First upper limits on the 21-cm signal power spectrum of neutral hydrogen at $z=9.16$ from the LOFAR 3C196 field

TL;DR

This paper establishes the first LOFAR-derived upper limits on the 21-cm power spectrum from the 3C196 field at $z\approx9.16$, using a dedicated 6-hour night and a revised processing pipeline. The authors build a wide-field sky model, apply DI and DD calibrations, and perform a residual foreground subtraction with a machine-learning enhanced Gaussian process regression (ML-GPR) that includes kernels for intrinsic and mode-mixing foregrounds as well as an excess component and a learned 21-cm kernel. They report a deepest 2$\sigma$ upper limit of $\Delta_{21}^2 < (146.61\ \mathrm{mK})^2$ at $k=0.078\ h\,\mathrm{cMpc}^{-1}$, with an excess power that differs in behavior from the NCP field, suggesting residual foreground origins. The study demonstrates that, with more nights and improved sky modelling, the 3C196 field can outperform the NCP in constraining the 21-cm signal on short timescales, and that combining the two fields incoherently could further tighten limits by $\sqrt{2}$. The work advances LOFAR's EoR program by addressing field-dependent systematics and validating the ML-GPR framework for robust foreground subtraction.

Abstract

The redshifted 21-cm signal of neutral hydrogen from the Epoch of Reionization (EoR) can potentially be detected using low-frequency radio instruments such as the Low-Frequency Array (LOFAR). So far, LOFAR upper limits on the 21-cm signal power spectrum have been published using a single target field: the North Celestial Pole (NCP). In this work, we analyse and provide upper limits for the 3C196 field, observed by LOFAR, with a strong ${\approx}80\,$Jy source in the centre. This field offers advantages such as higher sensitivity due to zenith-crossing observations and reduced geostationary radio-frequency interference, but also poses challenges due to the presence of the bright central source. After constructing a wide-field sky model, we process a single 6-hour night of 3C196 observations using direction-independent and direction-dependent calibration, followed by a residual foreground subtraction with a machine learned Gaussian process regression (ML-GPR). A bias correction is necessary to account for signal suppression in the GPR step. Still, even after this correction, the upper limits are a factor of two lower than previous single-night NCP results, with a lowest $2σ$ upper limit of $(146.61\,\text{mK})^2$ at $z = 9.16$ and $k=0.078\,h\,\text{cMpc}^{-1}$ (with $\text{d}k/k\approx 0.3$). The results also reveal an excess power, different in behaviour from that observed in the NCP field, suggesting a potential residual foreground origin. In future work, the use of multiple nights of 3C196 observations combined with improvements to sky modelling and ML-GPR to avoid the need for bias correction should provide tighter constraints per unit observing time than the NCP.

Figures (23)

• Figure 1: Baseline coverage in the $u\varv$-plane for the LOFAR-HBA observation of the 3C 196 field, before (left, zoomed out) and after (right, zoomed in) the flagging performed in the pre-processing step (see Section \ref{['sec:mod:baselines']} and Section \ref{['sec:proc:pre-proc']}). The antenna pairs are shown in different colours: core-to-core station baselines in light blue, core-to-remote (and remote-to-core) station baselines in medium blue, and remote-to-remote baselines in dark blue. In the right panel, the red circle marks the $5000\lambda$ limit that is usually applied during the DI calibration of the NCP field.
• Figure 2: Rendered model of the 3C 196 high-resolution model at 150 MHz (top) and the flux density over the 120--168 MHz range (bottom). The flux estimated by scaife_heald:2012 is plotted with the dashed blue line, with the $1\sigma$ uncertainties as the blue shaded area. The flux of the 3C 196 model used in this work is shown with the red line. We also show the peak brightness of the source at each frequency of the $z$-bin, extracted from the dirty images after the DI-calibration of the EoR pipeline (Section \ref{['sec:proc:di-cal']}), with the black line.
• Figure 3: The left panel shows the frequency-integrated (120--168 MHz) restored image of the 3C 196 field, where 3C 196 has been subtracted and the full primary beam correction applied. The image noise is $\sigma = 0.8\,\text{mJy/beam}$. The model image resulting from the imaging process is shown in the right panel, where the sources of the 47 clusters are highlighted by different colours. Both images have a pixel resolution of 3 arcsec and a field of view of $10^\circ\times10^\circ$. The 1, 7.5, and 50 per cent levels of the primary beam intensity are shown with the red contours. The 7.5 per cent level roughly corresponds to the $3.9^\circ$ radius that we used to select the sky model components. The brightest 3C and 4C sources are also indicated by black circles, in addition to J080135.35+500943.9 (shortened to J0801) and J080508+480151 (shortened to J0805) that have approximately 11 and 2 Jy of total flux, respectively.
• Figure 4: The 21-cm signal processing pipeline for the LOFAR 3C 196 field, from the pre-processing and DI calibration to the final power spectrum estimation.
• Figure 5: Frequency-integrated (134--147 MHz) dirty images of the 3C 196 field after the DI calibration with only 3C 196 subtracted (top row) and after the DD subtraction (bottom row). The left column shows the all sky images with a pixel scale of 5 arcmin, where a Gaussian taper with $\text{FWHM}=10\,\text{arcmin}$ and a Briggs weighting with robust parameter $-2$ have been applied to the $u\varv$-coverage to better highlight the bright sources. The same colour range has been used in the top and bottom panels to show the level of source sidelobe suppression after the DD subtraction step. The 1, 5, and 50 per cent levels of the time and frequency averaged primary beam are plotted with the dotted contours. The brightest sources are indicated with white circles, including the A-team sources. The right column reports the zoom-in of the 3C 196 central field, imaged with natural weighting and a pixel scale of 0.5 arcmin, covering a $10^\circ \times 10^\circ$ field of view. Only the baselines between 50 and 500$\lambda$ have been selected. Also here, the same colour range is used in the top and bottom panels. The dashed black circle highlight the $3.9^\circ$ radius extension of our sky model.