Koronis Family Research Articles

Spin vectors in the Koronis family: V. Resolving the ambiguous rotation period of (3032) Evans

A sidereal rotation counting approach is demonstrated by resolving an ambiguity in the synodic rotation period of Koronis family member (3032) Evans, whose rotation lightcurves’ features did not easily distinguish between doubly- and quadruply-periodic. It confirms that Evans’s spin rate does not exceed the rubble-pile spin barrier and thus presents no inconsistency with being a ∼14-km reaccumulated object. The full spin vector solution for Evans is comparable to those for the known prograde low-obliquity comparably-fast rotators in the Koronis family, consistent with having been spun up by YORP thermal radiation torques.

Spin vectors in the Koronis family: IV. Completing the sample of its largest members after 35 years of study

An observational study of Koronis family members’ spin properties was undertaken with two primary objectives: to reduce selection biases for object rotation period and lightcurve amplitude in the sample of members’ known spin vectors, and to better constrain future modeling of spin properties evolution. Here we report rotation lightcurves of nineteen Koronis family members, and derived results that increase the sample of determined spin vectors in the Koronis family to include 34 of the largest 36 family members, completing it to H≈11.3 (D∼16 km) for the largest 32 members. The program observations were made during a total of 72 apparitions between 2005–2021, and are reported here along with several earlier unpublished lightcurves. All of the reported data were analyzed together with previously published lightcurves to determine the objects’ sidereal rotation periods, spin vector orientations, and convex model shape solutions. The derived distributions of retrograde rotation rates and pole obliquities appear to be qualitatively consistent with outcomes of modification by thermal YORP torques. The distribution of spin rates for the prograde rotators remains narrower than that for the retrograde rotators; in particular, the absence of prograde rotators having periods longer than about 20 h is real, while among the retrograde rotators are several objects having longer periods up to about 65 h. None of the prograde objects newly added to the sample appear to be trapped in an s6 spin–orbit resonance that is characteristic of most of the largest prograde objects (Vokrouhlický et al., 2003); these smaller objects either could have been trapped previously and have already evolved out, or have experienced spin evolution tracks that did not include the resonance.

(208) Lacrimosa: A case that missed the Slivan state?

Context.The largest asteroids in the Koronis family (sizes ≥25 km) have very peculiar rotation state properties, with the retrograde- and prograde-rotating objects being distinctly different. A recent re-analysis of observations suggests that one of the asteroids formerly thought to be retrograde-rotating, 208 Lacrimosa, in reality exhibits prograde rotation, yet other properties of this object are discrepant with other members this group.Aims.We seek to understand whether the new spin solution of Lacrimosa invalidates the previously proposed model of the Koronis large members or simply reveals more possibilities for the long-term evolutionary paths, including some that have not yet been explored.Methods.We obtained additional photometric observations of Lacrimosa, and included thermal and occultation data to verify its new spin solution. We also conducted a more detailed theoretical analysis of the long-term spin evolution to understand the discrepancy with respect to the other prograde-rotating large Koronis members.Results.We confirm and substantiate the previously suggested prograde rotation of Lacrimosa. Its spin vector has an ecliptic longitude and latitude of (λ,β) = (15° ± 2°, 67° ± 2°) and a sidereal rotation periodP= 14.085734 ± 0.000007 h. The thermal and occultation data allow us to calibrate a volume equivalent size ofD= 44 ± 2 km of Lacrimosa. The observations also constrain the shape model relatively well. Assuming uniform density, the dynamical ellipticity is Δ = 0.35 ± 0.05. Unlike other large prograde-rotating Koronis members, Lacrimosa spin is not captured in the Slivan state. We propose that Lacrimosa differed from this group in that it had initially slightly larger obliquity and longer rotation period. With those parameters, it jumped over the Slivan state instead of being captured and slowly evolved into the present spin configuration. In the future, it is likely to be captured in the Slivan state corresponding to the proper (instead of forced) mode of the orbital plane precession in the inertial space.

