Cosmological and astrophysical parameters from the SDSS flux power spectrum and hydrodynamical simulations of the Lyman-alpha forest

TL;DR

The paper analyzes the SDSS Lyman-$\alpha$ flux power spectrum using large, high-resolution hydrodynamical simulations (GADGET-2) to constrain cosmological parameters and the IGM thermal history. By anchoring a best-guess model and applying a first-order Taylor expansion around it, the authors sample a multi-parameter space efficiently and fit to the data with corrections for instrumental and astrophysical systematics. They find that $\sigma_8$, $\Omega_{ m m}$, and the primordial spectral index $n$ are constrained by the SDSS data, while the IGM temperature evolution remains poorly determined unless priors are imposed, yielding $\Omega_{ m m}=0.28\pm0.03$, $n=0.95\pm0.04$, and $\sigma_8=0.91\pm0.07$ under priors, with $\tau_{ m eff}(z)$ following a power-law consistent with previous measurements. The work highlights the importance of controlling systematics (optical depth, data corrections, and IGM physics) for robust Lyman-$\alpha$ constraints and sets the stage for improved inferences with better data and modeling.

Abstract

(abridged) The flux power spectrum of the Lyman-alpha forest in quasar (QSO) absorption spectra is sensitive to a wide range of cosmological and astrophysical parameters and instrumental effects. Modelling the flux power spectrum in this large parameter space to an accuracy comparable to the statistical uncertainty of large samples of QSO spectra is very challenging. We use here a coarse grid of hydrodynamical simulations run with GADGET-2 to obtain a ``best guess'' model around which we calculate a finer grid of flux power spectra using a Taylor expansion of the flux power spectrum to first order. We find that the SDSS flux power spectrum alone is able to constrain a wide range of parameters including the amplitude of the matter power spectrum sigma_8, the matter density Omega_m, the spectral index of primordial density fluctuations n, the effective optical depth tau_eff and its evolution. The thermal history of the Intergalactic Medium (IGM) is, however, poorly constrained and the SDSS data favour either an unplausibly large temperature or an unplausibly steep temperature-density relation. By enforcing a thermal history of the IGM consistent with that inferred from high-resolution QSO spectra, we find the following values for the best fitting model (assuming a flat Universe with a cosmological constant and zero neutrino mass): Omega_ m=0.28 \pm 0.03, n=0.95\pm0.04, σ_8=0.91\pm0.07 (1σerror bars).We argue that the major uncertainties in this measurement are still systematic rather than statistical.

Figures (7)

• Figure 1: The dashed, solid and dotted curves show the effect of the error in the noise correction and resolution and the correction for strong absorption systems, respectively. We show fractional differences in the flux power spectrum at $z=3$. Note that we assume only the error of the noise correction to depend on redshift. The changes correspond to an error of 5% in the noise correction and of (7 km/s)$^2$ in the resolution (see section \ref{['datacorr']} for more details).
• Figure 2: Left (bottom panel): Evolution of $T_0$ with redshift for different thermal histories: B2, the fiducial equilibrium model with reionization at $z \sim 6$ (continuous curve); B2$_{\rm lr}$, simulation with a non- equilibrium solver with late reionization at $z\sim 4$ (dotted curve); B2$_{\rm hr}$, non-equilibrium, with early reionization at $z\sim 17$ (dot-dashed curve); B2$_{\rm ne}$, non-equilibrium with reionization at $z\sim 6$ (dashed curve); B2$_{\rm cold}$, equilibrium with reionization at $z\sim 6$ and with a colder equation of state (triple dotted-dashed curve). Left (top panel): Evolution of $\gamma$ with redshift. Right: Fractional differences between the flux power spectrum of the different model compared to the fiducial model B2 at $z=2.2,3,3.8$ (diamonds, triangles and squares, respectively). For B2$_{\rm cold}$ differences are only shown for $z=3$, the other two redshifts are very similar. The shaded region indicates the statistical errors at $z=3$.
• Figure 3: Top: Fractional differences in the flux power spectrum for variations of $\sigma_8$ value (dashed curve), the spectral index $n$ (continuous curve) and the effective optical depth $\tau_{\rm eff}$ (dotted curve) at $z=2.2,3,3.8$ (left, center and right panel, respectively). Middle: Fractional differences in the flux power spectrum for variations of $\Omega_{\rm m}$ value (continuous curve), the Hubble parameter $H_0$ (dashed curve). Bottom: Fractional differences in the flux power spectrum for variations of $\gamma$ (continuous curve) and $T_0$ (dashed curve).
• Figure 4: 1D marginalized likelihoods for our 22 parameters. Dashed curves represents the case without priors, while the continuous curves are obtained with the priors discussed in section \ref{['priors']}. Cosmological and astrophysical parameters were inferred with a Taylor expansion of the flux power spectrum of the best-guess model to first order.
• Figure 5: 2D likelihoods for some of the parameters used in our analysis. Filled (coloured), continuous and white dashed contours refer to the mean likelihood for the case with priors, the marginalized likelihood for the case with priors and the marginalized likelihood for the case without priors, respectively. Cosmological and astrophysical parameters were inferred with a Taylor expansion of the flux power spectrum of the best-guess model to first order.