Towards a Precise Measurement of Matter Clustering: Lyman-alpha Forest Data at Redshifts 2-4

TL;DR

This work uses high- and moderate-resolution Lyα forest spectra to extract flux statistics and infer the linear matter power spectrum $P(k)$ at $z\sim2.7$ via a refined FGPA-based approach that allows a scale-dependent bias $b(k)$. Calibrated against large-volume N-body simulations constrained by the observed mean opacity $\overline{\tau}_{\rm eff}$, the study obtains $\Delta^2(k_p)=0.74^{+0.20}_{-0.16}$ and a slope $\nu=-2.43\pm0.06$ at $k_p=0.03\,({\rm km\,s^{-1}})^{-1}$, with $\Gamma'\approx1.3\times10^{-3}\,({\rm km\,s^{-1}})^{-1}$. The results show evolution consistent with gravitational instability and favor a CDM-like shape parameter around $\Gamma\sim0.16$, consistent with large-scale structure measurements, COBE-normalized CMB constraints, and cluster normalization, while the amplitude suggests moderate fiducial cosmologies with $\Omega_m\sim0.3-0.4$. The Lyα forest thus provides a unique, redshifted window into the linear matter power spectrum over scales and epochs not accessible by other probes, reinforcing the inflationary CDM paradigm and offering a path to tighten constraints with larger surveys and improved IGM parameter measurements.

Abstract

We measure the filling factor, correlation function, and power spectrum of transmitted flux in a large sample of Lya forest spectra, comprised of 30 Keck HIRES spectra and 23 Keck LRIS spectra. We infer the linear matter power spectrum P(k) from the flux power spectrum P_F(k), using an improved version of the method of Croft et al. (1998) that accounts for the influence of z-space distortions, non- linearity, and thermal broadening on P_F(k). The evolution of the shape and amplitude of P(k) over the range z= 2-4 is consistent with gravitational instability, implying that non-gravitational fluctuations do not make a large contribution. Our fiducial measurement of P(k) comes from data with <z> = 2.72. It has amplitude Delta^2(k_p)=0.74^0.20_-0.16 at wavenumber k_p=0.03 (km/s)^-1 and is well described by a power-law of index -2.43 +/- 0.06 or by a CDM-like power spectrum with shape parameter Gamma'=1.3^+0.7_-0.5*10^-3 (km/s) at z=2.72. For Omega_m=0.4, Omega_Lam=0.6, the best-fit Gamma =0.16 (h^-1mpc)^-1, in good agreement with the 2dF Galaxy Redshift Survey, and the best-fit sigma_8=0.82 (Gamma/0.15)^-0.44. Matching the observed cluster mass function and our Delta^2(k_p) in spatially flat models requires Omega_m=0.38^+0.10_-0.08 + 2.2 (Gamma-0.15). Matching Delta^2(k_p) in COBE-normalized, flat CDM models with no tensor fluctuations requires Omega_m = (0.29 +/-0.04) n^-2.89 h_65^-1.9. The Lya forest complements other probes of P(k) by constraining a regime of redshift and lengthscale not accessible by other means, and the consistency of these inferred parameters with independent estimates provides further support for inflation, cold dark matter, and vacuum energy (abridged).

Figures (23)

• Figure 1: Histograms of the data. The horizontal bar above the histograms shows the length of a Ly$\alpha$ forest spectrum with a midpoint at $z=2.7$. Shading marks the boundaries of the different redshift subsamples (see Table \ref{['subtab']}).
• Figure 2: Determination of $\delta_F(\lambda)$, for the quasar Q1017+1055. ( a) LRIS spectrum (wiggly line), the continuum fitted over 100Å regions (upper smooth curve), and the spectrum smoothed with a 50Å Gaussian (lower smooth curve). ( b) Fluctuations $\delta_F(\lambda)$ derived using the continuum fitted spectrum and the smoothed spectrum. The continuum fitted curve is slightly higher where the two are distinguishable. ( c) Fluctuations $\delta_F(\lambda)$ from the HIRES spectrum of Q1077+1055. ( d) A zoom of the central 150Å showing the two variations of the LRIS spectrum, the HIRES spectrum, and (grey curve) the HIRES spectrum smoothed to the resolution of the LRIS data.
• Figure 3: (a) The filling factor FF of regions below a flux threshold of 0.5, computed as a function of redshift from the HIRES data. Error bars ($1\sigma$) are calculated using a jackknife estimator. (b) Confidence intervals (68%, 95%, 99.7%) on parameters $c_1$ and $c_2$, determined by fitting the functional form FF$=c_{1}\exp{(c_{2}z)}$ to the data points in (a). Best fit values (cross) are $c_{1}=0.0291$, $c_{2}=0.719$. In (a), the shaded bands show the region corresponding to the 68% confidence interval on $(c_1,c_2)$.
• Figure 4: The flux correlation function of the various data subsamples. The solid line in each case is the fiducial combined sample, with the length scaled so that the comoving lengths stay the same in an EdS model. The multiplicative factor used is $[(1+z_{i})/(1+z_{F})]^{1/2}$, where $z_{i}$, $z_{F}$ are the mean redshifts of subsample $i$ and the fiducial sample respectively. Filled circles represent the HIRES data and open circles the LRIS data. Error bars have been omitted from the latter, for clarity.
• Figure 5: Dependence of the flux power spectra $\Delta^{2}_{\rm F}(k)$ on spectral resolution and continuum fitting method. ( a) We use the four quasar spectra common to the LRIS and HIRES samples and show the power spectrum derived from the HIRES observations (circles) and the LRIS observations with 50Å Gaussian smoothing for determination of the mean level (triangles). Open circles correspond to negative values of $\Delta^{2}_{\rm F}(k)$. Lower panel shows the difference from the mean of the two power spectra in units of the mean. Error bars represent $1\sigma$ jackknife errors derived from the four spectra. ( b) Comparison of LRIS results using two methods of continuum fitting, smoothing with a 50Å Gaussian (triangles) and fitting over a 100Å region with a 3rd order polynomial (circles). Here we use all 23 LRIS spectra in the LRIS sample, and the error bars represent jackknife errors derived by partitioning those 23 spectra into 50 subsets of equal length (see §3.3.2).