Spin pairs in the Koronis asteroid family

Asteroid groups may either form because of collisions or the rotational failure of a parent body. Collisional asteroid families tend to be more spread in proper element domains, while young spin clusters are usually much more compact. Recently, it has been shown that young spin clusters may form at higher rates in extremely young asteroid families (families younger than ≃3 Myr) than in more evolved groups. Among asteroid families, the Koronis family is a natural laboratory to test this phenomenon. While the family itself is very evolved, with an estimated age of more than 2 Byr, two young sub-families are known to be located among Koronis members: the extremely young family of Karin, with an age of 5.75±0.05 Myr, and the relatively young sub-family of Koronis(2), with an age of 10±5 Myr. This fact allows studying the occurrence of young spin clusters in extremely young, young and evolved asteroid populations, all sharing the same physical properties. Using methods based on backward numerical integrations, we identify one possible pair candidate in the Karin family, and retrieved the pair 1741–258640 recently found in other works. No convincing spin pair candidate was found in the Koronis(2) sub-family. This suggests that the occurrence of young spin clusters in families older than ≃ 3 Myr may be a rarer event than what previously thought.

Transit of asteroids across the 7/3 Kirkwood gap under the Yarkovsky effect

The Yarkovsky effect plays an important role in asteroids drifting in the inner Solar System. In the main belt, many asteroids are continuously pushed by the Yarkovsky effect into regions of different mean motion resonances (MMRs) and then ejected after a period of time, due to the instability of MMRs. They are considered as the principal source of near-Earth objects. In this paper, we investigate the effects of the 7/3 MMR with Jupiter (J7/3 MMR) on the transportation of asteroids from the Koronis family and the Eos family that reside, respectively, on the inner and outer sides of the resonance using numerical simulations. The J7/3 MMR acts like a selective barrier to migrating asteroids. The fraction of asteroids that successfully cross through the resonance and the escape rate from the resonance are found to depend on the Yarkovsky drifting rate, the initial inclination and the migrating direction. The excitation of eccentricity and inclination due to the combined influence from both the resonance and the Yarkovsky effect are discussed. Only the eccentricity can be pumped up considerably, and it is attributed mainly to the resonance. In the observational data, family members are also found in the resonance and on the opposite side of the resonance with respect to the corresponding family centre. The existence of these family members is explained using our results of numerical simulations. Finally, the replenishment of asteroids in the J7/3 MMR and its transportation of asteroids are discussed.

Investigating Taxonomic Diversity within Asteroid Families through ATLAS Dual-band Photometry

Abstract We present here the c–o colors for identified Flora, Vesta, Nysa–Polana, Themis, and Koronis family members within the historic data set (2015–2018) of the Asteroid Terrestrial-impact Last Alert System (ATLAS). The Themis and Koronis families are known to be relatively pure C- and S-type Bus-DeMeo taxonomic families, respectively, and the extracted color data from the ATLAS broadband c- and o-filters of these two families are used to demonstrate that the ATLAS c–o color is a sufficient parameter to distinguish between the C- and S-type taxonomies. The Vesta and Nysa–Polana families are known to display a mixture of taxonomies possibly due to Vesta’s differentiated parent body origin and Nysa–Polana actually consisting of two nested families with differing taxonomies. Our data show that the Flora family also displays a large degree of taxonomic mixing and the data reveal a substantial H-magnitude dependence on color. We propose and exclude several interpretations for the observed taxonomic mix. Additionally, we extract rotation periods of all of the targets reported here and find good agreement with targets that have previously reported periods.

Search for the H Chondrite Parent Body among the Three Largest S-type Asteroids: (3) Juno, (7) Iris, and (25) Phocaea

Abstract Linking meteorites to source regions in the main asteroid belt is important for understanding the conditions under which their parent bodies formed. Ordinary chondrites are the most abundant class of meteorites on Earth, totaling 86% of all collected samples. Some S-type asteroids/families have been proposed as sources for the three different (H, L, and LL) types of ordinary chondrites with Hebe, Agnia, Merxia, and Koronis families being the source for H chondrites, Gefion for H/L chondrites, and Flora family for LL chondrites. However, the composition and meteorite affinity of several large S-type main belt asteroids remains unconstrained leaving the possibility of additional source regions for ordinary chondrite meteorites. Here we investigate the surface composition of three large S-type asteroids, (3) Juno, (7) Iris, and (25) Phocaea, using their near-infrared spectra (0.7–2.55 μm) to identify the parent body of the H chondrites. We use a Bayesian inference model to confirm the meteorite analogs of the three asteroids. Based on our Bayes classifier we find the following analogs and probabilities: Juno is likely H chondrite (89%), Iris is likely LL chondrite (97.5%), and Phocaea is likely H chondrite (98.6%). While Phocaea has the highest probability of being an H chondrite, it is dynamically unlikely to deliver material to near-Earth space. While Juno has spectral properties similar to H chondrites, its family is unlikely to produce sizeable H-chondrite-type near-Earth objects (NEOs). If Juno is the primary source of H chondrite meteorites, it suggests that an additional source is needed to explain the H-chondrite-type NEOs.

