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

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.