Inferring the dark matter power spectrum from the Lyman-alpha forest in high-resolution QSO absorption spectra

TL;DR

This work uses high-resolution Lyman-$\alpha$ forest data from LUQAS and Croft et al., paired with a suite of detailed hydrodynamical simulations, to reconstruct the linear dark matter power spectrum on scales $0.003 < k < 0.03\,{ m s/km}$. By calibrating a flux-to-matter bias $b(k)$ from simulations and applying it to observed flux power spectra, the authors infer $P_{\rm mat}(k)$ and quantify statistical and systematic uncertainties, notably the effective optical depth $\tau_{\rm eff}$ and the temperature-density relation. The results are consistent with a Lambda-CDM framework with a near-scale-invariant primordial spectrum ($n \approx 1$) and yield constraints on $\sigma_8$ when combined with CMB data, with a quantified error budget dominated by systematics. The analysis demonstrates gravitational growth between $z\sim2.72$ and $z\sim2.13$ and provides a pathway to tighten cosmological constraints by reducing systematics in $\tau_{\rm eff}$ and simulation biases.

Abstract

We use the LUQAS sample (Kim et al. 2004), a set of 27 high-resolution and high signal-to-noise QSO absorption spectra at a median redshift of z=2.25, and the data from Croft et al. (2002) at a median redshift of z=2.72, together with a large suite of high-resolution large box-size hydro-dynamical simulations, to estimate the linear dark matter power spectrum on scales 0.003 s/km < k <0.03 s/km. Our re-analysis of the Croft et al. data agrees well with their results if we assume the same mean optical depth and gas temperature-density relation. The inferred linear dark matter power spectrum at z=2.72 also agrees with that inferred from LUQAS at lower redshift if we assume that the increase of the amplitude is due to gravitational growth between these redshifts. We further argue that the smaller mean optical depth measured from high-resolution spectra is more accurate than the larger value obtained from low-resolution spectra by Press et al. (1993) which Croft et al. used. For the smaller optical depth we obtain a ~ 20% higher value for the rms fluctuation amplitude of the matter density. By combining the amplitude of the matter power spectrum inferred from the Lyman-alpha forest with the amplitude on large scales inferred from measurements of the CMB we obtain constraints on the primordial spectral index n and the normalisation sigma_8. For values of the mean optical depth favoured by high-resolution spectra, the inferred linear power spectrum is consistent with a LambdaCDM model with a scale-free (n=1) primordial power spectrum.

Figures (9)

• Figure 1: Triangles show the effective optical depth $\tau_{\rm eff}=-\ln\left<F\right>$ for the LUQAS sample (also given in Table 2). The dashed curve is the result of Kim et al. (2002) while the long-dashed and dot-dashed curves show the result of Schaye et al. (2003), with and without the removal of pixels contaminated by metals, respectively. The dotted curve is the effective optical depth obtained by Press, Rybicki & Schneider (1993). The solid curve shows the results from Bernardi et al. (2003). The empty diamond is the result of Tytler et al. (2004). The vertical extent of the two shaded regions indicates the values used in our analysis.
• Figure 2: Left panel: 1D flux power spectra of different simulations of model B2 at $z=2.75$, run with different box-sizes. All simulations are with 200$^3$ dark matter particles and 200$^3$ gas particles. Note that simulations have not been scaled to the same effective optical depth. The shaded region indicates the range of wavenumbers used to infer the linear dark matter power spectrum. Right panel: 3D flux power spectra for different simulations of model B2, for a range of box-sizes and resolutions, as indicated in the plot.
• Figure 3: Effect of rescaling simulations (60 $h^{-1}$ Mpc box $2\times 400^3$ particles), to reproduce different temperature-density relations and different values of $\sigma_8$. Left: Difference between the 1D flux power spectrum of the 'hot' simulation and the rescaled 'cold' simulation (solid curve) and vice versa (dashed curve). Middle: Difference between the 1D flux power spectrum of the simulation of the B2 model and the flux power spectra for three rescaled models with different values of the exponent $\gamma$ of the temperature-density relation. The difference between the 1D flux power spectra of two simulations of model B2 with two different resolutions is also shown (30 $h^{-1}$ Mpc box, $2\times 400^3$ particles). Right: The solid curve shows the difference between the 1D flux power spectra of a simulation of model B2 ($\sigma_{8}=0.85, z=2.72$) and an output of a simulation of model B3 ($\sigma_{8}=1$) at higher redshift which has the same rms density fluctuation (rescaled to the effective optical depth at $z=2.72$). The dashed curve shows the difference between the 1D flux power spectra of a simulation of model C3 ($\sigma_{8}=1.0, z=2.125$) and an output of a simulation of model C2 ($\sigma_{8}=0.85$) at lower redshift which has the same rms density fluctuation (rescaled to the effective optical depth at $z=2.125$). The dotted curve shows the difference between the 1D flux power spectra of a simulation of model B2 for two different values of $\tau_{\rm eff}$. The shaded regions indicate the range of wavenumbers used in our analysis.
• Figure 4: $b_{\rm fid}/b$ for three different simulations with different values of $\sigma_8$. Left: $b_{\rm fid}/b$ as a function of $\tau_{\rm eff}$ (no scaling of the temperature-density relation has been adopted here). We also show the scaling found by Croft et al. (2002) [C02] and Gnedin & Hamilton (2002) [GH02] as thin solid and dashed curves, respectively. Middle: $b_{\rm fid}/b$ as a function of $T_0$, the temperature at the mean density, for a fixed $\tau_{\rm eff}=0.305$ and $\gamma=1.2$. Right: $b_{\rm fid}/b$ as a function of $\gamma$, the power-law index of the temperature-density relation, for a fixed $\tau_{\rm eff}=0.305$ and $T_0=10^{4.15}$ K.
• Figure 5: Left: Flux power spectrum at $z=2.125$. The filled triangles are for the LUQAS subsample with a mean redshift of $z=2.125$ (see Table \ref{['tab1']}). The continuous curve is the power spectrum of the simulation that fits the data best. Right: Flux power spectrum at $z=2.72$. The filled triangles are for the fiducial sample of Croft et al. (2002). The continuous curve is the power spectrum of the simulation that fits the data best (with $\tau_{\rm eff}=0.305$). Shaded regions indicate the range of wavenumbers used in our analysis.