Analysis of Karin and Koronis2 asteroid families: new findings and challenges

We use our home catalog of the asteroid proper elements to study the Karin family. The hierarchical clustering method provides formal identification with 3,863 members, but this set also includes objects from the neighboring Koronis2 and Kuitaisi families, as well as interlopers originating from the much older Koronis family. By tracking the trajectories of cluster objects backward in time, we identified 2,161 asteroids whose orbits converged with that of their parent body (832) Karin at $5.72\pm 0.09$ My ago ($95$% C.L.). This method of calculating the family’s age is based on a novel convergence metric that is directly related to the velocities at which fragments were ejected from (832) Karin. We analyze the extent to which members $\leq 1.5$ km in diameter had drifted in semimajor axis due to Yarkovsky thermal forces and find it reflects the tilt of their rotation poles away from the ecliptic, recording the influence of the YORP torque. Karin’s size frequency distribution in the $\simeq(0.8-3)$ km range follows a power-law with a cumulative slope index $-3.20\pm 0.01$. Removing members of the Karin family from the original group, we examine the Koronis2 family, whose members are associated with (158) Koronis. We find it difficult for large members of the Koronis2 family to converge with the orbit of (158) Koronis within its previously estimated age of $7.6$ My. Achieving such convergence would require the Koronis2 family to be older than $10$ My, but our result must be verified with a direct numerical approach in the future.

💡 Research Summary

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This paper presents a comprehensive re‑examination of the Karin asteroid family and its neighboring Koronis2 family using the latest catalog of proper orbital elements (Nesvorný et al. 2024). The authors first apply the hierarchical clustering method (HCM) with a 10 m s⁻¹ velocity cutoff, which yields a large cluster of 3,863 objects. This cluster is known to be a mixture of Karin members, Koronis2 members, the younger Kuitaisi/Koronis3 groups, and interlopers from the much older Koronis family. To separate the true Karin family, the authors develop a novel backward‑integration convergence analysis that works directly in proper‑element space (a, e, sin I) augmented by the proper longitudes of the ascending node (Ω) and perihelion (ϖ).

The core of the method is a time‑dependent expression for the difference in proper angles between each asteroid j and the reference body (the largest remnant, (832) Karin). Using the proper secular frequencies s_j and g_j, the authors write

ΔΩ_j(T) = ΔΩ_j(0) + (s₀ − s_j) T + ½