Impact of Calibration and Position Errors on Astrophysical Parameters of the HI 21cm Signal

TL;DR

This work tackles the challenge of extracting HI $21\mathrm{cm}$ EoR/CD astrophysical parameters from the power spectrum in the presence of foregrounds and instrument systematics. It combines an end-to-end 21cm E2E pipeline with an artificial neural network emulator and Bayesian inference to directly map observed PS, including telescope layout effects, to $\{R_{\mathrm{mfp}}, T_{\mathrm{vir}}, \zeta\}$ for SKA-Low. Under ideal conditions, $T_{\mathrm{vir}}$ and $\zeta$ are well constrained, while $R_{\mathrm{mfp}}$ remains degenerate; with realistic impairments, the study identifies stringent tolerances: $0.001\%$ gain calibration errors and $0.048\arcsec$ sky-model position accuracy are needed to avoid bias. The results demonstrate the viability of emulator-based inference for fast, layout-aware parameter estimation and highlight the critical role of precise calibration and sky modeling for robust cosmological inferences with SKA-Low.

Abstract

The Epoch of Reionization (EoR) and Cosmic Dawn (CD) are pivotal stages during the first billion years of the universe, exerting a significant influence on the development of cosmic structure. The detection of the redshifted 21-cm signal from these epochs is challenging due to the dominance of significantly stronger astrophysical foregrounds and the presence of systematics. This work used the 21cm E2E (end to end) pipeline, followed by simulation methodology described \cite{2022Mazumder} to conduct synthetic observations of a simulated sky model that includes both the redshifted 21-cm signal and foregrounds. A framework was constructed using Artificial Neural Networks (ANN) and Bayesian techniques to directly deduce astrophysical parameters from the measured power spectrum. This approach eliminates the need for explicit telescope layout effects correction in interferometric arrays such as SKA-Low. The present work investigates the impact of gain calibration errors and sky model position errors on the recovery of the redshifted 21-cm power spectrum for the SKA-Low AA$^{\ast}$ array configuration. We assessed the effects of these inaccuracies on the deduced astrophysical parameters and established acceptable tolerance levels. Based on our results, the gain calibration error tolerance for ideal signal detection is 0.001 \%. However, if the sky model position errors exceed 0.048 arcseconds, the remaining foregrounds would obscure the target signal.

Figures (7)

• Figure 1: Telescope configuration utilized in the simulation: SKA-Low AA* (with a 2 km central core).
• Figure 2: Shows a comparison between the theoretical spherical power spectrum (PS) and the simulated observed PS for the same sky model. The theoretical PS for the signal models is represented by a black dashed line, while the simulated observed PS for the SKA-Low array configurations is shown as solid blue lines.
• Figure 3: The figure shows a comparison between the simulated true power spectrum (solid lines) and the emulated power spectrum by the ANN (dots). The left panel shows emulator predictions trained on theoretical power spectra, while the right panel presents predictions based on observed power spectra from SKA-Low.
• Figure 4: Depicts the posterior distribution of model parameters obtained through power spectrum analysis, comparing the theoretical power spectrum with the observed power spectrum from SKA-Low. The enclosed areas between the inner and outer contours signify the 1$\sigma$ and 2$\sigma$ confidence levels, respectively.
• Figure 5: (Left) Residual power spectra for gain calibration errors (0.001%, 0.01%, and 0.1%) compared to the signal power for SKA-Low array layouts. Error bars represent 1$\sigma$ uncertainties, including sample variance and thermal noise. (Right) Posterior distributions of model parameters from the power spectrum analysis (blue), with gain calibration errors of 0.001% (magenta) and 0.01% (orange) for SKA-Low.The shaded regions represent the 1$\sigma$ and 2$\sigma$ confidence intervals.