Linear map-making with LuSEE-Night

TL;DR

The paper investigates the feasibility of reconstructing low-frequency radio sky maps from LuSEE-Night data using a Wiener-filter linear map-making approach. By modeling the data as d = A m + n with a Gaussian prior on the sky and incorporating realistic beam patterns from HFSS and a radiometer-noise covariance, it demonstrates that ~5° angular resolution maps are achievable across 5–50 MHz, with fidelity strongest on large angular scales (ℓ ≲ 20–35). The authors examine systematics by including gain fluctuations and beam-model uncertainties in the noise covariance, showing robustness for plausible residuals (∼1–10%). Extending the observation duration and employing turntable rotations significantly improves intermediate-scale (ℓ ≳ 10) SNR, though the ultimate resolution is set by beam properties and short-baseline geometry. They outline future directions toward multi-frequency, polarization, point-source handling, and non-linear forward-modeling to further enhance sky-recovery accuracy.

Abstract

LuSEE-Night is a pathfinder radio telescope on the lunar far side employing four 3-m monopole antennas arranged as two horizontal cross pseudo-dipoles on a rotational stage and sensitive to the radio sky in the 1-50 MHz frequency band. LuSEE-Night measures the corresponding 16 correlation products as a function of frequency. While each antenna combination measures radiation coming from a large area of the sky, their aggregate information as a function of phase in the lunar cycle and rotational stage position can be deconvolved into a low-resolution map of the sky. We study this deconvolution using linear map-making based on the Wiener filter algorithm. We illustrate how systematic effects can be effectively marginalised over as contributions to the noise covariance and demonstrate this technique on beam knowledge uncertainty and gain fluctuations. With reasonable assumptions about instrument performance, we show that LuSEE-Night should be able to map the sub-50 MHz sky at a ~5-degree resolution.

Figures (9)

• Figure 1: Rendering of the LuSEE-Night instrument on top of the Blue Ghost Mission 2 Lander. Four monopole stacer antennas can be observed on the top. Rendering courtesy of Firefly Aerospace.
• Figure 2: Simulated beam patterns derived from HFSS simulations at 5, 15, 25, 35, and 45 MHz (columns left to right). Top row: Auto-correlation power pattern $B_{11}(\theta, \phi)$ for LuSEE-Night antenna 1 (nominally North). Middle row: Magnitude of the cross-correlation beam pattern $|B_{13}(\theta, \phi)|$ for the opposite antenna pair (1-3). Bottom row: Magnitude of the cross-correlation beam pattern $|B_{12}(\theta, \phi)|$ for the perpendicular antenna pair (1-2). Projection: Orthographic, zenith-centered ($\theta=0^\circ$), showing the hemisphere above the lunar surface. Orientation: North (antenna 1 axis projection) is up. Scale: All beam patterns are normalized to their peak intensity at each frequency to show relative structure (0 to 1, arbitrary units). Note the broad spatial response and its significant broadening towards lower frequencies. Beyond 25 MHz the antenna resonance causes the beam to bifurcate.
• Figure 3: Segment of the simulated visibility data vector $\mathbf{d}$ for the 25-MHz channel from the fiducial simulation (one lunar cycle, fixed turntable). The $x$-axis represents a flattened index where visibility data is grouped by antenna pair; each group forms a segment showing the pair's visibility evolution over all sampled time steps. Four large sections of the data vector with large positive values correspond to the auto-correlation products.
• Figure 4: Sky map reconstruction results. Top row: Input ULSA maps smoothed to $\ell_{\rm max}=47$. Middle row: Wiener filter reconstructed maps $\hat{\mathbf{m}}$ from simulated fiducial data (1 lunar cycle). Bottom row: difference $\hat{\mathbf{m}} - \mathbf{m}$, normalized by the mean temperature of the smoothed truth map. Maps are shown in Mollweide projection in Galactic coordinates. The unobserved region within $\sim$24 degrees of the North Celestial Pole, reconstructed purely from the prior, is delimited by a black dashed line in the reconstructed and difference maps. Prominent dark features correspond to regions of free-free absorption. Residuals (bottom row) are typically at the few-percent level, with larger errors visible near bright features due to limited resolution. Color scales (units assumed K) are consistent within each frequency column. Frequencies are 5, 15, 25, 35, and 45 MHz (left to right). The reconstructed maps may include negative values; these are artifacts from the Wiener filter's regularization in noise-dominated regions.
• Figure 5: Cross-correlation coefficient $\rho_\ell$ (Eq. \ref{['eq:rho_ell']}) between the Wiener filter reconstructed map and the smoothed ground truth map, as a function of spherical harmonic multipole $\ell$. Results are shown for frequencies from 5 to 50 MHz. The reconstruction used $\ell_{\rm max}=47$.