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We investigate the enrichment in elements produced by the slowneutron-capture process ($s$-process) in the globular clusters M4 (NGC 6121)and M22 (NGC 6656). Stars in M4 have homogeneous abundances of Fe andneutron-capture elements, but the entire cluster is enhanced in $s$-processelements (Sr, Y, Ba, Pb) relative to other clusters with a similar metallicity.In M22, two stellar groups exhibit different abundances of Fe and $s$-processelements. By subtracting the mean abundances of $s$-poor from $s$-rich stars,we derive $s$-process residuals or empirical $s$-process distributions for M4and M22. We find that the $s$-process distribution in M22 is more weightedtoward the heavy $s$-peak (Ba, La, Ce) and Pb than M4, which has been enrichedmostly with light $s$-peak elements (Sr, Y, Zr). We construct simple chemicalevolution models using yields from massive star models that include rotation,which dramatically increases $s$-process production at low metallicity. We showthat our massive star models with rotation rates of up to 50\% of the critical(break-up) velocity and changes to the preferred$^{17}$O($\alpha$,$\gamma$)$^{21}$Ne rate produce insufficient heavy$s$-elements and Pb to match the empirical distributions. For models thatincorporate AGB yields, we find that intermediate-mass yields (with a $^{22}$Neneutron source) alone do not reproduce the light-to-heavy $s$-element ratiosfor M4 and M22, and that a small contribution from models with a $^{13}$Cpocket is required. With our assumption that $^{13}$C pockets form for initialmasses below a transition range between 3.0 and 3.5 M$_\odot$, we match thelight-to-heavy s-element ratio in the s-process residual of M22 and predict aminimum enrichment timescale of between 240 and 360 Myr. Our predicted value isconsistent with the 300 Myr upper limit age difference between the two groupsderived from isochrone fitting.

The s-Process Enrichment of the Globular Clusters M4 and M22