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Using analytic modeling and simulations, we address the origin of anabundance of star-forming, clumpy, extended gas rings about massive centralbodies in massive galaxies at $z \!<\! 4$. Rings form by high-angular-momentumstreams and survive in galaxies of $M_{\rm star} \!>\! 10^{9.5-10} M_\odot$where merger-driven spin flips and supernova feedback are ineffective. Therings survive after events of compaction to central nuggets. Ring longevity wasunexpected based on inward mass transport driven by torques from violent discinstability. However, evaluating the torques from a tightly wound spiralstructure, we find that the timescale for transport per orbital time is longand $\propto\! \delta_{\rm d}^{-3}$, with $\delta_{\rm d}$ the cold-to-totalmass ratio interior to the ring. A long-lived ring forms when the ringtransport is slower than its replenishment by accretion and the interiordepletion by SFR, both valid for $\delta_{\rm d} \!<\! 0.3$. The central massthat lowers $\delta_{\rm d}$ is a compaction-driven bulge and/or dark matter,aided by the lower gas fraction at $z \!<\! 4$, provided that it is not toolow. The ring is Toomre unstable for clump and star formation. The high-$z$dynamic rings are not likely to arise form secular resonances or collisions.AGN feedback is not expected to affect the rings. Mock images of simulatedrings through dust indicate qualitative consistency with observed rings aboutbulges in massive $z\!\sim\!0.5\!-\!3$ galaxies, in $H_{\alpha}$ and deep HSTimaging. ALMA mock images indicate that $z\!\sim\!0.5\!-\!1$ rings should bedetectable. We quote expected observable properties of rings and their centralnuggets.

Origin of Star-Forming Rings around Massive Centres in Massive Galaxies at $z\!<\!4$