Rotation periods of asteroids from Kepler/K2's unintended observations
Authors: Sergeyev Alexey , Carry Benoît , Eggl Siegfried , Santerne Alexandre , Berthier Jerome 
Published: July 2024

IntroductionThe determination of asteroid spin periods is crucial for understanding the physical properties and evolutionary history of these celestial bodies. The Kepler Space Telescope, initially designed for exoplanet detection, provided valuable data on asteroid rotation periods during its K2 extension in the ecliptic see Fig. 1. This research summarizes the methods and findings from the Kepler/K2 observations of main-belt asteroids. It highlights the extraction and analysis of lightcurves, discusses the challenges encountered, and presents the results obtained. Additionally, the analysis includes the correlation between rotation periods and asteroid taxonomy, as well as a comparison with previously estimated rotation periods.
Fig. 1: Location and coverage of the Kepler/K2 observing fields in the sky. The ecliptic plane is shown as a solid line.
Asteroid spin periods offer significant insights into their internal structures, shapes, densities, and surface properties. This information is vital for understanding the formation and evolution of the solar system since asteroids are considered remnants of early planetary building blocks. Determining the rotation periods of asteroids also allows for the identification and study of binary systems, enhancing our knowledge of asteroid interactions and dynamics (Margot et al. 2015).Most asteroids exhibit rotation periods exceeding two hours, primarily due to the "spin barrier" phenomenon, which refers to the upper limit of the rotation speed at which asteroids can remain intact without disintegrating due to centrifugal forces (Holsapple 2007). Consequently, long-term observations are required to accurately determine these periods.Kepler&#8217;s DataKepler&#8217;s data are available in two cadences: long cadence (30-minute intervals) and short cadence (one-minute intervals). The data are stored in Target Pixel Files (TPF), which include two-dimensional arrays for pixel values and one-dimensional arrays for time stamps and cadence numbers. The time stamps are recorded in Barycentric Julian Date (BJD) format. Each TPF also contains metadata about the target star and specifics of the observation.Observation LimitsThe magnitude limit of Kepler&#8217;s observations restricts the accuracy of faint asteroid light curves. The Kepler dataset includes over one million asteroid events brighter than the observational depth magnitude limit of 20 mags. However, the presence of bright stars in the TPF&#8217;s field of view necessitates focusing on asteroids brighter than 18 magnitudes for reliable light curve extraction (Berthier et al. 2016).The limited field of view of approximately one square arcminute and the typical proper motion of main-belt asteroids (about 30 arcseconds per hour) constrain the ability to determine long spin periods. Therefore, asteroids appearing in the Kepler TPFs at least ten times were prioritized, covering half of the spin period range for most known asteroids.The integration time of the obtained frames limits the detection of rotation periods shorter than 30 minutes. This constraint is significant since most monolithic or rubble-pile asteroids have spin barriers for around 2-2.5 hours (Pravec &amp; Harris 2000).Light Curve ExtractionTo extract light curves from the TPF files, the total flux values across all frames were first calculated. Cotrending Basis Vectors (CBV) were then applied to correct the flux, followed by the selection of points with precomputed time crossings of the asteroids within the field of view. The Lomb-Scargle periodogram technique was used to identify periodic signals within noisy or unevenly sampled data, focusing on periods between one and ten hours (Scargle 1982). The example light curve of the asteroid 204557 Danmark is shown in Fig. 2.

Fig. 2: An example of a light curve extracted from Kepler K2 data for the asteroid 204557 Danmark. The plot shows the normalized flux as a function of time (in BKJD days), illustrating the periodic variations in brightness due to the asteroid's rotation.

&#160;ResultsThe rotation periods of several hundred asteroids were calculated, showing a strong correlation with data from ground-based observations, validating the approach. Comparisons with sparse light curves from the Palomar Transient Factory also demonstrated high accuracy. Future surveys like ZTF, Pan-STARRS, and LSST, combined with Kepler data, will further refine asteroid rotation period determinations.The analysis of rotation periods in relation to asteroid taxonomy revealed distinct patterns among different classes of asteroids. By comparing the rotation periods with known taxonomic categories, it was observed that certain types of asteroids, such as C-type (carbonaceous) and S-type (silicaceous), exhibit characteristic rotation periods that align with their physical properties and formation histories. This correlation helps in understanding the compositional diversity and evolutionary processes of asteroid populations (de Le&#243;n et al. 2020).The rotation periods obtained from the Kepler K2 data were compared with those estimated from ground-based observations and other sky surveys. The strong agreement between these datasets confirms the reliability of Kepler&#8217;s observations for asteroid spin period analysis. This comparison also highlights the potential for combining different observational techniques to achieve a more comprehensive understanding of asteroid rotational dynamics (Pravec et al.2002).ReferencesMargot, J. L., Pravec, P., Taylor, P., Carry, B., &amp; Jacobson, S. A. (2015). Binary asteroid population. Icarus, 248, 89-121.Holsapple, K. A. (2007). Spin limits of Solar System bodies: From the small fast-rotators to 2003 EL61. Icarus, 187(2), 500-509.Borucki, W. J., et al. (2010). Kepler planet-detection mission: Introduction and first results. Science, 327(5968), 977-980.Howell, S. B., et al. (2014). The K2 Mission: Characterization and Early Results. PASP, 126, 398.Berthier, J., et al. (2016). Prediction of transits of Solar system objects in Kepler/K2 images: an extension of the Virtual Observatory service SkyBoT. MNRAS, 458, 3394-3398.Pravec, P., &amp; Harris, A. W. (2000). Fast and slow rotation of asteroids. Icarus, 148(1), 12-20.Scargle, J. D. (1982). Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data. ApJ, 263, 835-853.de Le&#243;n, J., et al. (2020). Reflectance spectra and taxonomy of near-Earth and Mars-crossing asteroids. Icarus, 341, 113636.Pravec, P., Harris, A. W., &amp; Michalowski, T. (2002). Asteroid Rotations. Asteroids III, 113-122.