Synthesis imaging with a lunar orbit array: I. global sky map and its systematics

TL;DR

This work tackles global all-sky imaging below 30 MHz with a lunar-orbit DSL array by casting sky reconstruction as a linear inverse problem and applying Tikhonov regularization. It identifies sub-pixel noise aliasing in the beam construction as a major systematic and demonstrates that a pixel-averaging approach mitigates this aliasing, enabling reliable maps for baselines up to $b<2b_p$ where $b_p\sim\lambda/\theta_p$. A high-resolution mock sky with small-scale power is used to test the pipeline, with reconstruction quality assessed via scale-dependent metrics $\rho_l$ and ${\rm SNR}_l$, across 3, 10, and 30 MHz. The results show good global and patchwise reconstructions under sensible regularization, though polar regions lack short-baseline constraints and low-frequency performance benefits from more baselines, guiding future improvements including calibration and lunar-reflection effects.

Abstract

Ground-based radio astronomical observation at frequencies below 30 MHz is hampered by the Ionosphere and radio frequency interference (RFI). The Discovering Sky at the Longest wavelength (DSL) mission, also known as the Hongmeng mission, employs a linear array of satellites on a circular orbit around the Moon to make interferometric observations in this band. Though vastly different from the usual ground-based arrays, the interferometric visibility data collected by such an array is linearly related to the sky map, and the reconstruction is in principle an inversion problem of linear mapping. In this paper, we investigate a number of issues in the algorithm of global map reconstruction, focusing on the impact of sub-pixel noise induced by the finite pixelization of the sky, and errors due to regularization. We find that in the reconstruction process, if one builds up the beam matrix, which relates the sky pixels to the visibilities, by naively evaluating its elements at each of the pixel centers, then the sub-pixel noise can give rise to a significant aliasing effect. However, this effect can be effectively mitigated by a simple pixel-averaging method. Based on evaluation of the image quality using the correlation coefficient between the input and reconstructed map, and the signal-to-noise ratio, we discuss the selection strategy of the regularization parameter, and show that the sky can be well reconstructed with a reasonable choice of the regularization parameter.

Figures (19)

• Figure 1: The input sky model. (a) A patch of the sky of the diffuse component at 10 MHz, shown in the ecliptic coordinates ($\lambda_{ec}, \beta_{ec}$). The location of this patch is marked by the lowest red rectangle in Figure \ref{['fig:full_sky_map']}. (b) Cumulative flux distribution of the point sources as a function of the flux $S$ in units of Jy
• Figure 2: The full-sky map with both diffuse component and point sources in ecliptic coordinates at 10 MHz. The map is smoothed by a Gaussian filter with Full-Width-Half-Maximum (FWHM)$\approx 1.3^\circ$ to match the resolution of our reconstructed map. The red boxes mark small regions where we take detailed study.
• Figure 3: The geometric factor $q_0$ as a function of the compression ratio $\mathcal{R}$ for the satellites configuration. The blue, orange, and green lines correspond to the compression ratio between satellites 1 and 2 of $\mathcal{R}_2 =$3, 6, and 9, respectively.
• Figure 4: The integration time spent per unit baseline length as a function of baseline length $b$ for different compression ratios $\mathcal{R}_2$ and $\mathcal{R}$ of the 'breathing' of the satellite array, after one cycle of precession (1.3 years).
• Figure 5: The 3D distribution of the integration time volume density of baselines of the DSL array, generated after one cycle of precession(1.3 years), for the $\mathcal{R}_2=6$, $\mathcal{R}=3$ case.