The power spectrum of mass fluctuations measured from the Ly alpha forest at redshift z=2.5

We measure the linear power spectrum of mass-density fluctuations at redshi ft z = 2.5 from the Ly alpha forest absorption in a sample of 19 QSO spectr a, using the method introduced by Croft et al. The P(k) measurement covers the range 2 pi/k similar to 450-2350 km s(-1) (2-12 comoving h(-1) Mpc for Omega = 1), limited on the upper end by uncertainty in fitting the unabsorb ed QSO continuum and on the lower end by finite spectral resolution (0.8-2. 3 Angstrom FWHM) and by nonlinear 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 bac kground caused by the discreteness of the source population should have neg ligible effect on our P(k) measurement. We estimate statistical errors by d ividing the data set into ten subsamples. The statistical uncertainty in th e rms mass-fluctuation amplitude, a sigma proportional to [P(k)](1/2), is s imilar to 20%, and is dominated by the finite number of spectra in the samp le. We obtain consistent P(k) measurements (with larger statistical uncerta inties) 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 fit to our results yields a logarithmic slope n = -2.25 +/- 0 .18 and an amplitude Delta(rho)(2)(k(p)) = 0.57(-0.18)(+0.26), where Delta( rho)(2) is the contribution to the density variance from a unit interval of ln k and k(p) = 0.008(km s(-1))(-1). Direct comparison of our mass P(k) to the measured clustering of Lyman break galaxies shows that they are a high ly biased population, with a bias factor b similar to 2-5. The slope of the linear P(k), never previously measured on these scales, is close to that p redicted by models based on inflation and cold dark matter (CDM). The P(k) amplitude is consistent with some scale-invariant, COBE-normalized CDM mode ls (e.g., an open model with Omega(0) = 0.4) and inconsistent with others ( e.g., Omega = 1). Even with limited dynamic range and substantial statistic al uncertainty, a measurement of P(k) that has no unknown "bias factors" of fers many opportunities for testing theories of structure formation and con straining cosmological parameters.