Neutrinos in Non-linear Structure Formation - The Effect on Halo Properties

TL;DR

The paper investigates how massive neutrinos alter halo properties and the halo mass function using a hybrid N-body approach that treats high-velocity neutrinos linearly on a grid and low-velocity neutrinos as N-body particles across six momentum bins, validated against the N-one-body method. It demonstrates good agreement between full N-body results and the N-one-body predictions for neutrino halos, explains why the Tremaine-Gunn bound is not saturated, and shows that neutrinos delay halo formation and reduce concentrations slightly. The halo mass function is strongly suppressed with increasing neutrino mass, and semi-analytic predictions from Sheth–Tormen can match the relative neutrino-induced changes if the neutrino contribution to halo mass is neglected (i.e., using $\Omega_m=\Omega_c+\Omega_b$). These findings have practical implications for interpreting upcoming cluster surveys and for experiments aiming to detect the cosmic neutrino background, providing accurate semi-analytic tools for neutrino cosmology across plausible mass ranges.

Abstract

We use N-body simulations to find the effect of neutrino masses on halo properties, and investigate how the density profiles of both the neutrino and the dark matter components change as a function of the neutrino mass. We compare our neutrino density profiles with results from the N-one-body method and find good agreement. We also show and explain why the Tremaine-Gunn bound for the neutrinos is not saturated. Finally we study how the halo mass function changes as a function of the neutrino mass and compare our results with the Sheth-Tormen semi-analytic formulae. Our results are important for surveys which aim at probing cosmological parameters using clusters, as well as future experiments aiming at measuring the cosmic neutrino background directly.

Figures (8)

• Figure 1: CDM and $\sum m_\nu = 1.2\, {\rm eV}$ neutrino distributions for halo masses $\simeq 5\cdot 10^{14}{\rm M}_\odot$ (top), $\simeq 10^{14}{\rm M}_\odot$ (middle) and $\simeq 10^{13}{\rm M}_\odot$ (bottom), where the masses only correspond to the central halos in the upper two mosaics. Dimensions in each image are 5, 2 and 1 $h^{-1} \, {\rm Mpc}$, respectively. In each mosaic the images correspond to CDM, total neutrino, and $q/T = 1$ to 6 from top-left to bottom-right. Individual neutrino $N$-body particles can be identified.
• Figure 2: Neutrino halo profiles for $\sum m_\nu = 0.3 \, {\rm eV}$ (top), $\sum m_\nu = 0.6 \, {\rm eV}$ (middle) and $\sum m_\nu = 1.2 \, {\rm eV}$ (bottom) for halo masses of $10^{12}$, $10^{13}$, $10^{14}$ and $10^{15} \, {\rm M}_\odot$. Profiles are calculated with the $N$-one-body method (dotted) and the $N$-body method with a halo isolation criterion (solid) and without (dot-dashed).
• Figure 3: Halo profiles from $N$-body simulations for a model without massive neutrinos, with isolated halos (solid) and all halos (dot-dashed). The halo masses are $10^{12}$, $10^{13}$, $10^{14}$ and $10^{15} \, {\rm M}_\odot$. The profiles for the lowest 3 halo masses are taken from the $256 \, h^{-1} \, {\rm Mpc}$ box and the profile for the most massive halo is taken from the $1024 \, h^{-1} \, {\rm Mpc}$ box. NFW profiles are also shown (dotted), and the halo mass dependent virial radii are indicated by the '+' signs.
• Figure 4: Cumulative neutrino halo density profiles as a function of momentum in a $10^{15}{\rm M}_\odot$ halo, for $\sum m_\nu = 0.6 \, {\rm eV}$ (left) and $\sum m_\nu = 1.2 \, {\rm eV}$ (right). The neutrino density with $q/T > 6$ has been added as a homogeneous term to all profiles.
• Figure 5: The evolution of the neutrino density profile around a static NFW halo of $10^{14} {\rm M}_\odot$ for $\sum m_\nu = 0.3$ eV (left) and $\sum m_\nu = 0.6$ eV (right). The physical density perturbation, $a^{-3}\delta_\nu$, as a function of the physical radius, $ar$, is time-independent in the TG limit.