The Karma asteroid family is a group of primitive carbonaceous asteroids in the middle part of the asteroid belt between Mars and Jupiter, just at the outer edge of the 3J:1A mean-motion resonance. We obtained the family members’ initial list with 332 asteroids, but their surface reflectance properties suggested that 15 of them are interlopers. Therefore, the final list contains 317 members of the Karma family. We also estimated that it was formed by the catastrophic disruption of a parent body that was between 34 and 41 km in diameter.
Based on the V-shape method, the Karma family’s age is estimated to be about 137 Myr. A detailed dynamical map of the region combined with numerical simulations allowed us to reconstruct the family’s long-term dynamical evolution and identify the mechanisms responsible for this evolution. The numerical simulations successfully reproduced the main features in the orbital distribution of the family members but also showed that some regions of the Karma family could be missing. A more detailed analysis revealed that the critical role information of these regions is played by g-g6+s-s6 secular resonance, and the regions likely consist of very dark objects, fainter than absolute magnitude H=17, that have not yet been detected.
Based on the acquired results, we concluded that the magnitude-frequency distribution of family members up to H=16 mag is neither affected by dynamical erosion nor observational incompleteness. Therefore, it represents the result of collisional grinding of the original family population. We also investigated the escape rate from the family in the course of our simulations and found that the Karma family has lost about 1/3 of the members with H < 18.1 mag, which are objects larger than about 1.36 km in size.
Finally, we found that the Karma family has been supplying some asteroids to the near-Earth region via the 3J:1A resonance. Currently, there should be about ten family members larger than 1 km in diameter orbiting in the near-Earth space.