We report on the results of a systematic search for associated asteroid families for all active asteroids known to date. We find that 10 out of 12 main-belt comets (MBCs) and 5 out of 7 disrupted asteroids are linked with known or candidate families, rates that have ~0.1% and ~6% probabilities, respectively, of occurring by chance, given an overall family association rate of 37% for asteroids in the inner solar system. We find previously unidentified family associations between 238P/Read and the candidate Gorchakov family, 311P/PANSTARRS and the candidate Behrens family, 324P/La Sagra and the Alauda family, 354P/LINEAR and the Baptistina family, P/2013 R3-B (Catalina-PANSTARRS) and the Mandragora family, P/2015 X6 (PANSTARRS) and the Aeolia family, P/2016 G1 (PANSTARRS) and the Adeona family, and P/2016 J1-A/B (PANSTARRS) and the Theobalda family. All MBCs with family associations belong to families that contain asteroids with primitive taxonomic classifications and low average reported albedos (pV_avg < 0.10), while disrupted asteroids with family associations belong to families that contain asteroids that span wider ranges of taxonomic types and average reported albedos (0.06 < pV_avg < 0.25). These findings are consistent with MBC activity being closely correlated to composition (i.e., whether an object is likely to contain ice), while disrupted asteroid activity is not as sensitive to composition. Given our results, we describe a sequence of processes by which the formation of young asteroid families could lead to the production of present-day MBCs.
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