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.

Observations of the redshifted 21-cm hyperfine line of neutral hydrogen from early phases of the Universe such as Cosmic Dawn and the Epoch of Reionization promise to open a new window onto the early formation of stars and galaxies. We present the first upper limits on the power spectrum of redshifted 21-cm brightness temperature fluctuations in the redshift range z = 19.8 − 25.2 (54 − 68 MHz frequency range) using 14 hours of data obtained with the LOFAR-Low Band Antenna (LBA) array. We also demonstrate the application of a multiple pointing calibration technique to calibrate the LOFAR-LBA dual-pointing observations centred on the North Celestial Pole and the radio galaxy 3C220.3. We observe an unexplained excess of ∼ 30 − 50% in Stokes I noise compared to Stokes V for the two observed fields, which decorrelates on 12 seconds and might have a physical origin. We show that enforcing smoothness of gain errors along frequency direction during calibration reduces the additional variance in Stokes I compared Stokes V introduced by the calibration on sub-band level. After subtraction of smooth foregrounds, we achieve a 2σ upper limit on the 21-cm power spectrum of ∆ 2 21 < (14561 mK) 2 at k ∼ 0.038 h cMpc −1 and ∆ 2 21 < (14886 mK) 2 at k ∼ 0.038 h cMpc −1 for the 3C220 and NCP fields respectively and both upper limits are consistent with each other. The upper limits for the two fields are still dominated by systematics on most k modes.

We derive constraints on the thermal and ionization states of the intergalactic medium (IGM) at redshift ≈ 9.1 using new upper limits on the 21-cm power spectrum measured by the LO-FAR radio-telescope and a prior on the ionized fraction at that redshift estimated from recent cosmic microwave background (CMB) observations. We have used results from the reionization simulation code GRIZZLY and a Bayesian inference framework to constrain the parameters which describe the physical state of the IGM. We find that, if the gas heating remains negligible, an IGM with ionized fraction 0.13 and a distribution of the ionized regions with a characteristic size 8 h −1 comoving megaparsec (Mpc) and a full width at the half maximum (FWHM) 16 h −1 Mpc is ruled out. For an IGM with a uniform spin temperature T S 3 K, no constraints on the ionized component can be computed. If the large-scale fluctuations of the signal are driven by spin temperature fluctuations, an IGM with a volume fraction 0.34 of heated regions with a temperature larger than CMB, average gas temperature 7-160 K and a distribution of the heated regions with characteristic size 3.5-70 h −1 Mpc and FWHM of 110 h −1 Mpc is ruled out. These constraints are within the 95 per cent credible intervals. With more stringent future upper limits from LOFAR at multiple redshifts, the constraints will become tighter and will exclude an increasingly large region of the parameter space.