Mitigating gain calibration errors from EoR observations with SKA1-Low AA*

Abstract

The observation of the redshifted 21-cm signal from neutral hydrogen is a promising probe for understanding the phase transition of the early universe and its evolution during the Cosmic Dawn and the Epoch of Reionisation (EoR). One of the primary obstacles to the statistical detection of the target signal is the presence of residual foreground, which arises from gain calibration errors. Previous studies have shown that gain calibration errors as small as 0.01% can lead to a biased interpretation of the observed signal power spectrum estimation, by nearly an order of magnitude. A recent study further highlights that to retrieve astrophysical parameters accurately, the threshold gain calibration error should be lower than 0.01%. In this work, we develop a post-calibration mitigation strategy that combines foreground subtraction techniques with foreground avoidance to address residual contamination arising from gain calibration errors. We use an end-to-end pipeline 21cmE2E to simulate a realistic sky model and telescope configuration within the 138-146 MHz frequency range. To assess the impact of residual antenna-based gain calibration errors, we perform a detailed power spectrum analysis across several threshold levels. Our analysis shows that the extraction of the target signal over the wavenumber range $0.05 \leq k \leq 0.5$ Mpc$^{-1}$ is possible with a threshold gain calibration error of 1%, although with a significant SNR tradeoff on larger scales. Moreover, this work also offers a comparative assessment of foreground removal and avoidance techniques in the context of future SKA1-Low AA* observations.

Figures (11)

• Figure 1: Left : The SKA1-Low AA* stations layout for central 2000 m cutout. Right: UV coverage for the observational parameters in the table \ref{['tab:obs_params']}, with integration time of 4 hours ($\pm 2$ HA). The orange and blue colours represent the (U, V) and (-U,-V) points, respectively.
• Figure 2: Left: Simulated $3^\circ \times 3^\circ$ slice of the observed Hi signal. Right: Residual map after sky-model subtraction with 1% gain calibration error at 144.25 MHz.
• Figure 3: Proceeding clockwise from top-left, we show cylindrically averaged 2-D PS for the true Hi (perfect foreground subtraction), and the reconstructed PS of the residual data with 0.1%, 1%, and 10% gain calibration error. The minimum and maximum baselines were taken to be $\sim48 \lambda$ and $\sim948 \lambda$ and the black and white dotted lines represent the horizon limit and horizon plus 0.1 Mpc$^{-1}$ buffer, respectively.
• Figure 4: The 1D PS on logarithmically spaced, spherically averaged $k$-bins from 0.05 to 0.5 Mpc$^{-1}$. The markers represent 1-D power spectra for residual visibilities with various contamination percentages of gain calibration errors, as well as the true Hi. Vertical error bars indicate total uncertainty due to 2$\sigma$ sample variance and theoretical thermal noise; horizontal bars show bin widths.
• Figure 5: SNR plot for various cases, defined as the ratio of 1-D Hi power spectrum $\Delta^2_\text{HI}(k)$ to associated "noise" $\Delta^2_N(k)$. The noise is the per $k$-bin combined uncertainty due to thermal noise and sample variance, as indicated by vertical error bars in 1-D power spectra (Figure \ref{['fig_4:gain_err_1d_ps_comp']}). The brackets "hrzn" and "hrzn + 0.1" (dotted lines) indicate that foreground avoidance was applied about the horizon and horizon plus 0.1 Mpc$^{-1}$ buffer, respectively. Shaded regions represent total sensitivity ($\Delta^2_\text{th}(k) + \Delta^2_\text{sv}(k)$) for no avoidance (dark grey), avoidance about the horizon (medium grey), and the horizon plus buffer (light grey).