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, we find at 95% confidence that Δ²(k = 0.34 h Mpc⁻¹) ≤ 457 mK² at z = 7.9 and that Δ²(k = 0.36 h Mpc⁻¹) ≤ 3496 mK² 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, 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% credible interval excludes the local relationship between soft X-ray luminosity and star formation and thus requires heating driven by evolved low-metallicity stars.

The H i 21 cm absorption line is masked by bright foregrounds and systematic distortions that arise due to the chromaticity of the antenna used to make the observation coupling to the spectral inhomogeneity of these foregrounds. We demonstrate that these distortions are sufficient to conceal the 21 cm signal when the antenna is not perfectly achromatic and that simple corrections assuming a constant spatial distribution of foreground power are insufficient to overcome them. We then propose a new physics-motivated method of modelling the foregrounds of 21 cm experiments in order to fit the chromatic distortions as part of the foregrounds. This is done by generating a simulated sky model across the observing band by dividing the sky into N regions and scaling a base map assuming a distinct uniform spectral index in each region. The resulting sky map can then be convolved with a model of the antenna beam to give a model of foregrounds and chromaticity parametrized by the spectral indices of the N regions. We demonstrate that fitting this model for varying N using a Bayesian nested sampling algorithm and comparing the results using the evidence allows the 21 cm signal to be reliably detected in data of a relatively smooth conical log spiral antenna. We also test a much more chromatic conical sinuous antenna and find this model will not produce a reliable signal detection, but in a manner that is easily distinguishable from a true detection.

Maximally Smooth Functions (MSFs) are a form of constrained functions in which there are no inflection points or zero crossings in high-order derivatives. Consequently, they have applications to signal recovery in experiments where signals of interest are expected to be non-smooth features masked by larger smooth signals or foregrounds. They can also act as a powerful tool for diagnosing the presence of systematics. The constrained nature of MSFs makes fitting these functions a non-trivial task. We introduce maxsmooth, an open-source package that uses quadratic programming to rapidly fit MSFs. We demonstrate the efficiency and reliability of maxsmooth by comparison to commonly used fitting routines and show that we can reduce the fitting time by approximately two orders of magnitude. We introduce and implement with maxsmooth Partially Smooth Functions, which are useful for describing elements of non-smooth structure in foregrounds. This work has been motivated by the problem of foreground modelling in 21-cm cosmology. We discuss applications of maxsmooth to 21-cm cosmology and highlight this with examples using data from the Experiment to Detect the Global Epoch of Reionization Signature (EDGES) and the Large-aperture Experiment to Detect the Dark Ages (LEDA) experiments. We demonstrate the presence of a sinusoidal systematic in the EDGES data with a log-evidence difference of 86.19 ± 0.12 when compared to a pure foreground fit. MSFs are applied to data from LEDA for the first time in this paper and we identify the presence of sinusoidal systematics. maxsmooth is pip installable and available for download at https://github.com/htjb/maxsmooth.