Linear Cosmological Structure Limits on Warm Dark Matter

TL;DR

This work investigates how free streaming in warm dark matter, modeled as a sterile neutrino, suppresses small-scale linear power in a $\Lambda$CDM framework and uses a comprehensive data set (CMB, SDSS 3D galaxy clustering, and Ly$\alpha$ forest measurements) to bound the WDM free-streaming scale. By modeling the WDM transfer function $T_s(k)$ and jointly varying $m_s^{-1}$ with standard cosmological parameters in an MCMC analysis, the study derives progressively tighter lower limits on $m_s$: $>0.108$ keV from 3D galaxy clustering alone, $>1.71$ keV when including SDSS Ly$\alpha$, and $>3.00$ keV with high-resolution Ly$\alpha$, all at 95% CL, with caveats on systematic uncertainties in Ly$\alpha$ data. The results constrain sterile neutrino WDM (and gravitino WDM) and provide a conservative baseline using SDSS Ly$\alpha$ data, while highlighting the potential for tighter constraints or caveats from high-resolution Ly$\alpha$ analyses and X-ray decay bounds.

Abstract

I consider constraints from observations on a cutoff scale in clustering due to free streaming of the dark matter in a warm dark matter cosmological model with a cosmological constant. The limits are derived in the framework of a sterile neutrino warm dark matter universe, but can be applied to gravitinos and other models with small scale suppression in the linear matter power spectrum. With freedom in all cosmological parameters including the free streaming scale of the sterile neutrino dark matter, limits are derived using observations of the fluctuations in the cosmic microwave background, the 3D clustering of galaxies and 1D clustering of gas in the Lyman-alpha (Ly-alpha) forest in the Sloan Digital Sky Survey (SDSS), as well as the Ly-alpha forest in high-resolution spectroscopic observations. In the most conservative case, using only the SDSS main-galaxy 3D power-spectrum shape, the limit is m_s > 0.11 keV; including the SDSS Ly-alpha forest, this limit improves to m_s > 1.7 keV. More stringent constraints may be placed from the inferred matter power spectrum from high-resolution Ly-alpha forest observations, which has significant systematic uncertainties; in this case, the limit improves to m_s > 3.0 keV (all at 95% CL).

Figures (4)

• Figure 1: Shown are the resulting linear matter power spectra $P(k)$ for a standard flat cosmological model $\Omega_{\rm DM} = 0.26$, $\sigma_8 =0.9$, $\Omega_b=0.04$, and $h=0.7$ at $z=0$, and with sterile neutrino warm to cold dark matter in the mass range $0.3{\rm\ keV} < m_s < 140{\rm\ keV}$ (gray/cyan). The corresponding CDM case is dashed (black). Small-scale clustering data used here are the SDSS 3D power-spectrum of galaxies (diamonds), the inferred slope and amplitude of the matter power spectrum from SDSS Ly$\alpha$ forest observations (star point and slope between arrows), the inferred matter power spectrum from Ly$\alpha$ forest observations from Croft et al. Croft:2000hs (cross points) and the LUQAS (square points), as interpreted by VHS Viel:2004bf. Ly$\alpha$ forest measures are evolved to $z=0$ by the appropriate growth function. The solid (blue) line at high-$k$ is $P(k)$ for upper limit $m_s = 8.2\rm\ keV$ from observations of Virgo Abazajian:2001vt, the solid (red) line at low-$k$ is that for the lower limit from the SDSS Ly$\alpha$ forest in this work ($m_s = 1.7\rm\ keV$), and the dotted line is that for the lower limit using high-resolution Ly$\alpha$ forest data from this work ($m_s = 3.0\rm\ keV$).
• Figure 2: Shown here are the 1D marginalized likelihoods on chosen base and derived cosmological parameters for the CMB plus SDSS 3D $P_g(k)$ in solid (blue), plus SDSS Ly$\alpha$ forest in dashed (purple), plus the VHS high-resolution Ly$\alpha$ forest in dotted (red). The shaded (yellow) likelihoods are for the CMB plus SDSS 3D $P_g(k)$ plus SDSS Ly$\alpha$ forest for the standard CDM case, which shows that parameters are generally not biased when including the presence of WDM.
• Figure 3: Shown here are the 1D marginalized likelihoods for the (inverse) mass of the sterile neutrino dark matter, $m_s$ and the scale of the primordial spectrum cutoff $\alpha$, from the CMB plus SDSS 3D $P_g(k)$ in solid (blue), plus SDSS Ly$\alpha$ forest in dashed (purple), and plus the VHS high-resolution Ly$\alpha$ forest in dotted (red).
• Figure 4: The parameter space for sterile neutrino dark matter production and constraints. The red (dark grey) band is consistent with sterile neutrinos composing the dark matter consistent with $\Omega_{\rm DM} = 0.24\pm 0.04$abazajian05. Upper limits arise from radiative decay limits from XMM-Newton X-ray observations of the Virgo Cluster Abazajian:2001vt and the diffuse X-ray background Boyarsky:2005us. The lower limits of this work from the CMB plus SDSS 3D $P_g(k)$ plus SDSS Ly$\alpha$ are in solid (yellow) at $m_s<1.7\rm\ keV$ and all previous data plus VHS in dashed (yellow) at $m_s<3.0\rm\ keV$.