Although nuclear rings of gas and star formation are common in barred spiral galaxies, current theories of why and how they form do not provide the level of detail needed to quantify the effect that these rings can have on the fueling of active galactic nuclei and on the evolution of their host galaxy. In this paper we use detailed modeling to show that existence of nuclear rings is directly related to the existence of the orbit family whose major axis is perpendicular to the major axis of the bar (x_2). We explore a large range of barred galaxy potentials and for each potential we use a two-dimensional hydrodynamic simulation to determine whether and at what radius a nuclear ring forms. We compare the results of the hydrodynamic simulations to numerical integrations of periodic orbits in a barred potential and show that the rings only form when a minimum amount of x_2 orbits exists. Because the rings migrate inwards with time as they accumulate gas, the radius at which a nuclear ring is seen does not give direct information on the shape of the rotation curve. We also show that the common assumption that nuclear rings are related to an inner Lindblad resonance is incorrect. In fact, we show that there is no RESONANCE at the inner Lindblad resonance in barred galaxies. We also compare the predictions of this theory to HST observations and show that it correctly predicts the observed gas and star formation morphology of nuclear rings.

To be published in the Astrophysical Journal in January 2003. Due to the size limitations of astro-ph, no figures are in the astro-ph version. A full copy of the paper with figures can be found at http://www-int.stsci.edu/~mregan/nucrings.pdf