Spin state evolution of asteroid (367943) Duende during its 2013 earth flyby

On February 15, 2013 asteroid (367943) Duende, provisionally named 2012 DA14, experienced an extremely close earth encounter, passing within 27,700 km altitude. An observation campaign was made possible by one year's notice of the flyby. This campaign, discussed in detail in the companion paper by Moskovitz et al. (2019), yielded visible-wavelength photometry before and after closest approach. Post-flyby Goldstone Doppler-delay radar data were also obtained. These data indicated a roughly 40 m x 20 m object in non-principal axis rotation. Leveraging light curve frequency analysis from the Moskovitz et al. companion paper, dynamical and inertia constraints from the rough radar-derived elongations, and simulated photometry, only two post-flyby states were deemed viable. These were a long axis mode (LAM) with long axis convention periods P-(phi) over bar = 6.36 h and P-psi = 8.73 h and a short axis mode (SAM) with P-(phi) over bar = 8.71 h and P-psi = 23.7 h (each with nominal long-intermediate and long-short ellipsoid axis ratios of 1.7:1 and 2.3:1 respectively). The SAM solution was more consistent with the post-flyby photometry and radar data. Nevertheless, there were differences between the amplitude and phase of the post-flyby and best-fit simulated SAM light curves at some epochs. These discrepancies may be due to a non-ellipsoidal shape, non-uniform albedo, and/or incorrect spin state solution (attitude, inertias, tumbling periods, or rotation mode). Analysis of the sparse pre-flyby photometry by Moskovitz et al. yielded poor Fourier series solutions for all principal axis states and different peaks in the pre and post-flyby WindowCLEAN power spectra. This suggests the asteroid was tumbling before the encounter and that its spin state changed. Propagating the best-fitting LAM and SAM solutions backwards through the flyby with terrestrial tidal torques resulted in significant dispersion of the rotation states. The pre-flyby SAM states coincided with the notable Moskovitz et al. Fourier solution P-1 = 8.37 h and P-2 = 24.2 h. Overall, we propose Duende was tumbling before the 2013 flyby and that its spin state may have changed during the flyby. Furthermore, our analysis suggests Duende is currently in SAM with P-(phi) over bar = 8.71 h and P-psi= 23.7 h with pole J2000 ecliptic longitude and obliquity of roughly 70 degrees and 95 degrees or 245 degrees and 90 degrees respectively. The spin state characterization approach outlined in this paper could be used for future analyses with inertia, dynamical, and observational constraints.