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

Using analytic modeling and simulations, we address the origin of an abundance of star-forming, clumpy, extended gas rings about massive central bodies in massive galaxies at $z \!<\! 4$. Rings form by high-angular-momentum streams and survive in galaxies of $M_{\rm star} \!>\! 10^{9.5-10} M_\odot$ where merger-driven spin flips and supernova feedback are ineffective. The rings survive after events of compaction to central nuggets. Ring longevity was unexpected based on inward mass transport driven by torques from violent disc instability. However, evaluating the torques from a tightly wound spiral structure, we find that the timescale for transport per orbital time is long and $\propto\! \delta_{\rm d}^{-3}$, with $\delta_{\rm d}$ the cold-to-total mass ratio interior to the ring. A long-lived ring forms when the ring transport is slower than its replenishment by accretion and the interior depletion by SFR, both valid for $\delta_{\rm d} \!<\! 0.3$. The central mass that 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 too low. 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 simulated rings through dust indicate qualitative consistency with observed rings about bulges in massive $z\!\sim\!0.5\!-\!3$ galaxies, in $H_{\alpha}$ and deep HST imaging. ALMA mock images indicate that $z\!\sim\!0.5\!-\!1$ rings should be detectable. We quote expected observable properties of rings and their central nuggets.