Grid Based Linear Neutrino Perturbations in Cosmological N-body Simulations

TL;DR

This work tackles the challenge of accurately including light neutrinos in cosmological N-body simulations without prohibitive cost. It introduces a grid-based neutrino component evolved via linear perturbation theory and coupled to CDM through the long-range force in a TreePM code, validated against full non-linear neutrino simulations. The method achieves better than 1% accuracy for the matter power spectrum for $\sum m_\nu \lesssim 0.5\ \mathrm{eV}$ at $z=0$ (and even smaller errors at higher redshift) while delivering ~10x speedups, enabling precise neutrino-mass studies in large simulations. Moreover, the approach can be extended to other components with linear perturbations and can be integrated with particle-based neutrino treatments when needed for specific observables.

Abstract

We present a novel, fast and precise method for including the effect of light neutrinos in cosmological N-body simulations. The effect of the neutrino component is included by using the linear theory neutrino perturbations in the calculation of the gravitational potential in the N-body simulation. By comparing this new method with the full non-linear evolution first presented in \cite{Brandbyge1}, where the neutrino component was treated as particles, we find that the new method calculates the matter power spectrum with an accuracy better than 1% for \sum m_ν\lesssim 0.5 eV at z = 0. This error scales approximately as (\sum m_ν)^2, making the new linear neutrino method extremely accurate for a total neutrino mass in the range 0.05 - 0.3 eV. At z = 1 the error is below 0.3% for \sum m_ν\lesssim 0.5 eV and becomes negligible at higher redshifts. This new method is computationally much more efficient than representing the neutrino component by N-body particles.

Figures (8)

• Figure 1: Percentage differences in the total matter power spectrum at different redshifts between simulations where the neutrino component is represented in the $N$-body simulation either on a grid or as particles. A negative power difference indicates more power in the particle simulations. From top to bottom the total neutrino mass is $0.3 \, {\rm eV}$ ($B_1 / B_2$), $0.6 \, {\rm eV}$ ($C_1 / C_3$) and $1.2 \, {\rm eV}$ ($D_1 / D_3$), respectively. All the power spectra presented in this paper have been calculated on a $1024^3$ grid, using a deconvolved CIC mass assignment scheme for the $N$-body particles.
• Figure 2: Neutrino power spectra for a total neutrino mass of $0.3 \, {\rm eV}$ (left), $0.6 \, {\rm eV}$ (middle) and $1.2 \, {\rm eV}$ (right) at various redshifts. The linear theory neutrino power spectrum, convolved with our chosen random numbers, are shown with solid lines (models $B_1$, $C_1$ and $D_1$), simulations with $256^3$ neutrino particles with dotted lines (models $B_2$, $C_2$ and $D_2$) and finally simulations with $512^3$ neutrino particles are shown with dashed lines (models $C_3$ and $D_3$).
• Figure 3: Density grids for the CDM (left), neutrino particle (middle) and neutrino grid (right) components. In all cases the total neutrino mass is $0.6 \, {\rm eV}$. The top row is at $z = 49$, the middle row at $z = 4$, and the bottom row at $z = 0$. In the bottom row the square root has been taken of the first two density distributions. The images are centered at the highest density region in the simulation volume and they have a thickness of $20 \, h^{-1} {\rm Mpc}$ and a side length of $512 \, h^{-1} {\rm Mpc}$. The particle density distributions are found using the adaptive smoothing length kernel from monaghan (taken from model $C_3$), and the neutrino grid density distribution is an inverse FFT of the linear neutrino Fourier grid imbedded in the $N$-body simulation volume (model $C_1$).
• Figure 4: Evolution of the difference in the total matter power spectrum between a pure $\Lambda {\rm CDM}$ model ($A_1$) and a model with $\sum m_\nu = 0.6 \, {\rm eV}$ neutrinos on a grid ($C_1$). The difference expected from linear theory is also shown (black solid lines).
• Figure 5: The figure shows the effect of redshifting either the Fermi-Dirac thermal velocity or momentum from $z = 49$ until $z = 0$, for 3 different neutrino one-particle masses.