[Paper Review] Weighing the Neutrinos with the Galaxy Shape-Shape Correlations

Jounghun Lee, Suho Ryu|arXiv (Cornell University)|Jun 25, 2020

Astrophysics and Cosmic Phenomena4 citations

TL;DR

This paper proposes that galaxy shape-shape correlations, quantified by the correlation function $\eta(r)$, can serve as a novel probe of the total neutrino mass $M_\nu$. Using high-resolution $N$-body simulations from the MassiveNuS project, it demonstrates that $\eta(r)$ at $r \leq 5\,h^{-1}\text{Mpc}$ is sensitive enough to distinguish between $M_\nu = 0.0\,\text{eV}$ and $M_\nu = 0.1\,\text{eV}$, and is insensitive to differences in $\sigma_8$, suggesting it can break the $\sigma_8$--$M_\nu$ degeneracy.

ABSTRACT

The galaxies form and evolve in the early epochs through the anisotropic merging process along the primary narrow filaments, in the direction of which their shapes become elongated and intrinsically aligned. The nonlinear evolution of the cosmic web broadens the primary filaments, by entangling them with multiple secondary filaments, which has an effect of reducing the anisotropy of the merging process and in consequence weakens the galaxy shape-shape correlations in the later epochs. Assuming that the degree of the nonlinearity and complexity of the cosmic web depends on the nature of dark matter, we propose a hypothesis that the galaxy shape-shape correlation function, $η(r)$, may be a powerful complimentary probe of the total neutrino mass, $M_ν$. Testing this hypothesis against a high resolution N-body simulation, we show that the $M_ν$-dependence of $η(r)$ at $z=0$ is sensitive enough to distinguish between $M_ν=0.0$ eV and $M_ν=0.1$ eV. We also show that the differences in $η(r)$ at $r\le 5\,h^{-1}$Mpc between the models with massless and massive neutrinos cannot be explained by their differences in the small-scale density powers, $σ_{8}$, which implies that the galaxy shape-shape correlation function has a potential to break the notorious cosmic degeneracy between $M_ν$ and $σ_{8}$.

Motivation & Objective

• To investigate whether galaxy shape-shape correlations can serve as a complementary probe of the total neutrino mass $M_\nu$.
• To test the hypothesis that the nonlinear evolution of the cosmic web—affected by massive neutrinos—modulates the strength of shape correlations.
• To determine whether $\eta(r)$ can distinguish between $M_\nu = 0.0\,\text{eV}$ and $M_\nu = 0.1\,\text{eV}$, despite degeneracies with $\sigma_8$.
• To assess the robustness of $\eta(r)$ as a probe under various halo property controls and projection effects.

Proposed method

• The galaxy shape-shape correlation function $\eta(r)$ is defined as $\eta(r) \equiv \langle |\hat{\mathbf{e}}(\mathbf{x}) \cdot \hat{\mathbf{e}}(\mathbf{x}+\mathbf{r})|^2 \rangle - \frac{1}{3}$, where $\hat{\mathbf{e}}$ is the major principal axis of the halo's inertia tensor.
• High-resolution $N$-body simulations from the MassiveNuS project are used, with $\nu\Lambda\text{CDM}$ models at $M_\nu = 0.0$, $0.1$, and $0.6\,\text{eV}$, all with identical cosmological parameters except $M_\nu$.
• Distinct dark matter halos are identified using the Rockstar algorithm, with selection criteria of $M_h \geq 10^{12}\,h^{-1}M_\odot$ and $\geq 100$ particles to ensure resolution.
• The correlation function $\eta(r)$ is computed by binning halo pairs by separation $r$, computing the squared inner product of their shape vectors, and subtracting $1/3$.
• Statistical significance is assessed using the Kolmogorov-Smirnov (KS) test on the cumulative distribution of $|\hat{\mathbf{e}}_{2d}(\mathbf{x}) \cdot \hat{\mathbf{e}}_{2d}(\mathbf{x}+\mathbf{r})|$ for projected 2D shapes at $r \approx 1\,h^{-1}\text{Mpc}$.
• Robustness is tested by controlling for halo mass ($M_h$), axial ratio ($S$), and concentration ($c_p$), and comparing results across different samples.

Experimental results

Research questions

• RQ1 Can the galaxy shape-shape correlation function $\eta(r)$ detect differences in total neutrino mass $M_\nu$?
• RQ2 Is the $M_\nu$-dependence of $\eta(r)$ robust against variations in $\sigma_8$ and other cosmological parameters?
• RQ3 Does the projected 2D shape correlation retain statistical significance when observational projection effects are considered?
• RQ4 Can $\eta(r)$ break the degeneracy between $\sigma_8$ and $M_\nu$ that plagues standard cosmological probes?

Key findings

• The shape-shape correlation function $\eta(r)$ at $r \leq 5\,h^{-1}\text{Mpc}$ shows statistically significant differences between $M_\nu = 0.0\,\text{eV}$ and $M_\nu = 0.1\,\text{eV}$ models, with a KS test p-value $< 0.1\%$.
• The difference in $\eta(r)$ between $M_\nu = 0.0\,\text{eV}$ and $M_\nu = 0.1\,\text{eV}$ cannot be explained by differences in $\sigma_8$, indicating $\eta(r)$ is sensitive to $M_\nu$ beyond $\sigma_8$.
• Even when projected onto 2D planes, the shape correlations remain significantly different between $M_\nu = 0.0\,\text{eV}$ and $M_\nu = 0.1\,\text{eV}$, with KS statistics rejecting the null hypothesis at $>99.9\%$ confidence.
• The $M_\nu$-dependence of $\eta(r)$ is robust under control for halo mass, axial ratio, and concentration, indicating it is not driven by selection effects.
• The signal at $r \sim 3\,h^{-1}\text{Mpc}$ is weakened by projection effects, suggesting larger galaxy samples are needed to detect the signal in real observations.
• The study identifies a path forward requiring hydrodynamic simulations to model baryonic shapes and account for misalignments and feedback effects before observational application.