On the oldest asteroid families in the main belt

Asteroid families are groups of minor bodies produced by high-velocity collisions. After the initial dispersions of the parent bodies fragments, their orbits evolve because of several gravitational and non-gravitational effects,such as diffusion in mean-motion resonances, Yarkovsky and YORP effects, close encounters of collisions, etc. The subsequent dynamical evolution of asteroid family members may cause some of the original fragments to travel beyond the conventional limits of the asteroid family. Eventually, the whole family will dynamically disperse and no longer be recognizable. A natural question that may arise concerns the timescales for dispersion of large families. In particular, what is the oldest still recognizable family in the main belt? Are there any families that may date from the late stages of the Late Heavy Bombardment and that could provide clues on our understanding of the primitive Solar System? In this work, we investigate the dynamical stability of seven of the allegedly oldest families in the asteroid main belt. Our results show that none of the seven studied families has a nominally mean estimated age older than 2.7 Gyr, assuming standard values for the parameters describing the strength of the Yarkovsky force. Most "paleo-families" that formed between 2.7 and 3.8 Gyr would be characterized by a very shallow size-frequency distribution, and could be recognizable only if located in a dynamically less active region (such as that of the Koronis family). V-type asteroids in the central main belt could be compatible with a formation from a paleo-Eunomia family.

Constraints on the original ejection velocity fields of asteroid families

Asteroid families form as a result of large-scale collisions among main belt asteroids. The orbital distribution of fragments after a family-forming impact could inform us about their ejection velocities. Unfortunately, however, orbits dynamically evolve by a number of effects, including the Yarkovsky drift, chaotic diffusion, and gravitational encounters with massive asteroids, such that it is difficult to infer the ejection velocities eons after each family's formation. Here we analyze the inclination distribution of asteroid families, because proper inclination can remain constant over long time intervals, and could help us to understand the distribution of the component of the ejection velocity that is perpendicular to the orbital plane ($v_{W}$). From modeling the initial breakup, we find that the distribution of $v_{W}$ of the fragments, which manage to escape the parent body's gravity, should be more peaked than a Gaussian distribution (i.e., be leptokurtic) even if the initial distribution was Gaussian. We surveyed known asteroid families for signs of a peaked distribution of $v_{W}$ using a statistical measure of the distribution peakedness or flatness known as kurtosis. We identified eight families whose $v_{W}$ distribution is significantly leptokurtic. These cases (e.g. the Koronis family) are located in dynamically quiet regions of the main belt, where, presumably, the initial distribution of $v_{W}$ was not modified by subsequent orbital evolution. We suggest that, in these cases, the inclination distribution can be used to obtain interesting information about the original ejection velocity field.

Characterizing the original ejection velocity field of the Koronis family

An asteroid family forms as a result of a collision between an impactor and a parent body. The fragments with ejection speeds higher than the escape velocity from the parent body can escape its gravitational pull. The cloud of escaping debris can be identified by the proximity of orbits in proper element, or frequency, domains. Obtaining estimates of the original ejection speed can provide valuable constraints on the physical processes occurring during collision, and used to calibrate impact simulations. Unfortunately, proper elements of asteroids families are modified by gravitational and non-gravitational effects, such as resonant dynamics, encounters with massive bodies, and the Yarkovsky effect, such that information on the original ejection speeds is often lost, especially for older, more evolved families.It has been recently suggested that the distribution in proper inclination of the Koronis family may have not been significantly perturbed by local dynamics, and that information on the component of the ejection velocity that is perpendicular to the orbital plane (vW), may still be available, at least in part. In this work we estimate the magnitude of the original ejection velocity speeds of Koronis members using the observed distribution in proper eccentricity and inclination, and accounting for the spread caused by dynamical effects. Our results show that (i) the spread in the original ejection speeds is, to within a 15% error, inversely proportional to the fragment size, and (ii) the minimum ejection velocity is of the order of 50 m/s, with larger values possible depending on the orbital configuration at the break-up.

