The Nonlinear Cosmological Matter Power Spectrum with Massive Neutrinos I: The Halo Model

Abstract

Measurements of the linear power spectrum of galaxies have placed tight constraints on neutrino masses. We extend the framework of the halo model of cosmological nonlinear matter clustering to include the effect of massive neutrino infall into cold dark matter (CDM) halos. The magnitude of the effect of neutrino clustering for three degenerate mass neutrinos with m_nu=0.9 eV is of order ~1%, within the potential sensitivity of upcoming weak lensing surveys. In order to use these measurements to further constrain--or eventually detect--neutrino masses, accurate theoretical predictions of the nonlinear power spectrum in the presence of massive neutrinos will be needed, likely only possible through high-resolution multiple particle (neutrino, CDM and baryon) simulations.

Figures (4)

• Figure 1: A comparison of the spatial distribution of accreted neutrinos for an NFW CDM profile for a $10^{14} h^{-1} M_\odot$ halo that has evolved in the fit of Ref. Wechsler (solid line) and with a static profile (dashed line). The virial radius for this halo is $4.8~\rm Mpc$ for a an $h=0.7, \Omega_c = 0.26$ cosmology.
• Figure 2: A comparison of the Fourier transform of the accreted neutrino profile into an NFW CDM halo of $10^{14} h^{-1}M_\odot$ that has evolved with redshift (lower line) and with a static profile (upper line). The Fourier transform for the CDM NFW profile is shown for reference of scale.
• Figure 3: The estimated change in the nonlinear matter power spectrum at z=0 calculated with the halo model, $\delta P_{\rm NL}(k) = (P^\nu_{\rm NL}(k)-P^0_{\rm NL}(k))/P^0_{\rm NL}(k)$ due to late time neutrino clustering only. (Both $P^0_{\rm NL}(k)$ and $P^\nu_{\rm NL}(k)$, are calculated with a transfer function that includes the same early neutrino free streaming.) The lines of increasing magnitudes denote models with three neutrinos with masses of 0.1 eV, 0.3 eV, 0.6 eV, 0.9 eV, respectively.
• Figure 4: The weak lensing convergence power spectrum (upper panel) for nonzero neutrino mass models of $0.1\rm~eV$, $0.3\rm~eV$, $0.6~\rm eV$, and $0.9~\rm eV$, with decreasing peak convergence, respectively. The power spectra are normalized at $\sigma_8= 0.9$, therefore showing a pivot at $\ell \sim 200$. The deviations including and excluding this effect are plotted in the lower panel, with increasing mass neutrinos corresponding to an increased amplitude of the effect. Gray (cyan) boxes are expected errors for an LSST-like survey as described in the text.