Robust Extraction of Global 21 cm Spectrum from Experiments with a Chromatic Beam Based on Physics-Motivated Error Modeling

TL;DR

This work addresses the challenge of extracting the sky-averaged $T_{21}( u)$ signal from a foreground-dominated, chromatic-beam environment in a lunar-orbit global 21 cm experiment. It introduces a physics-motivated foreground model combined with a simulation-based covariance to account for correlations in the residuals across time and frequency, together with a sky-division strategy into $N_r$ regions. The key finding is that correlated modeling yields unbiased extractions across multiple beam types and sky divisions, even for moderate beam chromaticity and weaker signals, while uncorrelated modeling leads to biased or fake-unbiased results due to sky non-uniformity and time-varying responses. This approach relaxes stringent antenna design requirements and offers a practical pathway for robust global 21 cm measurements in space or on the ground, contingent on realistic beam and Moon-reflection assumptions.

Abstract

The extraction of the sky-averaged 21 cm signal from Cosmic Dawn and the Epoch of Reionization faces significant challenges. The bright and anisotropic Galactic foreground, which is 4 - 5 orders of magnitude brighter than the 21 cm signal, when convolved with the inevitably chromatic beam, introduces additional spectral structures that can easily mimic the real 21 cm signal. In this paper, we investigate the signal extraction for a lunar-orbit experiment, where the antenna moves fast in orbit and data from multiple orbits have to be used. We propose a physics-motivated and correlated modeling of both the foreground and the measurement errors. By dividing the sky into multiple regions according to the spectral index distribution and accounting for the full covariance of modeling errors, we jointly fit both the foreground and the 21 cm signal using simulated data for the Discovering the Sky at the Longest wavelength lunar orbit experiment. This method successfully extracts the 21 cm signals of various amplitudes from the simulated data even for a testing antenna with a relatively high level of chromaticity. This approach, which is robust against moderate beam chromaticity, significantly relaxes the stringent design and manufacturing requirements for the antenna, offering a practical solution for future 21 cm global signal experiments either on the ground or in space.

Figures (12)

• Figure 1: The brightness temperature map of the input foreground sky at 100 MHz (above) and the spectral index map derived from GSM408 and GSM230 (bottom) in the ecliptic coordinate system.
• Figure 2: Diagrams of the ice-cream antenna (left panel) and the disc-cone antenna (right panel). The exact dimensions are subject to change during the detailed design phase.
• Figure 3: The cross sections of the simulated beam profiles of the dipole-like antenna (left panel), the ice-cream antenna (middle panel), and the chromatic disc-cone antenna (right panel), respectively, at three different frequencies as indicated in the legend.
• Figure 4: The spectral index map after the sky division. We divide the whole sky into 10 (upper), 15 (middle) and 20 regions (bottom), respectively.
• Figure 5: Two-dimensional histogram between logarithmic brightness temperature of GSM408 and spectral indices $\beta$. The red and orange lines represent $5\%$ and $95\%$ quantiles of spectral indices in each logarithmic bin, respectively.