FOSSIL: I. The Spin Rate Limit of Jupiter Trojans

Rotation periods of 53 small (diameters $2<D<40$ km) Jupiter Trojans (JTs) were derived using the high-cadence light curves obtained by the FOSSIL phase I survey, a Subaru/Hyper Suprime-Cam intensive program. These are the first reported periods measured for JTs with $D<10$ km. We found a lower limit of the rotation period near 4 hr, instead of the previously published result of 5 hr (Ryan et al. 2017; Szabo et al. 2017, 2020) found for larger JTs. Assuming a rubble-pile structure for JTs, a bulk density of 0.9 gcm${}^{-3}$ is required to withstand this spin rate limit, consistent with the value $0.8-1.0$ gcm${}^{-3}$ (Marchis et al. 2006; Mueller et al. 2010; Buie et al. 2015; Berthier et al. 2020) derived from the binary JT system, (617) Patroclus-Menoetius system.