The Excited Spin State of 1I/2017 U1 `Oumuamua

We show that `Oumuamua's excited spin could be in a high energy LAM state, which implies that its shape could be far from the highly elongated shape found in previous studies. CLEAN and ANOVA algorithms are used to analyze `Oumuamua's lightcurve using 818 observations over 29.3~days. Two fundamental periodicities are found at frequencies (2.77\(\pm\)0.11) and (6.42\(\pm\)0.18)~cycles/day, corresponding to (8.67\(\pm\)0.34)~h and (3.74\(\pm\)0.11)~h, respectively. The phased data show that the lightcurve does not repeat in a simple manner, but approximately shows a double minimum at 2.77~cycles/day and a single minimum at 6.42~cycles/day. This is characteristic of an excited spin state. `Oumuamua could be spinning in either the long (LAM) or short (SAM) axis mode. For both, the long axis precesses around the total angular momentum vector with an average period of (8.67\(\pm\)0.34)~h. For the three LAMs we have found, the possible rotation periods around the long axis are 6.58, 13.15, or 54.48~h, with 54.48~h being the most likely. `Oumuamua may also be nutating with respective periods of half of these values. We have also found two possible SAM states where `Oumuamua oscillates around the long axis with possible periods at 13.15 and 54.48~h, the latter as the most likely. In this case any nutation will occur with the same periods. Determination of the spin state, the amplitude of the nutation, the direction of the TAMV, and the average total spin period may be possible with a direct model fit to the lightcurve. We find that `Oumuamua is "cigar-shaped"', if close to its lowest rotational energy, and an extremely oblate spheroid if close to its highest energy state for its total angular momentum.