Cosmology with massive neutrinos I: towards a realistic modeling of the relation between matter, haloes and galaxies

TL;DR

This paper addresses how massive neutrinos affect the non-linear relation between matter, haloes, and galaxies. It uses a large suite of particle-based N-body simulations with neutrino masses up to 0.60 eV and analyzes halo bias via power spectrum and correlation function, then populates galaxies with a simple HOD tuned to SDSS DR7. Key results show a scale-dependent halo bias in neutrino cosmologies that largely disappears when the bias is defined relative to the CDM distribution, and a partial Omega_nu–sigma8 degeneracy on large scales; HOD parameters M_min and M1 shift with neutrino mass, affecting small-scale galaxy clustering. The findings clarify how to incorporate neutrino effects in halo and galaxy statistics, informing joint analyses with CMB data to constrain neutrino masses from large-scale structure.

Abstract

By using a suite of large box-size N-body simulations that incorporate massive neutrinos as an extra set of particles, we investigate the impact of neutrino masses on the spatial distribution of dark matter haloes and galaxies. We compute the bias between the spatial distribution of dark matter haloes and the overall matter and cold dark matter distributions using statistical tools such as the power spectrum and the two-point correlation function. Overall we find a scale-dependent bias on large scales for the cosmologies with massive neutrinos. However, our results indicate that the scale-dependence in the bias is reduced if the latter is computed with respect to the cold dark matter distribution only. We find that the value of the bias on large scales is reasonably well reproduced by the Tinker fitting formula once the linear cold dark matter power spectrum is used, instead of the total matter power spectrum. We investigate whether scale-dependent bias really comes from purely neutrino's effect or from nonlinear gravitational collapse of haloes. For this purpose, we address the $Ω_ν$-$σ_8$ degeneracy and find that such degeneracy is not perfect, implying that neutrinos imprint a slight scale dependence on the large-scale bias. Finally, by using a simple halo occupation distribution (HOD) model, we investigate the impact of massive neutrinos on the distribution of galaxies within dark matter haloes. We use the main galaxy sample in the Sloan Digital Sky Survey II Data Release 7 to investigate if the small-scale galaxy clustering alone can be used to discriminate among different cosmological models with different neutrino masses. Our results suggest that different choices of the HOD parameters can reproduce the observational measurements relatively well, and we quantify the difference between the values of the HOD parameters between massless and massive neutrino cosmologies.

Figures (14)

• Figure 1: Halo-matter bias, computed as the ratio of the halo-matter cross-power spectrum to the matter power spectrum, for massless and massive neutrino simulations. We show the bias for haloes with masses, $M_{200}$, larger than $2\times10^{13}~h^{-1}{\rm M}_\odot$ (left column) and for haloes with masses larger than $4\times10^{13}~h^{-1}{\rm M}_\odot$ (right column) at redshifts $z=0$, $z=0.5$ and $z=1$ (as indicated on each panel). The results are shown for three different cosmologies with the same value of $\Omega_{\rm m}=0.2708$ and $A_s$ but different neutrino masses: $\Sigma_i m_{\nu_i}$ = 0.0 eV (red), $\Sigma_i m_{\nu_i}$ = 0.3 eV (green) and $\Sigma_i m_{\nu_i}$ = 0.6 eV (blue). The points and the error bars represent the mean value and the standard deviation from the set of 8 independent realizations comprising each cosmological model. The horizontal lines show the value of the bias on large scales as predicted by the Tinker Tinker_2010 fitting formula. We have used two different prescriptions when using that formula: the matter prescription (thin dashed lines), consisting in using the linear power spectrum for the whole matter and the cold dark matter prescription (thick solid lines), in which we use the linear matter power spectrum of the CDM component. In both prescriptions we take $\rho_{\rm cdm}$ as the value of $\rho_{\rm m}$. Note that the results for the $\Sigma_i m_{\nu_i}$ = 0.3 eV and $\Sigma_i m_{\nu_i}$ = 0.6 eV cosmologies have been slightly displaced in the $x-$axis for clarity.
• Figure 2: Same as Fig. \ref{['bias_hm']} but with the bias computed as $b_{\rm hh}^2(k)=P_{\rm hh}(k)/ P_{\rm mm}(k)$.
• Figure 3: $\Omega_\nu-\sigma_8$ degeneracy in the halo-matter bias. We plot the bias, $b_{hm}$, between the spatial distribution of haloes with masses, $M_{200}$, above $2\times10^{13}~h^{-1}{\rm M}_\odot$, and this of the underlying dark matter, comparing different cosmologies with the same value of $\sigma_8$ but different $\Sigma_i m_{\nu_i}$ . The bias is shown at three different redshifts: $z=0$ (top-left), $z=0.5$ (top-right) and $z=1$ (bottom). Models with a value of $\sigma_8=0.675$ are represented by the magenta and the blue points, which have $\Sigma_i m_{\nu_i}=0$ eV and $\Sigma_i m_{\nu_i}=0.6$ eV respectively. The red and black lines correspond to models with $\Sigma_i m_{\nu_i}$ = 0 eV and $\Sigma_i m_{\nu_i}$ = 0.6 eV respectively, with the same value of $\sigma_8=0.832$. The horizontal lines show the prediction of the bias on large scales using the Tinker formula plus the cold dark matter prescription for neutrinos. The error bars are the dispersion around the mean bias value from the set of 8 independent realizations comprising each simulation.
• Figure 4: Bias ratio for different cosmological models. We show the bias of dark matter haloes with masses above $2\times10^{13}~h^{-1}{\rm M}_\odot$ for the simulations H6 (blue), H3 (green), H6s8 (black) and H0s8 (magenta) normalized by the bias of the simulation H0 (reference model). The results are shown at four different redshifts, whose value is indicated on each panel. The solid lines show the results when the bias is computed using the total matter distribution, i.e. CDM plus massive neutrinos, whereas the dashed lines represent the results when the bias is calculated by using just the CDM distribution. In our companion paper Castorina, we show that only by computing the bias with respect to the cold dark matter distribution, the bias on large scale becomes scale-independent and universal.
• Figure 5: The panels show the 2-pt autcorrelation function of the CDM (red), the neutrinos (blue) and their cross-correlation (green) for the cosmologies with $\Sigma_i m_{\nu_i}$ = 0.3 eV (left panel) and $\Sigma_i m_{\nu_i}$ = 0.6 eV (right panel) at $z=0$. The thin solid lines correspond to the linear theory prediction obtained from CAMB (see text for details). The bottom panels show the relative difference between computing the correlation function for the entire matter with and without the last two term in the right hand side of Eq. \ref{['cross_correlation']}, i.e. the contribution of massive neutrinos to the total matter correlation function.