RR Lyrae Stars in Intermediate-age Magellanic Clusters: Membership Probabilities and Delay Time Distribution

Recent works have challenged our canonical view of RR Lyrae (RRL) stars as tracers of exclusively old populations ($\gtrsim10$~Gyr) by proposing a fraction of these stars to be of intermediate ages ($\sim$2-5~Gyr). Since it is currently not possible to infer stellar ages directly for individual RRL stars, our goal in this work is to search for these in association to intermediate-age clusters whose reliable ages can then be safely be attributed to the RRL. We used the Gaia DR3 Specific Object Study and OGLE IV public catalogues to search for RRL stars around stellar clusters older than 1~Gyr in the Large and Small Magellanic Clouds. Modelling membership probabilities based on proper motion and photometric distance we obtained a list of 259 RRL stars associated with Magellanic clusters. Of these, 23 RRL are likely members of 10 intermediate-age clusters: 3 and 7 in the Small and Large Magellanic Clouds, respectively. By modelling the inferred expectation values of the number of RRL stars per cluster, we inferred the delay time distribution of the RRL in three age ranges. For the old population ($>8$~Gyr) we find $2.5^{+0.4}_{-0.3}$ RRL$/10^5 M_\odot$. For the young (1-2 Gyr) and intermediate age (2-8 Gyr) populations we find rates of $0.34^{+0.17}_{-0.12}$ and $0.071^{+0.073}_{-0.041}$ RRL$/10^5 M_\odot$, respectively, after further decontamination from control field tests. While radial velocities are necessary for definitively confirming cluster memberships, the high-probability list of intermediate-age RRL stars presented here offers a promising opportunity for the first direct confirmation of these enigmatic stars.