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

Asteroid Kamooalewa is the target of the Tianwen-2 sample-return mission by CNSA. Because of its orbit and its spectral properties, it was proposed that Kamooalewa originated from the Moon as impact ejecta, possibly from the Giordano Bruno crater. We aim at estimating the relative contribution of Kamooalewa-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 Kamooalewa, and then get an estimate of the average number of Kamooalewa-like objects using the fraction computed before. Similarly, we obtain an estimate for the number of Kamooalewa-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 Kamooalewa-like objects. We found that the main belt accounts for 1.23 \pm 0.13 Kamooalewa-like objects on average. The expected number of Kamooalewa-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 Kamooalewa-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.