_{\rm min}$ is fixed to $0.1\pi/L_{1\rm G}\simeq 3\times 10^{-4} [\, h\, {\rm Mpc}^{-1}]$. The vertical dotted line indicates the fiducial input value of $f\sigma_{8}$.
• Figure 3: Constraints on model parameters from simulation boxes with different sizes and subdivided boxes. The upper and lower panels show the constraints on the growth rate $f\sigma_{8}$ and the scale-cut parameter $k_{\rm min}$. The blue and red points show results obtained using the full and diagonal covariance matrices, respectively. In the upper panel, the triangles show the results when we fix $k_{\rm min}=0$. The true value of $f\sigma_{8}$ from the simulations is indicated by the horizontal dotted line.
• Figure 4: Ratios of the velocity correlation functions of halos with certain mass ranges and those of subhalos determined from the HOD modeling of the SDSS-III BOSS LOWZ galaxy sample. The host subhalo mass of the LOWZ sample is very similar to that of the group subsample.