The Linear Theory Power Spectrum from the Lyman-alpha Forest in the Sloan Digital Sky Survey

TL;DR

This work converts SDSS Lyα forest PF(k,z) measurements into constraints on the linear matter power spectrum using a suite of hydrodynamic and hydro-PM simulations, explicitly modeling damping wings and UV background fluctuations. It parameterizes the linear power spectrum by $\Delta^2_L(k_p,z_p)$, $n_{ m eff}(k_p,z_p)$, and $\alpha_{ m eff}(k_p,z_p)$ at a pivot and fits these to SDSS and HIRES data with a comprehensive set of nuisance parameters. The main result is $\Delta^2_L(k_p,z_p)=0.452_{-0.057-0.116}^{+0.069+0.141}$ and $n_{ m eff}(k_p,z_p)=-2.321_{-0.047-0.102}^{+0.055+0.131}$, consistent with LCDM and providing a powerful cross-check with CMB constraints; the analysis also constrains systematic effects from damping wings and UV fluctuations. The paper highlights the robustness of the inference to modeling choices and outlines concrete steps for improvement, including more hydrodynamic simulations and enhanced treatment of feedback and radiative processes.

Abstract

We analyze the SDSS Ly-alpha forest P_F(k,z) measurement to determine the linear theory power spectrum. Our analysis is based on fully hydrodynamic simulations, extended using hydro-PM simulations. We account for the effect of absorbers with damping wings, which leads to an increase in the slope of the linear power spectrum. We break the degeneracy between the mean level of absorption and the linear power spectrum without significant use of external constraints. We infer linear theory power spectrum amplitude Delta^2_L(k_p=0.009s/km,z_p=3.0)=0.452_{-0.057-0.116}^{+0.069+0.141} and slope n_eff=-2.321_{-0.047-0.102}^{+0.055+0.131} (possible systematic errors are included through nuisance parameters in the fit - a factor >~5 smaller errors would be obtained on both parameters if we ignored modeling uncertainties). The errors are correlated and not perfectly Gaussian, so we provide a chi^2 table to accurately describe the results. The result corresponds to sigma_8=0.85, n=0.94, for a LCDM model with Omega_m=0.3, Omega_b=0.04, and h=0.7, but is most useful in a combined fit with the CMB. The inferred curvature of the linear power spectrum and the evolution of its amplitude and slope with redshift are consistent with expectations for LCDM models, with the evolution of the slope, in particular, being tightly constrained. We use this information to constrain systematic contamination, e.g., fluctuations in the UV background. This paper should serve as a starting point for more work to refine the analysis, including technical improvements such as increasing the size and number of the hydrodynamic simulations, and improvements in the treatment of the various forms of feedback from galaxies and quasars.

Figures (20)

• Figure 1: $P_F(k,z)$ prediction from our basic hydrodynamic simulation (FULL). The lines show, from bottom to top, $a=0.32$, 0.24, and 0.20, with $\bar{F}=0.85$, 0.67, and 0.4.
• Figure 2: Resolution test for the hydrodynamic simulation, showing the ratio of $P_F(k,z)$ in a (5,128) run to $P_F(k,z)$ in a (5,256) run. The (red/dashed, black/solid, green/dotted) lines show $a=$(0.32, 0.24, 0.20), with $\bar{F}=$(0.85, 0.67, 0.4). Thin and thick lines, respectively, show before and after the redshift of reionization adjustment. The vertical cyan (dotted) lines mark the upper limits on $k$ used for SDSS and HIRES $P_F(k,z)$ measurements, while the horizontal dotted line guides the eye to 1. We use these same cyan/dotted lines in many figures (and occasionally another at $k=0.0013\, {\rm s\, km}^{-1}$, which marks the lower limit on $k$ used in our fits).
• Figure 3: Comparison of hydro simulations including different physics. (a) shows the ratio of $P_F(k,z)$ in the NOSN (no energy feedback from supernovae) simulation to the FULL simulation. (b) shows $P_{\rm NOMETAL} / P_{\rm FULL}$ (NOMETAL means no metal cooling). The thick lines show the power after we correct for differences in the bulk temperature-density relations in the simulations, while the thin lines show the uncorrected power. The (red/dashed, black/solid, green/dotted) lines show $a=$(0.32, 0.24, 0.20), with $\bar{F}=$(0.85, 0.67, 0.4). The horizontal dotted line guides the eye to 1, while the vertical dotted lines mark the $k$ to which we use SDSS and HIRES data [$k<0.02~\, {\rm s\, km}^{-1}$ and $k<0.05~\, {\rm s\, km}^{-1}$, respectively].
• Figure 4: Convergence of $P_F(k,z)$ with decreasing time step size for the (10,256) HPM simulations that we compare to hydro simulations. Note that, of the simulations of this size, only the ones with the smallest timestep (most total steps) are used in our analysis. The denominator is the result for 876 times steps down to $z=1.5$, while solid, dotted, dashed, and long-dashed lines show, respectively, 429, 205, 89, and 42 steps. Red, black, and green indicate $P_F(k,z)$ at, respectively, $a=0.32$, 0.24, and 0.20, with $\bar{F}=0.85$, 0.67, and 0.4 (these run from bottom to top in each case when looking at $k=0.05\, {\rm s\, km}^{-1}$).
• Figure 5: Comparison of the hydrodynamic results to the HPM results, for the same initial conditions and temperature-density relation. (a), (b), and (c) show, respectively, the comparison for the FULL, NOSN, and NOMETAL hydro simulations. The (red/dashed, black/solid, green/dotted) lines show $a=$(0.32, 0.24, 0.20), with $\bar{F}=$(0.85, 0.67, 0.4).