A new upper limit on the 21-cm signal power spectrum at a redshift of z ≈ 9.1 is presented, based on 141 hours of data obtained with the Low-Frequency Array (LOFAR). The analysis includes significant improvements in spectrally-smooth gain-calibration, Gaussian Process Regression (GPR) foreground mitigation and optimally-weighted power spectrum inference. Previously seen 'excess power' due to spectral structure in the gain solutions has markedly reduced but some excess power still remains with a spectral correlation distinct from thermal noise. This excess has a spectral coherence scale of 0.25 − 0.45 MHz and is partially correlated between nights, especially in the foreground wedge region. The correlation is stronger between nights covering similar local sidereal times. A best 2-σ upper limit of ∆ 2 21 < (73) 2 mK 2 at k = 0.075 h cMpc −1 is found, an improvement by a factor ≈ 8 in power compared to the previously reported upper limit. The remaining excess power could be due to residual foreground emission from sources or diffuse emission far away from the phase centre, polarization leakage, chromatic calibration errors, ionosphere, or low-level radio-frequency interference. We discuss future improvements to the signal processing chain that can further reduce or even eliminate these causes of excess power.

The 21 cm brightness temperature δT b fluctuations from reionization promise to provide information on the physical processes during that epoch. We present a formalism for generating the δT b distribution using dark matter simulations and an one-dimensional radiative transfer code. Our analysis is able to account for the spin temperature T S fluctuations arising from inhomogeneous X-ray heating and Lyα coupling during cosmic dawn. The δT b power spectrum amplitude at large scales (k ∼ 0.1 Mpc −1 ) is maximum when ∼ 10% of the gas (by volume) is heated above the cosmic microwave background temperature. The power spectrum shows a "bump"-like feature during cosmic dawn and its location measures the typical sizes of heated regions. We find that the effect of peculiar velocities on the power spectrum is negligible at large scales for most part of the reionization history. During early stages (when the volume averaged ionization fraction 0.2) this is because the signal is dominated by fluctuations in T S . For reionization models that are solely driven by stars within high mass ( 10 9 M ⊙ ) haloes, the peculiar velocity effects are prominent only at smaller scales (k 0.4 Mpc −1 ) where patchiness in the neutral hydrogen density dominates the signal. The conclusions are unaffected by changes in the amplitude or steepness in the X-ray spectra of the sources.