Determining the Reliability of Measured Rotation Periods for Small Solar System Bodies

Chan-Kao Chang^1*, Ying-Tung Chen¹, Shiang-Yu Wang¹, Matthew J. Lehner¹

¹Institute of Astronomy and Astrophysics, Academia Sinica, Taipei, Taiwan

* Presenter:Chan-Kao Chang, email:rckchang@asiaa.sinica.edu.tw

We present a new algorithm, called the ``two-χ² test'', which mimics manual review to select reliable measured rotation periods for small solar system bodies (SSSBs) obtained from wide-field high-cadence observations. This algorithm was developed based on the 100,000 synthetic lightcurves, which were generated according to the observational conditions and data properties of the FOSSIL I survey, a program aiming at SSSB lightcurve collection using Subaru/Hyper Suprime-Cam. We found that the successful and unsuccessful recoveries of the input rotation periods of the synthetic lightcurves can be distinguished well using the two parameters extracted from periodogram (i.e., the two-χ² test), which are the reduced χ² of the best-fit period normalized to the background level of the periodogram (χ²_best) and a tracer indicating the significance of the best-fit spin rate in the periodogram being detected (χ²_32%). On the 2D histogram of the two-χ² test, the successful and the unsuccessful recoveries of the input rotation periods are distributed in different regions. While the successful recoveries mainly occupy in a region of low χ²_best with low χ²_32%, the unsuccessful recoveries mostly populate in a region of moderate to high χ²_best with moderate χ²_32%. Using the 2D histogram of the two-χ² test, a true-positive rate map was also created, which indicates the possibility of being true positives for measured rotation periods and translates it to the conventional quality code of manual review, U, defined by Warner et al. (2009). Therefore, the two-χ² test provides a good way to substitute the formidably time-consuming process of manual review and shows a feasible way to conduct observational bias correction for measured rotation periods obtained from wide-field high-cadence observations.

Keywords: Asteroid, Rotation Period