Analytic model for galaxy and dark matter clustering

TL;DR

An analytic halo-model framework is developed to predict nonlinear clustering by treating all matter as virialized halos with mass-dependent profiles and a halo mass function, yielding dark matter, galaxy, and cross-power spectra through halo-halo and intra-halo (Poisson) terms with occupancy functions $\langle N\rangle(M)$ and $\langle N(N-1)\rangle^{1/2}(M)$. The results show that for $\Lambda$CDM with plausible $c(M)$ and inner slope $\alpha$, the model reproduces N-body nonlinear spectra, and that the galaxy power spectrum $P_{\rm gg}(k)$ behaves approximately as a power law with a nearly constant large-scale bias that is scale-dependent and nonmonotonic; red galaxies can show distinct occupancy leading to different bias evolution. Cross-correlations between galaxies and dark matter, such as galaxy–galaxy lensing, yield a cross-correlation coefficient $r(k)$ near unity on Mpc scales, enabling partial reconstruction of $P_{\rm dm}(k)$ from galaxy statistics while warning against naive halo-profile interpretations. The framework thus provides a practical, data-driven route to infer the dark matter power spectrum from galaxy clustering and cross-correlations, with observational prospects to constrain the occupancy functions from current and future surveys.

Abstract

We investigate an analytic model to compute nonlinear power spectrum of dark matter, galaxies and their cross-correlation. The model is based on Press-Schechter halos, which cluster and have realistic dark matter profiles. The total power spectrum is a sum of two contributions, one from correlations betwen the halos and one from correlations within the same halo. We show that such a model can give dark matter power spectra which match well with the results of N-body simulations, provided that concentration parameter decreases with the halo mass. Galaxy power spectrum differs from dark matter power spectrum because pair weighted number of galaxies increases less rapidly than the halo mass, as predicted by theoretical models and observed in clusters. In this case the resulting power spectrum becomes a power law with the slope closed to the observed. Such a model also predicts a later onset of nonlinear clustering compared to the dark matter, which is needed to reconcile the CDM models with the data. Generic prediction of this model is that bias is scale dependent and nonmonotonic. For red or elliptical galaxies bias in power spectrum may be scale dependent even on very large scales. Our predictions for galaxy-dark matter correlations, which can be observed through the galaxy-galaxy lensing, show that these cannot be interpreted simply as an average halo profile of a typical galaxy, because different halo masses dominate at different scales and because larger halos host more than one galaxy. We discuss the prospects of using cross-correlations in combination with galaxy clustering to determine the dark matter power spectrum (ABRIDGED).

Figures (7)

• Figure 1: Comparison between the power spectrum predicted with our model and the PD nonlinear power spectrum for $\Lambda CDM$ model. Also shown are the linear power spectrum and the two individual contributions, $P^P$ and $P^{hh}$. Top is the $\alpha=-1.5$ profile, bottom is $\alpha=-1$. Other parameters are given in the text.
• Figure 2: Contribution to the $P^P(k)$ from different halo mass intervals for the two models in figure \ref{['fig1']}. Short dashed lines from left to right are $M>10^{14}h^{-1}M_{\hbox{$\odot$}}$, $10^{14}h^{-1}M_{\hbox{$\odot$}}>M>10^{13}h^{-1}M_{\hbox{$\odot$}}$, $10^{13}h^{-1}M_{\hbox{$\odot$}}>M>10^{12}h^{-1}M_{\hbox{$\odot$}}$ and $10^{12}h^{-1}M_{\hbox{$\odot$}}>M>10^{11}h^{-1}M_{\hbox{$\odot$}}$. Solid line is the total $P(k)$, dotted the correlated term $P^{hh}(k)$.
• Figure 3: Top figure shows $\langle N(N-1)\rangle^{1/2}$ and $\langle N\rangle$ versus $M$ for galaxies selected by absolute magnitude $M_B<-19.5$ (upper curves) and color $M_B<-19.5$, $M_B-M_V>0.8$ (lower curves) from semi-analytic models. Bottom figure shows the same functions divided by $Mh/10^{13}M_{\hbox{$\odot$}}$.
• Figure 4: Comparison between galaxy and dark matter power spectrum predictions for galaxies selected by absolute magnitude $M_B<-19.5$ as in figure \ref{['fig3']}. Poisson, halo-halo and combined terms are shown for the two spectra. Also shown is the measured power spectrum of galaxies. Note that at low $k$ the Poisson term for the galaxies is lower than that for the dark matter and this delays the onset of nonlinear clustering in galaxies.
• Figure 5: Comparison between galaxy and dark matter power spectrum predicted by our model and the results of N-body simulations and semi-analytic models. Predictions for galaxies selected by absolute magnitude $M_B<-19.5$ and $M_B-M_V>0.8$ are shown.