New limits on 21 cm epoch of reionization from paper-32 consistent with an x-ray heated intergalactic medium at z = 7.7

We present new constraints on the 21 cm Epoch of Reionization (EoR) power spectrum derived from three months of observing with a 32 antenna, dual-polarization deployment of the Donald C. Backer Precision Array for Probing the Epoch of Reionization in South Africa. In this paper, we demonstrate the efficacy of the delay-spectrum approach to avoiding foregrounds, achieving over eight orders of magnitude of foreground suppression (in mK²). Combining this approach with a procedure for removing off-diagonal covariances arising from instrumental systematics, we achieve a best 2σ upper limit of (41 mK)² for k = 0.27 h Mpc^-1 at z = 7.7. This limit falls within an order of magnitude of the brighter predictions of the expected 21 cm EoR signal level. Using the upper limits set by these measurements, we generate new constraints on the brightness temperature of 21 cm 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 H I has been warmed from its cold primordial state, probably by X-rays from high-mass X-ray binaries or miniquasars. 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.