The Power Spectrum of Mass Fluctuations Measured from the Lyman-alpha Forest at Redshift Z=2.5

We measure the linear power spectrum of mass density fluctuations at redshift z = 2.5 from the Lyα forest absorption in a sample of 19 QSO spectra, using the method introduced by Croft et al. (1998). The P (k) measurement covers the range 2π/k ∼ 450 − 2350 km s (2 − 12 comoving hMpc for Ω = 1), limited on the upper end by uncertainty in fitting the unabsorbed QSO continuum and on the lower end by finite spectral resolution (0.8− 2.3Å FWHM) and by non-linear dynamical effects. We examine a number of possible sources of systematic error and find none that are significant 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 effect on our P (k) measurement. We estimate statistical errors by dividing the data set into ten subsamples. The statistical uncertainty in the rms mass fluctuation