Meng Zhou

Ground-based radio observations below 30 MHz are severely limited by ionospheric interference and radio-frequency interference from Earth. A lunar-orbiting radio interferometer mission, the Discovering the Sky at the Longest wavelengths (DSL, also known by its Chinese name “Hongmeng”), has been proposed to overcome these obstacles. However, for such a mission, there are new challenges, such as the nearly all-sky field of view and dynamic 3D baselines, which require a huge computational cost for interferometric image reconstruction. In this work, we present augmented Lagrangian multiplier imaging using gradient descent optimization (AMIGO), a novel imaging algorithm tailored to lunar-orbiting arrays like DSL, combining the minibatch gradient descent (MBGD) method with the augmented Lagrangian multiplier (ALM) technique. MBGD reduces the computational complexity and memory cost, enabling efficient handling of large datasets. ALM flexibly incorporates physical priors like nonnegative sky temperature and prior angular power spectrum into the imaging algorithm, with adjustable stopping criteria to quantitatively control prior strength. We validate AMIGO using mock visibility data generated under realistic DSL orbit configurations. Reconstructed sky maps at various frequencies and spatial resolutions show that this approach provides a computationally feasible framework for all-sky imaging with a lunar-orbiting array.

A lunar orbit interferometer array suffers from a number of systematics. Beyond systematics induced by the imaging algorithm itself and thermal noise considered in F. Deng et al., phase errors due to instrumental inconsistency between receivers, geometric error in baseline determination, and clock synchronization error between satellites will also affect synthesis imaging with the space array. In this paper, we model different sources of phase errors and quantify their impacts on all-sky and patchy-sky map-making, respectively, for the ultra-long wavelength sky ( f ≲ 30 MHz), using the Discovering the Sky at the Longest wavelength mission (also known as the Hongmeng mission) as an example. We find that in the scheme of all-sky imaging, the angular power spectrum can be suppressed uniformly for various sources of phase errors. To ensure a reconstruction of large-scale structures with ≳95% of the angular power spectrum, the phase error should be controlled below ∼12° on the random instrumental component, or below ∼12° for constant deviation, or below 1.1 ns on the temporal component. With multiple baseline measurements, the baseline determination errors below 1 m can also meet the requirement. In the scheme of patchy-sky imaging, the signal-to-noise ratio of point-source detections does not change significantly, except with instrumental phase errors or at high frequencies. The impact of geometric phase error is relatively stronger in the patchy-sky imaging with higher resolution because longer baselines are used and fewer times of baseline measurements can be averaged over within an integration time. When scaled with wavelength, these results set the basic reference for instrumental requirements for future space interferometers.

The 21 cm line and the patchy kinetic Sunyaev–Zel’dovich (kSZ) effect are promising and complementary probes of the Epoch of Reionization. A challenge for cross correlating these two signals is that foreground avoidance or removal algorithms applied to the 21 cm data inevitably sacrifice Fourier modes with long wavelengths along the line of sight (i.e., low-k _∥ modes), yet only these same modes contribute to the kSZ signal. Here we show that a suitable kSZ² × 21 cm² cross-correlation statistic nevertheless remains nonvanishing, even after filtering out the corrupted low-k _∥Fourier modes from the 21 cm data. We simulate the kSZ² × 21 cm² cross-correlation signal across reionization-era redshifts and find distinctive redshift evolution. This signal peaks early in the reionization history, when the volume-averaged fraction is around 0.1 ≲ x _HII ≲ 0.2, after which it changes sign and reaches a minimum near reionization’s midpoint (x _HII ∼ 0.5), while the signal gradually vanishes as reionization completes. These trends appear generic across three simulated models which differ in their reionization histories. We forecast the detectability of the kSZ² × 21 cm² cross-power spectrum for the HERA and SKA1-Low 21 cm experiments in combination with current and next-generation cosmic microwave background (CMB) surveys including the Simons Observatory, CMB-S4, and CMB-HD. We find that a high-significance detection (signal-to-noise ratio ≳ 5σ) is possible with SKA1-Low and CMB-S4.

The initial density distribution provides a basis for understanding the complete evolution of cosmological density fluctuations. While reconstruction in our local Universe exploits the observations of galaxy surveys with large volumes, observations of high-redshift galaxies are performed with a small field of view and therefore can hardly be used for reconstruction. Here, we propose reconstructing the initial density field using the H i 21 cm and CO line intensity maps from the epoch of reionization. Observations of these two intensity maps provide complementary information on the density field—the H i 21 cm field is a proxy of matter distributions in the neutral regions, while the CO line intensity maps are sensitive to the high-density, star-forming regions that host the sources for reionization. Technically, we employ the conjugate gradient method and develop the machinery for minimizing the cost function for the intensity mapping observations. Analytical expressions for the gradient of cost function are derived explicitly. We show that the resimulated intensity maps match the input maps of mock observations using semi-numerical simulations of reionization with an rms error ≲7% at all stages of reionization. This reconstruction is also robust with an rms error of ∼10% when an optimistic level of shot noise is applied to the CO map or white noise at the level of ≲10% of the standard deviation is applied to each map. Our proof-of-concept work demonstrates the robustness of the reconstruction method, thereby providing an effective technique for reconstructing the cosmological initial density distribution from high-redshift observations.

Intensity mapping of the H i 21 cm line and the CO 2.61 mm line from the epoch of reionization has emerged as powerful, complementary, probes of the high-redshift universe. However, both maps and their cross-correlation are dominated by foregrounds. We propose a new analysis by which the signal is unbiased by foregrounds, i.e., it can be measured without foreground mitigation. We construct the antisymmetric part of two-point cross-correlation between intensity maps of the H i 21 cm line and the CO 2.61 mm line, arising because the statistical fluctuations of two fields have different evolution in time. We show that the sign of this new signal can distinguish model independently whether inside-out reionization happens during some interval of time. More importantly, within the framework of the excursion-set model of reionization, we demonstrate that the slope of the dipole of H i–CO cross-power spectrum at large scales is linear to the rate of change of global neutral fraction of hydrogen in a manner independent of reionization parameters, until the slope levels out near the end of reionization, but this trend might possibly depend on the framework of reionization modeling. The H i–CO dipole may be a smoking-gun probe for the speed of reionization, or “standard speedometer” for cosmic reionization. Observations of this new signal will unveil the global reionization history from the midpoint to near the completion of reionization.