Halo bias in mixed dark matter cosmologies

TL;DR

This paper develops an analytic framework to compute scale-dependent halo bias in mixed dark matter cosmologies with massive neutrinos by combining spherical collapse on long-wavelength modes with the peak-background-split formalism. The authors derive a bias relation that depends on the CDM and neutrino components, showing a neutrino-induced step in the halo bias near the neutrino free-streaming scale, with amplitude increasing for more massive halos and larger neutrino fractions. They numerically evaluate the scale-dependent derivative $d\delta_{crit}/d\delta_{c,L}(k)$ and propagate it through a mass-function-based bias model to predict changes in the halo power spectra, finding that scale-dependent bias reduces the suppression of $P_{nn}(k)$ on small scales relative to $P_{mm}(k)$ and can relax neutrino mass constraints from galaxy surveys. The neutrino feature in the bias also provides a novel signature to study massive neutrinos independently, and the work highlights the importance of accounting for multi-component perturbations in interpreting large-scale structure data.

Abstract

The large-scale distribution of cold dark matter halos is generally assumed to trace the large-scale distribution of matter. In a universe with multiple types of matter fluctuations, as is the case with massive neutrinos, the relation between the halo field and the matter fluctuations may be more complicated. We develop a method for calculating the bias factor relating fluctuations in the halo number density to fluctuations in the mass density in the presence of multiple fluctuating components of the energy density. In the presence of massive neutrinos we find a small but pronounced feature in the halo bias near the neutrino free-streaming scale. The neutrino feature is a small step with amplitude that increases with halo mass and neutrino mass density. The scale-dependent halo bias lessens the suppression of the small-scale halo power spectrum and should therefore weaken constraints on neutrino mass from the galaxy auto-power spectrum and correlation function. On the other hand, the feature in the bias is itself a novel signature of massive neutrinos that can be studied independently.

Figures (8)

• Figure 1: Left: The scale-dependent changes to the matter power spectrum in a cosmology with a single massive neutrino $m_{\nu} = 0.1\,eV$. Right: The ratio of the CDM power spectrum and CDM-matter cross-power spectrum to the matter power spectrum in a cosmology with a single massive neutrino $m_{\nu} = 0.1\,eV$. Both quantities are plotted at $z =0$.
• Figure 2: Left: The scale dependence of $\dot\delta_{c}/\delta_{c}$ at $z_i$, plotted for a number of different neutrino mass hierarchies. Also shown is the horizon scale at $z_i = 200$ and the matter radiation equality scale. Right: The scale dependence of the linear evolution of CDM and baryon perturbations between $z= 200$ and $z = 0$. In both panels $\Omega_c$ is fixed so varying $\Omega_\nu$ changes the total matter density $\Omega_m$.
• Figure 3: Plotted is the relationship between the initial perturbation values $\delta_{c,iS}$ and $\delta_{c,iL}(k)$ for halos of $M = 10^{13}M_\odot$ that collapse at the same time $z_{collapse} =0.5$ for a range of $k$, the wave number of the long-wavelength mode. Left: $m_{\nu 1} = m_{\nu 2} = m_{\nu 3} = 0\,eV$, Right: $m_{\nu 1} = 0.05\,eV$, $m_{\nu 2} = m_{\nu 3} = 0\,eV$.
• Figure 4: Plotted is the relationship between $\delta_{c,S}(z_{collapse})$ and $\delta_{c,iL}(k,z_{collapse})$ (the initial perturbation amplitudes linearly extrapolated to the collapse redshift) for halos of $M = 10^{13}M_\odot$ that collapse at the same time $z_{collapse} =0.5$ for a range of values of $k$. Left: $m_{\nu 1} = m_{\nu 2} = m_{\nu 3} = 0\,eV$, Right: $m_{\nu 1} = 0.05\,eV$, $m_{\nu 2} = m_{\nu 3} = 0\,eV$.
• Figure 5: The slopes of the relationships plotted in Fig. (\ref{['fig:deltaczSdeltaczL']}) -- that is the slope of the line relating $\delta_{c,S}$ to $\delta_{c,L}$. The left panel plots the relationship between the initial values of the two quantities. The right panel plots it with $\delta_{c,S}$ and $\delta_{c,L}$ evaluated at $z_{collapse}$ (using the scale-dependent linear growth functions). Each curve has a fixed $\Omega_m$, but varying $\Omega_c$ and $\Omega_\nu \approx \sum_i m_{\nu i}$ where the neutrino masses are listed in the plot legend.