Lunar Orbit Measurement of Cosmic Dawn 21 cm Global Spectrum

A redshifted 21 cm line absorption signature is commonly expected from the cosmic dawn era, when the first stars and galaxies formed. The detailed traits of this signal can provide important insight on the cosmic history. However, high precision measurement of this signal is hampered by the ionosphere refraction and absorption, as well as radio frequency interference (RFI). A space observation can solve the problem of the ionosphere, and the Moon can shield the RFI from the Earth. In this paper, we present simulations of the global spectrum measurement in the 30 -- 120 MHz frequency band on the lunar orbit, from the proposed Discovering the Sky at the Longest wavelength (DSL) project. In particular, we consider how the measured signal varies as the satellite moves along the orbit, take into account the blockage of different parts of the sky by the Moon and the antenna response. We estimate the sensitivity for such a 21 cm global spectrum experiment. An RMS noise level of $\le 0.05$ K is expected at 75 MHz after 10 orbits ($\sim$ 1 day) observation, for a frequency channel width of 0.4 MHz. We also study the influence of a frequency-dependent beam, which may generate complex spectral structures in the spectrum. Estimates of the uncertainties in the foreground and 21 cm model parameters are obtained.