Improved Constraints on the 21 cm EoR Power Spectrum and the X-Ray Heating of the IGM with HERA Phase I Observations

We report the most sensitive upper limits to date on the 21 cm epoch of reionization power spectrum using 94 nights of observing with Phase I of the Hydrogen Epoch of Reionization Array (HERA). Using similar analysis techniques as in previously reported limits (HERA Collaboration 2022a), we find at 95 confidence that Δ^2(k = 0.34 h Mpc^-1) ≤ 457 mK^2 at z = 7.9 and that Δ^2 (k = 0.36 h Mpc^-1) ≤ 3,496 mK^2 at z = 10.4, an improvement by a factor of 2.1 and 2.6 respectively. These limits are mostly consistent with thermal noise over a wide range of k after our data quality cuts, despite performing a relatively conservative analysis designed to minimize signal loss. Our results are validated with both statistical tests on the data and end-to-end pipeline simulations. We also report updated constraints on the astrophysics of reionization and the cosmic dawn. Using multiple independent modeling and inference techniques previously employed by HERA Collaboration (2022b), we find that the intergalactic medium must have been heated above the adiabatic cooling limit at least as early as z = 10.4, ruling out a broad set of so-called "cold reionization" scenarios. If this heating is due to high-mass X-ray binaries during the cosmic dawn, as is generally believed, our result's 99 relationship between soft X-ray luminosity and star formation and thus requires heating driven by evolved low-metallicity stars.