The Power Spectrum of Mass Fluctuations Measured from the Lyα Forest at Redshift z = 2.5

Abstract

We measure the linear power spectrum of mass-density Ñuctuations at redshift z \ 2.5 from the Lya forest absorption in a sample of 19 QSO spectra, using the method introduced by Croft et al. The P(k) measurement covers the range 2n/k D 450È2350 km s~1 (2È12 comoving h~1 Mpc for) \ 1), limited on the upper end by uncertainty in Ðtting the unabsorbed QSO continuum and on the lower end by Ðnite spectral resolution (0.8È2.3 FWHM) and by nonlinear dynamical e †ects. We examine a number A Ž of possible sources of systematic error and Ðnd none that are signiÐcant on these scales. In particular, we show that spatial variations in the UV background caused by the discreteness of the source population should have negligible e †ect on our P(k) measurement. We estimate statistical errors by dividing the data set into ten subsamples. The statistical uncertainty in the rms mass-Ñuctuation amplitude, p P [P(k)]1@2, is D20%, and is dominated by the Ðnite number of spectra in the sample. We obtain consistent P(k) measurements (with larger statistical uncertainties) from the high-and low-redshift halves of the data set, and from an entirely independent sample of nine QSO spectra with mean redshift z \ 2.1. A power-law Ðt to our results yields a logarithmic slope n \ [2.25 ^ 0.18 and an amplitude where * o 2(k p) \ 0.57 ~0.18`0 18`0.26, is the contribution to the density variance from a unit interval of ln k and s~1)~1. * o 2 k p \ 0.008(km Direct comparison of our mass P(k) to the measured clustering of Lyman break galaxies shows that they are a highly biased population, with a bias factor b D 2È5. The slope of the linear P(k), never previously measured on these scales, is close to that predicted by models based on inÑation and cold dark matter (CDM). The P(k) amplitude is consistent with some scale-invariant, COBE-normalized CDM models (e.g., an open model with and inconsistent with others (e.g.,) \ 1). Even with limited dynamic) 0 \ 0.4) range and substantial statistical uncertainty, a measurement of P(k) that has no unknown "" bias factors ÏÏ o †ers many opportunities for testing theories of structure formation and constraining cosmological parameters.