Rotational properties of Kuiper belt objects as seen by the K2 mission
Authors: Kecskeméthy Viktória , Kiss Csaba , Szakáts Róbert , Pál András , Szabó Gyula M. , Molnár László , Sárneczky Krisztián , Vinkó József , Szabó Róbert , Marton Gábor , Farkas-Takács Anikó , Kalup Csilla , Kiss László L. 
Published: September 2022

&lt;p&gt;&lt;br /&gt;Earlier reviews of trans-Neptunian light curves reported mean rotation periods of P = 7-8 h (Duffard et al., 2009), and it was also found that the binary trans-Neptunian population rotates slower (Thirouin &amp; Sheppard, 2014), and objects in the cold classical population have larger variability and rotate slower than the non-cold classical TNOs (Benecchi et al., 2013,Thirouin &amp; Sheppard, 2019). While ground-based observations have obvious limitations in detecting long-period light curves the K2 mission of the Kepler Space Telescope allowed long (up to ~80 days), uninterrupted observations of many Solar system objects, including main belt asteroids, Hildas, Jovian trojans, and also the irregular satellites of giant planets. Light curves were also published for a few, selected trans-Neptunian objects based on K2 observations (see Kiss et al., 2020, for a summary). A common outcome of the studies of larger samples, across all dynamical classes, was the identification of an increased number of targets with long rotation periods compared to previous ground-based studies. A similar trend is observed among the data of nearly 10 000 main belt asteroids obtained by the TESS Space Telescope (P&amp;#225;l et al., 2020), and asteroids with long rotation periods were identified in other surveys like the Asteroid Terrestrial-impact Last Alert System (ATLAS), the Zwicky Transient Facility (Erasmus et al., 2021) and the All-Sky Automated Survey for Supernovae (Hanus et al., 2021).&amp;#160;&lt;/p&gt;
&lt;p&gt;We have collected the K2 trans-Neptunian object observations between Campaigns C03 (November 2014 -- February 2015) to C19 (August -- September, 2018), which includes 67 targets. Due to the faintness of our targets the detectability rate of a light curve period is ~57 %, notably lower than in the case of other small body populations, like Hildas or Jovian trojans. We managed to obtain light curve periods with an acceptable confidence for 36 targets; the majority of these cases are new identifications. We were able to give light curve amplitude upper limits for the other 31 targets. Several of the newly detected light curve periods are longer than ~24 h, in many cases close to ~100 h, i.e., slow rotators.&lt;/p&gt;
&lt;p&gt;There is a very significant difference between the rotation rates of the LCDB and K2 TNO samples (Figs. 1 and 2). The mean LCD spin frequency is 2.71 c/d (8.8 h), while it is 0.87 c/d (27.6 h) in the K2 sample which is more similar to the K2 Hilda and Jovian Trojan spin frequency distrbutions. Thirouin &amp; Sheppard (2019) obtained 9.48&amp;#177;1.53 h and &amp;#160;8.45&amp;#177;0.58 h mean rotation periods for the cold classical and the non-cold classical TNOs. Our mean values for the same dynamical groups (but using different targets) are notably longer: 1.21&lt;sup&gt;+1.58&lt;/sup&gt;&lt;sub&gt;-0.63 &lt;/sub&gt;c/d (19.83 h) and 0.83&lt;sup&gt;+1.81&lt;/sup&gt;&lt;sub&gt;-0.23 &lt;/sub&gt;c/d (P=28.91 h), respectively. The K2 mean frequency is higher than that of the K2 Jovian Trojans and Hildas, but we could not detect the very long period targets that were observed in these other K2 samples. &amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; width=&quot;472&quot; height=&quot;354&quot; /&gt;&lt;br /&gt;&lt;em&gt;Figure 1: frequency distribution of asteroids. The cyan, magenta, green and blue colours represent the TNOs in the LCDB and Jovian trojans, Hildas and TNOs from K2, respectively. &lt;/em&gt;&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; width=&quot;469&quot; height=&quot;352&quot; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;em&gt;Figure 2: Frequency as a function of absolute magnitude. Big circles with error bars mark the median values standard deviations for the different samples. The horizontal dashed lines mark the spin frequencies of fast, slow, and very slow rotators (Pravec et al., 2002). &amp;#160;&lt;/em&gt;&lt;/p&gt;
&lt;p&gt;While there are only three objects with D&gt;500 km in our sample, there are a number of objects -- both with and without detected light curve periods -- that fall in the 300&amp;#8804;D&amp;#8804;500 km transitional zone where asphericity -- hence light curve amplitude -- is expected to drop assuming a single rotating body, assuming main belt composition. Main belt asteroids are already almost extinct in this size range, and so are Centaurs -- for these bodies irregular shapes are expected in most cases.&amp;#160;&lt;/p&gt;
&lt;p&gt;While the general trend is that larger objects have smaller light curve amplitudes among TNOs -- a trend followed both by our sample and the LCDB TNOs -- there are a considerable number of TNOs with high asphericity in the 300&amp;#8804;D&amp;#8804;500 km size range. This contradiction could be resolved if TNOs had higher-than-expected compressive strength and become spherical for sizes larger than their main belt counterparts, and remain 'irregular' in the 300&amp;#8804;D&amp;#8804;500 km range. However, their general low density and high porosity point against this scenario. A notable fraction of contact or semi-contact binary systems in which the members themselves are in hydrostatical equlibrium could produce a population of high-amplitude light curves in this size range (Lacerda et al., 2006, 2014). As some authors pointed out, contact binaries may be very frequent, especially in the plutino population (Thirouin &amp; Sheppard, 2018,2019). The long term stability of such systems against their tidal evolution, however, should be investigated to answer the reliability of this assumption.&amp;#160;Finally, spherical (rotationally flattened) bodies with large albedo variegations could also explain the observed amplitudes. While the general expectation in most TNO light curve studies was a double peak light curve, in our sample most light curves were found to be single-peak, after comparing the single-peak and double-peak solutions.&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; width=&quot;475&quot; height=&quot;340&quot; /&gt;&lt;/p&gt;
&lt;p&gt;Fgiure 3: Light curve amplitude versus the estimated size of the targets in our sample. The region between the vertical dashed lines mark the irregular-to-spherical transition size range in the main belt. Blue and red symbols mark the K2 targets and K2 upper limits, small grey symbols correspond to main belt asteroids. Large gray symbols represent the theoretical maximum light curve amplitudes the of large main belt objects if it was solely caused by the elongated shape of a body with homogeneous albedo. &lt;br /&gt;&lt;br /&gt;&lt;/p&gt;