The tumbling rotational state of 1I/`Oumuamua

The discovery of 1I/2017 U1 ('Oumuamua) has provided the first glimpse of a planetesimal born in another planetary system. This interloper exhibits a variable colour within a range that is broadly consistent with local small bodies such as the P/D type asteroids, Jupiter Trojans, and dynamically excited Kuiper Belt Objects. 1I/'Oumuamua appears unusually elongated in shape, with an axial ratio exceeding 5:1. Rotation period estimates are inconsistent and varied, with reported values between 6.9 and 8.3 hours. Here we analyse all available optical photometry reported to date. No single rotation period can explain the exhibited brightness variations. Rather, 1I/'Oumuamua appears to be in an excited rotational state undergoing Non-Principal Axis (NPA) rotation, or tumbling. A satisfactory solution has apparent lightcurve frequencies of 0.135 and 0.126 hr-1 and implies a longest-to-shortest axis ratio of 5:1, though the available data are insufficient to uniquely constrain the true frequencies and shape. Assuming a body that responds to NPA rotation in a similar manner to Solar System asteroids and comets, the timescale to damp 1I/'Oumuamua's tumbling is at least a billion years. 1I/'Oumuamua was likely set tumbling within its parent planetary system, and will remain tumbling well after it has left ours.