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We present new constraints on the 21cm Epoch of Reionization (EoR) power spectrum derived from 3 months of observing with a 32-antenna, dual-polarization deployment of the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER) in South Africa. In this paper, we demonstrate the efficacy of the delay-spectrum approach to avoiding foregrounds, achieving over 8 orders of magnitude of foreground suppression (in $\textrm{mK}^2$). Combining this approach with a procedure for removing off-diagonal covariances arising from instrumental systematics, we achieve a best 2-sigma upper limit of $(41\,\textrm{mK})^2$ for $k=0.27 h\textrm{Mpc}^{-1}$ at $z=7.7$. This limit falls within an order of magnitude of the brighter predictions of the expected 21cm EoR signal level. Using the upper limits set by these measurements, we generate new constraints on the brightness temperature of 21cm emission in neutral regions for various reionization models. We show that for several ionization scenarios, our measurements are inconsistent with cold reionization. That is, heating of the neutral intergalactic medium (IGM) is necessary to remain consistent with the constraints we report. Hence, we have suggestive evidence that by $z=7.7$, the HI has been warmed from its cold primordial state, probably by X-rays from high-mass X-ray binaries or mini-quasars. The strength of this evidence depends on the ionization state of the IGM, which we are not yet able to constrain. This result is consistent with standard predictions for how reionization might have proceeded., Comment: 24 pages, 11 figures, 3 appendices. Replaced with version accepted to ApJ

We present new observations with the Precision Array for Probing the Epoch of Reionization (PAPER) with the aim of measuring the properties of foreground emission for 21cm Epoch of Reionization experiments at 150 MHz. We focus on the footprint of the foregrounds in cosmological Fourier space to understand which modes of the 21cm power spectrum will most likely be compromised by foreground emission. These observations confirm predictions that foregrounds can be isolated to a "wedge"-like region of 2D (k-perpendicular, k-parallel)-space, creating a window for cosmological studies at higher k-parallel values. We also find that the emission extends past the nominal edge of this wedge due to spectral structure in the foregrounds, with this feature most prominent on the shortest baselines. Finally, we filter the data to retain only this "unsmooth" emission and image specific k-parallel modes of it. The resultant images show an excess of power at the lowest modes, but no emission can be clearly localized to any one region of the sky. This image is highly suggestive that the most problematic foregrounds for 21cm EoR studies will not be easily identifiable bright sources, but rather an aggregate of fainter emission., Comment: 6 pages, 5 figures, updated to match version accepted to ApJL