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

We measure the linear power spectrum of mass density fluctuations at redshiftz=2.5 from the \lya forest absorption in a sample of 19 QSO spectra, using themethod introduced by Croft et al. (1998). The P(k) measurement covers the range2\pi/k ~ 450-2350 km/s (2-12 comoving \hmpc for \Omega=1). We examine a numberof possible sources of systematic error and find none that are significant onthese scales. In particular, we show that spatial variations in the UVbackground caused by the discreteness of the source population should havenegligible effect on our P(k) measurement. We obtain consistent results fromthe high and low redshift halves of the data set and from an entirelyindependent sample of nine QSO spectra with mean redshift z=2.1. A power lawfit to our measured P(k) yields a logarithmic slope n=-2.25 +/- 0.18 and anamplitude \Delta^2(k_p) = 0.57^{+0.26}_{-0.18}, where $\Delta^2$ is thecontribution to the density variance from a unit interval of lnk and k_p=0.008(km/s)^{-1}. Direct comparison of our mass P(k) to the measured clustering ofLyman Break Galaxies shows that they are a highly biased population, with abias factor b~2-5. The slope of the linear P(k), never previously measured onthese scales, is close to that predicted by models based on inflation and ColdDark Matter (CDM). The P(k) amplitude is consistent with some scale-invariant,COBE-normalized CDM models (e.g., an open model with \Omega_0=0.4) andinconsistent with others (e.g., \Omega=1). Even with limited dynamic range andsubstantial statistical uncertainty, a measurement of P(k) that has no unknown``bias factors'' offers many opportunities for testing theories of structureformation and constraining cosmological parameters. (Shortened)Comment: Submitted to ApJ, 27 emulateapj pages w/ 19 postscript fig