Extending the modeling of the anisotropic galaxy power spectrum to $k = 0.4 \ h\mathrm{Mpc}^{-1}$

TL;DR

This work presents a comprehensive extension of redshift-space galaxy power-spectrum modeling to $k$-modes up to $0.4\ h\mathrm{Mpc}^{-1}$ by integrating a halo-model framework with Eulerian perturbation theory and a distribution-function mapping to redshift space. The model explicitly decomposes galaxies into centrals and satellites (with subtypes) to capture FoG and halo-occupation effects, and calibrates key components against high-fidelity $N$-body simulations (RunPB, N-series) and realistic BOSS CMASS mocks. Validation shows small biases in $f\sigma_8$ and modest AP parameter biases, while including $P_4$ and extending to $k_{\max}=0.4$ significantly improves parameter precision (roughly 15–30% for $f\sigma_8$ and 10–15% for $\alpha_\perp$) relative to $k_{\max}=0.2$. The results highlight both the gains from modeling down to small scales and the necessity of simulation-calibrated, physically motivated parameters, suggesting that simpler Fourier-space RSD models may underestimate uncertainties at these scales. The framework, including a 13-parameter, physically motivated set and a public pyRSD implementation, provides a robust path for extracting growth and geometric information from current and upcoming galaxy surveys.

Abstract

We present a new model for the redshift-space power spectrum of galaxies and demonstrate its accuracy in modeling the monopole, quadrupole, and hexadecapole of the galaxy density field down to scales of $k = 0.4 \ h\mathrm{Mpc}^{-1}$. The model describes the clustering of galaxies in the context of a halo model and the clustering of the underlying halos in redshift space using a combination of Eulerian perturbation theory and $N$-body simulations. The modeling of redshift-space distortions is done using the so-called distribution function approach. The final model has 13 free parameters, and each parameter is physically motivated rather than a nuisance parameter, which allows the use of well-motivated priors. We account for the Finger-of-God effect from centrals and both isolated and non-isolated satellites rather than using a single velocity dispersion to describe the combined effect. We test and validate the accuracy of the model on several sets of high-fidelity $N$-body simulations, as well as realistic mock catalogs designed to simulate the BOSS DR12 CMASS data set. The suite of simulations covers a range of cosmologies and galaxy bias models, providing a rigorous test of the level of theoretical systematics present in the model. The level of bias in the recovered values of $f σ_8$ is found to be small. When including scales to $k = 0.4 \ h\mathrm{Mpc}^{-1}$, we find 15-30\% gains in the statistical precision of $f σ_8$ relative to $k = 0.2 \ h\mathrm{Mpc}^{-1}$ and a roughly 10-15\% improvement for the perpendicular Alcock-Paczynski parameter $α_\perp$. Using the BOSS DR12 CMASS mocks as a benchmark for comparison, we estimate an uncertainty on $f σ_8$ that is $\sim$10-20\% larger than other similar Fourier-space RSD models in the literature that use $k \leq 0.2 \ h\mathrm{Mpc}^{-1}$, suggesting that these models likely have a too-limited parametrization.

Figures (14)

• Figure 1: The dependence of the second-order nonlinear effective biases, $b_2^{00}$ (blue, solid) and $b_2^{01}$ (red, dashed), on the linear bias $b_1$ used in this work, as determined from the RunPB simulations. For comparison, the best-fit bias parameters from Vlah:2013 are shown as circles.
• Figure 2: The accuracy of the dark matter HZPT modeling results used in this work, in comparison to the results from the RunPB simulation. We compare the dark matter power spectrum $P_{00}$ (top), density -- radial momentum cross-power $P_{01}^S$ (middle), and the small-scale correlation function $\xi_{00}$ (bottom). We give results for three redshift outputs: $z=1$ (left), $z=0.55$ (center), and $z=0$ (right). The updated HZPT model parameters are presented in Appendix \ref{['app:hzpt-P00']}.
• Figure 3: The accuracy of the HZPT model for the auto power spectrum of the dark matter radial momentum $P_{11}^S[\mu^4]$ in comparison to the results from the RunPB simulations. We give results for three redshift outputs: $z=1$ (left), $z=0.55$ (center), and $z=0$ (right). The best-fit HZPT model parameters are presented in Appendix \ref{['app:hzpt-P11']}.
• Figure 4: The deviation of the halo stochasticity $\Lambda(k)$, as defined in equation \ref{['eq:lambda']}, from the Poisson shot noise, for the case of (a) the same halo mass bin and (b) different halo mass bins. Results are measured from the RunPB simulations for three separate combinations of bins. The average halo mass increases from left to right; see Table \ref{['tab:mass-bins']} for halo mass bin details. For each subplot, we show the results for 10 redshifts, ranging from $z=1$ (dark) to $z=0$ (light). Even when the mean halo mass is similar, the scale dependence and amplitude in the cases of auto and cross halo stochasticity can differ significantly.
• Figure 5: The accuracy of the HZPT model used in this work for the halo-matter cross-correlation, in comparison to the results from the RunPB simulation. We compare the cross power spectrum $P_{hm}$ (top) and the correlation function $\xi^{hm}$ (bottom) for 5 halo mass bins at $z = 0.55$ (see table \ref{['tab:mass-bins']} for bin details). We show the measurement uncertainties as error bars for $P^{hm}$ and as the grey shaded region for $\xi^{hm}$. The HZPT parameters have been fit using only $P^{hm}(k)$ from $0.005 \ h\text{Mpc}^{-1} < k < 0.5 \ h\text{Mpc}^{-1}$. The model is a good description of $P^{hm}$ on these scales, as well as $\xi^{hm}$ down to $r \sim 5 \ \text{Mpc}/h$, but fails once entering the 1-halo regime on small scales.