Distribution function approach to redshift space distortions, Part III: halos and galaxies

TL;DR

The paper extends a phase-space distribution-function approach to redshift-space distortions (RSD) to biased tracers such as halos and galaxies, expressing the RSD power spectrum as a sum over cross-spectra of number-weighted velocity moments. Using large N-body simulations with halo catalogs and a mock LRG sample from HOD, it analyzes 2D power spectra, multipoles, μ^2 expansions, and configuration-space statistics to quantify nonlinear and scale-dependent bias in velocity moments and the impact of Fingers-of-God. It finds strong scale dependence in bias terms for momentum-density correlators, with FoG effects small for halos but significant when satellites drive internal velocity dispersion, leading to notable deviations from linear theory in the quadrupole (≈10% at k<0.1 h/Mpc for LRG-like samples). These results imply that accurate cosmological inferences from RSD require modeling nonlinear, scale-dependent bias and FoG effects, and that the μ^2 expansion and FoG resummation are important tools for interpreting upcoming redshift surveys.

Abstract

It was recently shown that the power spectrum in redshift space can be written as a sum of cross-power spectra between number weighted velocity moments. We investigate the properties of these power spectra for simulated galaxies and dark matter halos and compare them to the dark matter power spectra, generalizing the concept of the bias. Because all of the quantities are number weighted this approach is well defined even for sparse systems such as massive halos, in contrasts to the previous approaches to RSD where velocity correlations have been explored. We find that the number density weighting leads to a strong scale dependence of the bias terms for momentum density auto-correlation and cross-correlation with density. This trend becomes more significant for the more biased halos and leads to an enhancement of RSD power relative to the linear theory. Fingers-of-god effects, which in this formalism come from the correlations of the higher order moments beyond the momentum density, lead to smoothing of the power spectrum and can reduce this enhancement of power, but are relatively small for halos with no small-scale velocity dispersion. In comparison, for a more realistic galaxy sample with satellites the velocity dispersion generated by satellite motions inside the halos leads to a larger power suppression on small scales, but this depends on the satellite fraction. We investigate several statistics such as the two-dimensional power spectrum, its multipole moments, its powers of mu^2, and configuration space statistics. Overall we find that the nonlinear effects in realistic galaxy samples such as luminous red galaxies affect the redshift space clustering on very large scales: for example, the quadrupole moment is affected by 10% for k<0.1h/mpc, which means that these effects need to be understood if we want to extract cosmological information from the redshift space distortions.

Figures (12)

• Figure 1: Power spectra measured in redshift space $P^{s}_{\rm ref}(k,\mu)$ and individual contributions to it from the terms of the moments expansion up to 4-th order at $z=0.5$ for halos (left), LRGs (middle) and dark matter (right). The halo subsample has almost the same bias value as the LRG sample. The width of $\mu$ bin is 0.2, centered around the values shown in each panel. The dashed lines show the positive values while the dotted lines negative values.
• Figure 2: Bias parameters, $(b^{hh}_{00})^{1/2}(k)$ and $(b^{mh}_{00})^{1/2}(k)$ (top), $b^{hh}_{01}(k)$ (second), $b^{hh}_{11}(k)$ (third), and $b^{hh}_{02-11}(k)$ (bottom) for halos and LRGs. The light blue lines at $z=0.5$ show the results for LRGs, while all the other lines for halos of different mass bins. In the top panels the bias parameters computed using the auto ($P^h_{00}$) and cross ($P^{mh}_{00}$) power spectra are plotted as the dashed and dotted lines, respectively.
• Figure 3: Velocity dispersion parameter with (upper panels) and without (lower panels) shot noise. The color of each line corresponds to the one with the same color in figure \ref{['fig:bias']}. The black line is for dark matter. The quantity $\Delta\sigma_v$ and $\Delta\bar{\sigma}_v$ are respectively shown in the top and bottom panels for $z=0.5$ as the dotted gray line (see the text).
• Figure 4: Same as figure \ref{['fig:bias']}, but the three power spectra which contain linear order contributions, $P^{mm}_{00}$, $P^{mm}_{01}$ and $P^{mm}_{11}$ in the definitions of bias parameters, are replaced by the linear theory power spectrum: from the top to bottom row, $(b^{hh}_{00,{\rm lin}})^{1/2}(k)/b_1^{hh}$, $(b^{mh}_{00,{\rm lin}})^{1/2}(k)/b_1^{mh}$, $b^{hh}_{01,{\rm lin}}(k)/(b^{mh}_{00})^{1/2}$, $b^{hh}_{01,{\rm lin}}(k)/(b^{hh}_{00})^{1/2}$, and $b^{hh}_{11,{\rm lin}}(k)$. The horizontal lines at the value of unity in each panel show the prediction for these quantities from linear theory with the input cosmological parameters in our simulations.
• Figure 5: Top set: Multipole power spectra of halos and LRGs. The corresponding linear theory predictions are shown as the dashed line with the same color for monopoles and quadrupoles, while as the black line for hexadecapoles. Artificial cuts are put for the plots of the hexadecapoles at low $k$ because of large sampling variance. Bottom set: Monopole and quadrupole spectra divided by linear theory. The color of the lines corresponds to the one with the same color in the top set. The results for dark matter, obtained in Okumura:2012, are also shown as the dot-dashed black lines for comparison.