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The 2:1 mean-motion resonance with Jupiter harbours two distinct groups ofasteroids. The short-lived population is known to be a transient groupsustained in steady state by the Yarkovsky semimajor axis drift. The long-livedasteroids, however, can exhibit dynamical lifetimes comparable to$4\,\mathrm{Gyr}$. They reside near two isolated islands of the phase spacedenoted $\mathrm{A}$ and $\mathrm{B}$, with an uneven population ratio$\mathrm{B}/\mathrm{A} \simeq 10$. The orbits of $\mathrm{A}$-island asteroidsare predominantly highly inclined, compared to island $\mathrm{B}$. Thesize-frequency distribution is steep but the orbital distribution lacks anyevidence of a collisional cluster. These observational constraints are somewhatpuzzling and therefore the origin of the long-lived asteroids has not beenexplained so far.  With the aim to provide a viable explanation, we first update the resonantpopulation and revisit its physical properties. Using an $N$-body model withseven planets and the Yarkovsky effect included, we demonstrate that thedynamical depletion of island $\mathrm{A}$ is faster, in comparison with island$\mathrm{B}$. Then we investigate (i) the survivability of primordial resonantasteroids and (ii) capture of the population during planetary migration,following a recently described scenario with an escaping fifth giant planet anda jumping-Jupiter instability. We also model the collisional evolution of theresonant population over past $4\,\mathrm{Gyr}$. Our conclusion is that thelong-lived group was created by resonant capture from a narrow part ofhypothetical outer main-belt family during planetary migration. Primordialasteroids surviving the migration were probably not numerous enough tosubstantially contribute to the observed population.

The origin of long-lived asteroids in the 2:1 mean-motion resonance with Jupiter