Precision requirements for interferometric gridding in 21-cm power spectrum analysis

Abstract

We analyse the accuracy of radio interferometric gridding of visibilities with the aim to quantify the Epoch of Reionization (EoR) 21-cm power spectrum bias caused by gridding, ultimately to determine the suitability of different imaging algorithms and gridding settings for 21-cm power spectrum analysis. We simulate realistic LOFAR data, and construct power spectra with convolutional gridding and w-stacking, w-projection, image domain gridding and without w-correction. These are compared against directly Fourier transformed data. The influence of oversampling, kernel size, w-quantization, kernel windowing function and image padding are quantified. The gridding excess power is measured with a foreground subtraction strategy, for which foregrounds have been subtracted using Gaussian progress regression, as well as with a foreground avoidance strategy. Constructing a power spectrum that has a bias significantly lower compared to the expected EoR signals is possible with the tested methods, but requires a kernel oversampling factor > 4000 and, when using w-correction, > 500 w-quantization levels. These values are higher than typical values used for imaging, but are computationally feasible. The kernel size and padding factor parameters are less crucial. Among the tested methods, image domain gridding shows the highest accuracy with the lowest imaging time. LOFAR 21-cm power spectrum results are not affected by gridding. Image domain gridding is overall the most suitable algorithm for 21-cm EoR experiments, including for future SKA EoR analyses. Nevertheless, convolutional gridding with tuned parameters results in sufficient accuracy. This holds also for w-stacking for wide-field imaging. The w-projection algorithm is less suitable because of the kernel oversampling requirements, and a faceting approach is unsuitable due to the resulting spatial discontinuities.

arXiv commentAccepted for publication in A&A ; abstract abridged

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• First upper limits on the 21 cm signal power spectrum from cosmic dawn from one night of observations with NenuFAR
• The AARTFAAC Cosmic Explorer: observations of the 21-cm power spectrum in the EDGES absorption trough
• A numerical study of 21-cm signal suppression and noise increase in direction-dependent calibration of LOFAR data
• Deeper multi-redshift upper limits on the Epoch of Reionization 21-cm signal power spectrum from LOFAR between z=8.3 and z=10.1
• Validation of the HERA Phase I Epoch of Reionization 21 cm Power Spectrum Software Pipeline
• Assessing the impact of two independent direction-dependent calibration algorithms on the LOFAR 21-cm signal power spectrum
• Statistical analysis of the causes of excess variance in the 21 cm signal power spectra obtained with the Low-Frequency Array
• Observing the Reionization : Effect of Calibration and Position Errors on Realistic Observation Conditions
• Beyond the horizon: Quantifying the full sky foreground wedge in the cylindrical power spectrum
• The Role of the Instrumental Response in 21 cm EoR Power Spectrum Gridding Analyses
• Measurement of the Anisotropy Power Spectrum of the Radio Synchrotron Background
• Improved upper limits on the 21-cm signal power spectrum at $z=17.0$ and $z=20.3$ from an optimal field observed with NenuFAR
• Spectral modelling of Cygnus A between 110 and 250 MHz. Impact on the LOFAR 21-cm signal power spectrum
• Ionospheric contributions to the excess power in high-redshift 21-cm power-spectrum observations with LOFAR
• First upper limits on the 21-cm signal power spectrum of neutral hydrogen at $z=9.16$ from the LOFAR 3C196 field
• Robust direction-dependent gain-calibration of beam-modelling errors far from the target field
• Exploring One-point Statistics in HERA Phase I Data: Effects of Foregrounds and Systematics on Measuring One-Point Statistics
• Mitigating incoherent excess variance in high-redshift 21 cm observations with multi-output cross-Gaussian process regression