Synthesis imaging with a lunar orbit array: II. Impacts of instrument-induced phase errors

Abstract

A lunar orbit interferometer array suffers from a number of systematics. Beyond systematics induced by the imaging algorithm itself and thermal noise considered in Paper I, 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 ($f\lesssim30$ MHz), using the Discovering the Sky at the Longest wavelength (DSL) 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 $\gtrsim 95\%$ of the angular power spectrum, the phase error should be controlled below $\sim 12^\circ$ on the random instrumental component, or below $\sim 12^\circ$ 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 S/N 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.

Figures (10)

• Figure 1: Illustration of the "Single" model of baseline measurement errors. The left star represents the mother satellite, while the middle and right stars represent the daughter satellite $i$ and $j$, respectively. The black arrows represent the position vectors from the mother satellite to the daughter satellites, while the red arrows represent the baseline vectors between the daughter satellite $i$ and $j$. The solid arrows represent the vectors without errors, while the dashed ones represent the vectors with errors. The random errors of position vectors are distributed inside the blue spheres.
• Figure 2: Illustrative examples with random phase errors. We plot the reconstructed images without phase errors (Left), with direction-independent random phase errors (Middle), and with direction-dependent random phase errors (Right). The x- and y-axes show relative pixel coordinate, and the color bar indicates relative brightness value. These are representative illustrative examples, and no absolute physical units are assigned.
• Figure 3: The correlation coefficient $r_\ell$ between the reconstructed maps with and without phase errors as a function of $\ell$ for various instrumental phase errors. We model the error as constant deviations of $\Delta\phi_0=12^\circ$ (blue), $25^\circ$ (orange), and $50^\circ$ (green) in the right panel, while Gaussian random values of $\Delta\phi_0=12^\circ$ (blue), $25^\circ$ (orange), and $50^\circ$ (green) in the left panel, respectively.
• Figure 4: The ratio $C_\ell^{error} /C_\ell^{0}$ as a function of $\ell$ for various instrumental phase errors. We model the error as constant deviations of $\Delta\phi_0=12^\circ$ (blue), $25^\circ$ (orange), and $50^\circ$ (green) in the right panel, while Gaussian random values of $\Delta\phi_0=12^\circ$ (blue), $25^\circ$ (orange), and $50^\circ$ (green) in the left panel, respectively. The solid lines are the simulated results, while the colored dashed lines are the theoretical estimations.
• Figure 5: The ratio $C_\ell^{error} /C_\ell^{0}$ as a function of $\ell$ for geometric phase errors. We vary the error models of $\Delta r_0=1$ m (blue for "Real" model and orange for "Single" model), $3$ m (green), and $5$ m (red) at 30 MHz in the left panel, while vary the frequency of $f=3$ MHz (blue), $10$ MHz (orange), and $30$ MHz (green) with the fixed "Real" error model of 1 m in the right. The solid lines are the simulated results, while the colored dashed lines are the theoretical estimations.