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We report measurements of the cosmic microwave background (CMB) powerspectrum from the complete 2008 South Pole Telescope (SPT) data set. We analyzetwice as much data as the first SPT power spectrum analysis, using an improvedcosmological parameter estimator which fits multi-frequency models to the SPT150 and $220\,$GHz bandpowers. We find an excellent fit to the measuredbandpowers with a model that includes lensed primary CMB anisotropy, secondarythermal (tSZ) and kinetic (kSZ) Sunyaev-Zel'dovich anisotropies, unclusteredsynchrotron point sources, and clustered dusty point sources. In addition tomeasuring the power spectrum of dusty galaxies at high signal-to-noise, thedata primarily constrain a linear combination of the kSZ and tSZ anisotropycontributions at $150\,$GHz and $\ell=3000$: $D^{tSZ}_{3000} +0.5\,D^{kSZ}_{3000} = 4.5\pm 1.0 \,\mu{\rm K}^2$. The 95% confidence upperlimits on secondary anisotropy power are $D^{tSZ}_{3000} < 5.3\,\mu{\rm K}^2$and $D^{kSZ}_{3000} < 6.5\,\mu{\rm K}^2$. We also consider the potentialcorrelation of dusty and tSZ sources, and find it incapable of relaxing the tSZupper limit. These results increase the significance of the lower than expectedtSZ amplitude previously determined from SPT power spectrum measurements. Wefind that models including non-thermal pressure support in groups and clusterspredict tSZ power in better agreement with the SPT data. Combining the tSZpower measurement with primary CMB data halves the statistical uncertainty on$\sigma_8$. However, the preferred value of $\sigma_8$ varies significantlybetween tSZ models. Improved constraints on cosmological parameters from tSZpower spectrum measurements require continued progress in the modeling of thetSZ power.

Improved constraints on cosmic microwave background secondary anisotropies from the complete 2008 South Pole Telescope data