COMPOSITION OF POTENTIALLY HAZARDOUS ASTEROID (214869) 2007 PA8: AN H CHONDRITE FROM THE OUTER ASTEROID BELT

Potentially hazardous asteroids (PHAs) represent a unique opportunity for physical characterization during their close approaches to Earth. The proximity of these asteroids makes them accessible for sample-return and manned missions, but could also represent a risk for life on Earth in the event of collision. Therefore, a detailed mineralogical analysis is a key component in planning future exploration missions and developing appropriate mitigation strategies. In this study we present near-infrared spectra (0.7-2.55 microns) of PHA (214869) 2007 PA8 obtained with the NASA Infrared Telescope Facility during its close approach to Earth on November 2012. The mineralogical analysis of this asteroid revealed a surface composition consistent with H ordinary chondrites. In particular, we found that the olivine and pyroxene chemistries of 2007 PA8 are Fa18(Fo82) and Fs16, respectively. The olivine-pyroxene abundance ratio was estimated to be 47%. This low olivine abundance and the measured band parameters, close to the H4 and H5 chondrites, suggest that the parent body of 2007 PA8 experienced thermal metamorphism before being catastrophically disrupted. Based on the compositional affinity, proximity to the J5:2 resonance, and estimated flux of resonant objects we determined that the Koronis family is the most likely source region for 2007 PA8.

Do Slivan states exist in the Flora family?

Context. It is known that the Yarkovsky effect moves small astroids to larger/smaller semimajor axes depending on their prograde/retrograde spins. The YORP effect influences asteroid spin periods and spin axis orientations so that they evolve in time. The alignment of the spin vectors and correlations of the spin rates, now known as Slivan states and observed among members of the Koronis family, are interpreted in terms of the YORP effect and spin-orbit resonances. Splitting asteroid families into prograde and retrograde groups has recently been proposed as a result of the Yarkovsky effect. Prograde and retrograde asteroids drift in different directions, and this has never been observed directly. Aims. The influence of the Yarkovsky and YORP effects should be observable among objects in asteroid families, especially in the Flora family, which lies close to the Sun and consists of many small objects. Methods. The Flora family asteroids were modelled using the lightcurve inversion technique. As a result the orientation of spin vectors, shapes, and sidereal periods of rotation were obtained. Results. Results of modelling of the Flora family asteroids show the family splitting into prograde and retrograde groups as a result of the Yarkovsky effect. The observed ratio between prograde and retrograde asteroids is 2.6. The positions of spin vectors, as well as their similar latitudes suggest, that the Slivan states are observed among the Flora family asteroids.Conclusions. The influence of the Yarkovsky and YORP effect is clearly visible in the Flora family. The location of the Flora family close to the ν 6 resonance explains the lack of retrograde objects and confirms the excess of retrograde rotators among NEAs and their origin from the ν 6 . The Slivan states that I searched seem to be present among prograde rotators in this family even though they were not expected.

Do Slivan states exist in the Flora family?

Context. Recent studies have uncovered evidence that the statistical properties of asteroids’ physical parameters are a fundamental source of information on the physics of their collisions and evolution. The analysis of the spin rates and spin vector distributions helps us to understand the role of various known and new effects. The alignment of spin vectors and the correlation of spin rates are for the first time observed for ten members of the Koronis family. These unexpected non-random orientations of the spin axes and correlations of the spin rates, now known as Slivan states are interpreted in terms of a YORP effect and spin-orbit resonances. Aims. To study non-gravitational-effects, there appears to be a need for new observational campaigns devoted to determining the physical parameters of the asteroid families. Methods. We analysed the photometric observations of the asteroids, which are the most efficient method of studying asteroid physical parameters.Results. We report the results of a ten-year long observational survey of the light variations of objects in the Flora region. We present 544 individual lightcurves of 55 objects obtained at various observing geometries. These lightcurves yield new or refined synodic periods for 32 asteroids and confirm period determinations for 23 objects in our sample. To improve the statistics of the Flora family objects, we add to our dataset 91 objects with reliably determined periods. The distribution of rotation rates for the Flora family is non-Maxwellian at a confidence level of 94% and different from those of the Koronis and the Hungaria families. It seems to be consistent with the long-term influence of the YORP effect, although it is also indicative of a younger age for the Flora family compared to both the Koronis and the Hungaria families. Conclusions. Our new data is a foundation for the spin vector and shape determinations that will be the objectives of the second paper of the series. We search for spin vector and spin periods correlations in order to determine whether Slivan states exist in the Flora family.

