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Origin of asteroid (469219) Kamo`oalewa: the main asteroid belt or the Giordano Bruno crater on the Moon?

Asteroid Kamo`oalewa is the target of the Tianwen-2 sample-return mission by CNSA. Because of its orbit and its spectral properties, it was proposed that Kamo`oalewa originated from the Moon as impact ejecta, possibly from the Giordano Bruno crater. We aim at estimating the relative contribution of Kamo`oalewa-like objects originating from the general near-Earth asteroid (NEA) population which originated in the main asteroid belt, and compare it with the relative contribution of Giordano Bruno ejecta. We first estimate the average fraction of quasi-satellite orbits at any given time. By using recently developed NEA population models, we extract the expected number of Earth co-orbitals of the same size of Kamo`oalewa, and then get an estimate of the average number of Kamo`oalewa-like objects using the fraction computed before. Similarly, we obtain an estimate for the number of Kamo`oalewa-like objects that may originate as ejecta from the Giordano Bruno impact. We also performed survey simulations to estimate their efficiency in the detection of Kamo`oalewa-like objects. We found that the main belt accounts for 1.23 \pm 0.13 Kamo`oalewa-like objects on average. The expected number of Kamo`oalewa-like objects originated as Giordano Bruno ejecta is 0.042, which is more than order of magnitude smaller. We found a discovery efficiency of Earth quasi-satellites between 95% and 70% for absolute magnitude between 22 and 25 for the Pan-STARRS survey, and population models show that this is in agreement with the known population. The Vera Rubin Observatory should reach an efficiency of 92% down to absolute magnitude 25. These estimates show that population models of NEAs are capable to account for Kamo`oalewa-like objects, thus supporting the hypothesis that that Kamo'oalewa originated from the main belt. This will be further investigated by the in-situ exploration of the Tianwen-2 mission.