Lyman-alpha constraints on warm and on warm-plus-cold dark matter models

TL;DR

The study constrains warm and cold-plus-warm dark matter models using Lyman-α forest data, combining WMAP5 with VHS and SDSS Ly-α measurements while rigorously accounting for systematics and employing both Bayesian and frequentist analyses. It derives transfer-function-based characterizations of CWDM, including the plateau in small-scale power and the key scales set by free-streaming, then maps these into Ly-α flux-power constraints via hydrodynamical simulations and nuisance-parameter marginalization. For pure WDM, the SDSS+WMAP5 analysis yields a Bayesian 95% CL lower bound of m_nrp ≈ 12.1 keV (with VHS giving weaker VHS-only limits), while CWDM allows modest WDM fractions at lower masses (e.g., m_nrp ≈ 5 keV with F_WDM ≲ 0.35 at 95% CL); frequentist bounds are somewhat weaker. The results have important implications for sterile-neutrino DM scenarios and their X-ray bounds, highlighting a region of parameter space where Ly-α data and X-ray constraints are simultaneously informative, and motivate more extensive simulations and higher-redshift data to sharpen the limits.

Abstract

We revisit Lyman-alpha bounds on the dark matter mass in Lambda Warm Dark Matter (Lambda-WDM) models, and derive new bounds in the case of mixed Cold plus Warm models (Lambda-CWDM), using a set up which is a good approximation for several theoretically well-motivated dark matter models. We combine WMAP5 results with two different Lyman-alpha data sets, including observations from the Sloan Digital Sky Survey. We pay a special attention to systematics, test various possible sources of error, and compare the results of different statistical approaches. Expressed in terms of the mass of a non-resonantly produced sterile neutrino, our bounds read m_NRP > 8 keV (frequentist 99.7% confidence limit) or m_NRP > 12.1 keV (Bayesian 95% credible interval) in the pure Lambda-WDM limit. For the mixed model, we obtain limits on the mass as a function of the warm dark matter fraction F_WDM. Within the mass range studied here (5 keV < m_NRP < infinity), we find that any mass value is allowed when F_WDM < 0.6 (frequentist 99.7% confidence limit); similarly, the Bayesian joint probability on (F_WDM, 1/m_NRP) allows any value of the mass at the 95% confidence level, provided that F_WDM < 0.35.

Figures (14)

• Figure 1: Transfer functions $T(k) \equiv \left[{P_{\Lambda {\textsc{cwdm}}\xspace}(k)} / {P_{\Lambda {\textsc{cdm}}}(k)} \right]^{1/2}$ for $m_\textsc{nrp} = 2~\mathrm{keV}$ and different WDM fractions: from left to right, $\Omega_\textsc{wdm}\xspace / (\Omega_\textsc{wdm}\xspace+ \Omega_{\textsc{cdm}}) = 1, 0.8, 0.6, 0.4, 0.2, 0.1$. Other parameters are fixed to $\Omega_\textsc{b}\xspace=0.05$, $\Omega_\textsc{m}\xspace=0.3$, $\Omega_{\Lambda}=0.7$, $h=0.7$.
• Figure 2: The height of plateau in the transfer function $T(k) \equiv \left[{P_{\Lambda {\textsc{cwdm}}\xspace}(k)} / {P_{\Lambda {\textsc{cdm}}}(k)} \right]^{1/2}$ depends only on $f_\textsc{wdm}\xspace$ only and does not change with the mass. In these examples, the mass is equal to $2 \, \:\mathrm{eV}$ (solid line) or $20 \, \:\mathrm{eV}$ (dashed-dotted line), while $\Omega_\textsc{wdm}\xspace / (\Omega_\textsc{wdm}\xspace+ \Omega_{\textsc{cdm}}) = 0.1$ (red) or $0.05$ (green). Other parameters are fixed to $\Omega_\textsc{b}\xspace=0.05$, $\Omega_\textsc{m}\xspace=0.3$, $\Omega_{\Lambda}=0.7$, $h=0.7$.
• Figure 3: Suppression factor $T_\mathrm{plateau}=[{P_{\Lambda {\textsc{cwdm}}\xspace}(k)}/{P_{\Lambda {\textsc{cdm}}}(k)}]^{1/2}$ computed today at $k = 10^2 \: h/\mathrm{Mpc}$ with the Boltzmann code CAMB, for different values of ${f_\textsc{wdm}\xspace}\xspace \equiv \Omega_\textsc{wdm}\xspace / \Omega_\textsc{m}\xspace$ and $\Omega_\textsc{b}\xspace$. Other parameters are kept fixed: $\Omega_\Lambda=0.7$, $\Omega_\textsc{m}\xspace=0.3$, $h=0.7$. The dashed curve corresponds to the analytic prediction of Eq. (\ref{['eq:tfit']}) with $\alpha \equiv {a_0 g(a_0)}/{a_{\mathrm{eq}}} = 2.75 \times 10^3$.
• Figure 4: Variation of $T(k)=[{P_{\Lambda {\textsc{cwdm}}\xspace}(k)}/{P_{\Lambda {\textsc{cdm}}}(k)}]^{1/2}$ with redshift, for various values of $m$ and $\Omega_\textsc{wdm}\xspace / (\Omega_\textsc{wdm}\xspace+ \Omega_{\textsc{cdm}})$; other parameters are fixed to the same values as in previous figures. (Left) For $m=0.5~\mathrm{keV}$, the variation is clearly visible at large $k > k_\textsc{fs}(z)$. (Right) For $m=5~\mathrm{keV}$, the free-streaming wavenumber is too large for any variation to be seen on the scales displayed here.
• Figure 5: Dependence of the flux PS of $\Lambda$WDM models (divided by that of $\Lambda$CDM) on thermal velocities in hydrodynamical simulations. The points show $P_F^{\Lambda \mathrm{WDM}}/P_F^{\Lambda \mathrm{CDM}}$ at $k= 0.14 \: h/\mathrm{Mpc}$ and $z=2.2$, extracted from GADGET-II simulations for three different masses, with and without thermal velocities in the initial conditions. The lines are the results of linear interpolation between these points.