Spin vectors in the Koronis family: III. (832) Karin

Studies of asteroid families constrain models of asteroid collisions and evolution processes, and the Karin cluster within the Koronis family is among the youngest families known (Nesvorný, D., Bottke, Jr., W.F., Dones, L., Levison, H.F. [2002]. Nature 417, 720–722). (832) Karin itself is by far the largest member of the Karin cluster, thus knowledge of Karin’s spin vector is important to constrain family formation and evolution models that include spin, and to test whether its spin properties are consistent with the Karin cluster being a very young family. We observed rotation lightcurves of Karin during its four consecutive apparitions in 2006–2009, and combined the new observations with previously published lightcurves to determine its spin vector orientation and preliminary model shape. Karin is a prograde rotator with a period of (18.352±0.003) h, spin obliquity near (42±5)°, and pole ecliptic longitude near either (52±5)° or (230±5)°. The spin vector and shape results for Karin will constrain models of family formation that include spin properties; in the meantime we briefly discuss Karin’s own spin in the context of those of other members of the Karin cluster and the parent body’s siblings in the Koronis family.

Space weathering of small Koronis family asteroids in the SDSS Moving Object Catalog

Following the work of Rivkin et al. (Rivkin, A.S., Thomas, C.A., Trilling, D.E., Enga, M., Grier, J.A. [2011]. Icarus 211, 1294–1297) and Thomas et al. (Thomas, C.A., Rivkin, A.S, Trilling, D.E., Enga, M., Grier, J.A. [2011a]. Icarus 212, 158–166), we investigate space weathering trends in the Koronis family using the larger sample size of the Sloan Digital Sky Survey Moving Object Catalog. We confirm the trend in spectral slope seen in our earlier work and extend our results by investigating the trend in band depth (i−z color index) to show that Koronis family asteroids smaller than 4km show the transition from fresh Q-type to weathered S-type surfaces.

Spectral properties of (854) Frostia, (1333) Cevenola and (3623) Chaplin

Near-infrared spectroscopy can play a key role in establishing the mineralogical composition of objects and supporting other physical data obtained by complementary observational techniques such as adaptive optics, radar and photometry. The objective of our survey was asteroids that present large variations in their light curves. We report observations for asteroids (854) Frostia, (1333) Cevenola and (3623) Chaplin carried out in the 0.8-2.5 μm spectral range using SpeX/Infrared Telescope Facility (IRTF) in LowRes mode. The spectral modelling of these asteroids gives new insights into these peculiar objects in the main belt. (854) Frostia is a V-type asteroid, and its spectral properties are similar to those of basalts. The most probable mineralogical solution Wo 8 Fs 43 En 49 was calculated for Frostia. (1333) Cevenola was estimated to have an Sq spectral type, in agreement with its membership of the Eunomia family. (3623) Chaplin is an S-type asteroid, in agreement with the taxonomic type of the Koronis family.

Space weathering of small Koronis family members

The space weathering process and its implications for the relationships between S- and Q-type asteroids and ordinary chondrite meteorites is an often debated topic in asteroid science. Q-type asteroids have been shown to display the best spectral match to ordinary chondrites (McFadden, L.A., Gaffey, M.J., McCord, T.B. [1985]. Science 229, 160–163). While the Q-types and ordinary chondrites share some spectral features with S-type asteroids, the S-types have significantly redder spectral slopes than the Q-types in visible and near-infrared wavelengths. This reddening of spectral slope is attributed to the effects of space weathering on the observed surface composition. The analysis by Binzel et al. (Binzel, R.P., Rivkin, A.S., Stuart, J.S., Harris, A.W., Bus, S.J., Burbine, T.H. [2004]. Icarus 170, 259–294) provided a missing link between the Q- and S-type bodies in near-Earth space by showing a reddening of spectral slope in objects from 0.1 to 5km that corresponded to a transition from Q-type to S-type asteroid spectra, implying that size, and therefore surface age, is related to the relationship between S- and Q-types. The existence of Q-type asteroids in the main-belt was not confirmed until Mothé-Diniz and Nesvorny (Mothé-Diniz, T., Nesvorny, D. [2008]. Astron. Astrophys. 486, L9–L12) found them in young S-type clusters. The young age of these families suggest that the unweathered surface could date to the formation of the family. This leads to the question of whether older S-type main-belt families can contain Q-type objects and display evidence of a transition from Q- to S-type. To answer this question we have carried out a photometric survey of the Koronis family using the Kitt Peak 2.1m telescope. This provides a unique opportunity to compare the effects of the space weathering process on potentially ordinary chondrite-like bodies within a population of identical initial conditions. We find a trend in spectral slope for objects 1–5km that shows the transition from Q- to S-type in the main-belt. This data set will prove crucial to our understanding of the space weathering process and its relevant timescales.

