Reconstructing the Anisotropic Ultra-long Wavelength Spectra using a Single Antenna on Lunar-orbit

TL;DR

This work tackles reconstructing direction-dependent ultra-long wavelength spectra ($\nu \lesssim 30$ MHz) with a single antenna aboard a lunar-orbit satellite, exploiting lunar occultation and beam anisotropy to encode sky information. It introduces a region-based spectral model using a smoothly broken power law with turnover frequency $\nu_t$, and fits 60 parameters across 12 sky regions (via MCMC) using mock data generated from the ULSA sky model over 1–30 MHz. The analysis rigorously accounts for averaging, discretization, and model errors in a composite covariance, demonstrating successful recovery of $\nu_t$ and absorption features, with Galactic-plane regions showing stronger absorption ($\nu_t$ higher) than high-latitude regions. The findings establish the feasibility of anisotropic spectrum reconstruction with very limited instrumentation on a lunar orbit and offer a framework to constrain the Galactic free-electron distribution from ultra-long wavelength observations.

Abstract

The ultra-long wavelength sky ($ν\lesssim 30$ MHz) is still largely unexplored, as the electromagnetic wave is heavily absorbed and distorted by the ionosphere on Earth. The far-side of the Moon, either in lunar-orbit or on lunar-surface, is the ideal site for observations in this band, and the upcoming Moon-based interferometers will obtain multi-frequency high-resolution sky maps. Making use of the lunar occultation of the sky and the anisotropy of antenna primary beam response, we propose a novel method to reconstruct the ultra-long wavelength spectral shape in multiple directions in the sky using only one antenna on lunar orbit. We apply the method to one antenna on one of the nine daughter satellites of the proposed Discovering the Sky at Longest wavelength (DSL) project. Using simulated observation data between 1 - 30 MHz from one dipole antenna, we find that the spectra for different regions on the sky can be reconstructed very well and the free-free absorption feature in each region can be derived from the reconstructed spectra. This work demonstrates the feasibility to reconstruct the anisotropic ultra-long wavelength spectra with very limited instrumentation on a lunar-orbit, with mature technologies already in place. It extends the application of such kind of satellite in revealing the distribution of free electrons in the Galactic interstellar medium from the distribution of absorption features in the ultra-long wavelength sky.

Figures (10)

• Figure 1: The sky map with frequency of 5 MHz in the Galactic coordinate system.
• Figure 2: In one precession period, the antenna wire repeatedly points into same pixels on sky. This figure shows the number of pointing times for each sky pixel in lunar equatorial coordinate system. The sky is pixelized by HEALPix scheme with $N_{\rm side}=8$.
• Figure 3: Our mock data sample for 416 pixels on the sky in the lunar equatorial coordinate system. Note that this is not the sky temperature distribution, but the mean antenna temperature when antenna wire is pointing into the corresponding pixel.
• Figure 4: The position of 12 regions in the Galactic coordinate system. The sequence of each region is marked in the figure.
• Figure 5: The averaging errors described by Eq. (\ref{['eq:C_ii2']}) compared with thermal noise.