Lyman-alpha Forest Constraints on the Mass of Warm Dark Matter and the Shape of the Linear Power Spectrum

TL;DR

This study tests warm dark matter (WDM) by comparing high-resolution N-body simulations and synthetic Ly-$\alpha$ forest spectra to Keck observations at $z\approx 3$. It explores CDM and several WDM masses, plus a Broken Scale Invariance model, and calibrates the simulated spectra to the observed mean flux. The authors find that a WDM particle mass of $m_W \ge 750\\, {\rm eV}$ is required to reproduce both the flux power spectrum $P_F(k)$ and the flux PDF, making more severe suppression incompatible with the Ly-$\alpha$ forest; this bound is robust to $T_0$ uncertainties and complements other small-scale structure constraints. The work highlights the Ly-$\alpha$ forest as a sensitive probe of the linear power spectrum on quasi-linear scales and places strong constraints on the shape of the initial power spectrum in WDM and related scenarios.

Abstract

High resolution N-body simulations of cold dark matter (CDM) models predict that galaxies and clusters have cuspy halos with excessive substructure. Observations reveal smooth halos with central density cores. One possible resolution of this conflict is that the dark matter is warm (WDM); this will suppress the power spectrum on small scales. The Lyman-alpha forest is a powerful probe of the linear power spectrum on these scales. We use collisionless N-body simulations to follow the evolution of structure in WDM models, and analyze artificial Lyman-alpha forest spectra extracted from them. By requiring that there is enough small-scale power in the linear power spectrum to reproduce the observed properties of the Lyman-alpha forest in quasar spectra, we derive a lower limit to the mass of the WDM particle of 750 eV. This limit is robust to reasonable uncertainties in our assumption about the temperature of the mean density gas (T0) at z=3. We argue that any model that suppresses the CDM linear theory power spectrum more severely than a 750 eV WDM particle cannot produce the Lyman-alpha forest.

Figures (4)

• Figure 1: Power spectra of the mass density fields in different models. (a) Linear mass power spectra at $z=3$ from the Boltzmann code. (b) Non-linear power spectra at $z=3$ from simulation output, computed by cloud-in-cell binning onto a $256^{3}$ grid, taking its Fourier transform, and squaring the amplitudes of its Fourier components. Note that WDM750T025K has the same mass power spectrum as WDM750.
• Figure 2: Examples of artificial spectra at $z=3$ along four random lines of sight in the simulations. All simulations have identical phases for the Fourier components of the initial density fields. In each panel, black line shows results for CDM, blue line shows WDM500, and red line shows WDM750.
• Figure 3: Power spectrum of the transmitted flux at $z=3$ from 400 artificial spectra for each model. Solid points with error bars show the flux power spectrum at $z\approx 3$ measured by McDonald et al. (1999) from eight Keck HIRES quasar spectra.
• Figure 4: Probability distribution functions (PDF) of the transmitted flux at $z=3$, computed using 400 artificial spectra for each model. Solid points with error bars show the flux PDF at $z=3$ measured by McDonald et al. (1999) using Keck HIRES spectra of eight quasars.