Ordinary chondrite-like colors in small Koronis family members

A survey of small (<5–10 km diameter) members of the Koronis family shows some objects with visible-wavelength broadband colors consistent with membership in the Q-class (Tholen, D.J. [1984]. Asteroid taxonomy from cluster analysis of photometry. Ph.D. Dissertation, University of Arizona, Tucson, AZ; Bus, S.J., Binzel, R.P. [2002]. Icarus 158, 146–177). This agrees with an ordinary chondritic composition for this family and suggests the timescale for changing Q-class to S-class spectra in the main belt is roughly comparable to the regolith refresh time in the 2–5 km size range.

Polarimetric evidence of close similarity between members of the Karin and Koronis dynamical families

We present the results of a campaign of polarimetric observations of small asteroids belonging to the Karin and Koronis families, carried out at the ESO Cerro Paranal Observatory using the VLT-Kueyen 8-m telescope. The Karin family is known to be very young, having likely been produced by the disruption of an original member of the Koronis family less than 6 Myr ago. The purpose of our study was to derive polarimetric properties for a reasonable sample of objects belonging to the two families, in order to look for possible systematic differences between them, to be interpreted in terms of differences in surface properties, in particular albedo. In turn, systematic albedo differences might be caused by different times of exposure to space weathering processes experienced by the two groups of objects. The results of our analysis indicate that no appreciable difference exists between the polarimetric properties of Karin and Koronis members. We thus find that space-weathering mechanisms may be very efficient in affecting surface properties of S-class asteroids on very short timescales. This result complements some independent evidence found by recent spectroscopic studies of very young families.

Spin vectors in the Koronis family: II. Additional clustered spins, and one stray

We recorded 101 new rotation lightcurves of five Koronis family members, and then combined the new observations with previous data to determine the objects' sidereal rotation periods, spin vector orientations, and model shape solutions. The observing program was tailored specifically for spin vector analyses by determining single-apparition Lumme–Bowell solar phase coefficients, and by measuring synodic rotation periods precisely enough to unambiguously count the rotations between two consecutive oppositions, which is a prerequisite for identifying the correct sidereal period. The new data make possible first pole and shape determinations for (263) Dresda, (462) Eriphyla, and (1289) Kutaïssi, and they improve the models for (277) Elvira and (534) Nassovia, two objects previously studied by Slivan et al. [Slivan, S.M., Binzel, R.P., Crespo da Silva, L.D., Kaasalainen, M., Lyndaker, M.M., Krčo, M., 2003. Icarus 162, 285–307]. Our results increase the number of Koronis family spin vectors reported in the literature to fourteen, a sample which now includes the seven largest family members. The spin properties of Eriphyla (rotation period P = 8.66 h , spin vector obliquity ε = 51 ° ) and Kutaïssi ( P = 3.62 h , ε = 165 ° ) are consistent with the markedly nonrandom distribution reported by Slivan [Slivan, S.M., 2002. Nature 419, 49–51], and explained by Vokrouhlický et al. [Vokrouhlický, D., Nesvorný, D., Bottke, W.F., 2003. Nature 425, 147–151] as the result of the effects of thermal “YORP” torques combined with solar and planetary gravitational torques. Dresda ( P = 16.81 h , ε = 16 ° ) is the first prograde Koronis member whose spin obliquity and spin rate significantly differ from the clustered spin properties previously found for other prograde Koronis members; nevertheless, its spin vector is consistent with several of the spin evolution possibilities that were identified in the YORP modeling.