Nonbarred ringed galaxies are relatively normal galaxies showing bright rings of star formation in spite of lacking a strong bar. This morphology is interesting because it is generally accepted that a typical ring forms when material collects near a resonance, set up by the pattern speed of a bar or bar-like perturbation. Our goal in this paper is to examine whether the ring star formation properties are related to the non-axisymmetric gravity potential in general. For this purpose, we obtained H{alpha} emission line images and calculated the line fluxes and star formation rates (SFRs) for 16 nonbarred SA galaxies and four weakly barred SAB galaxies with rings. For comparison, we combine our observations with a re-analysis of previously published data on five SA, seven SAB, and 15 SB galaxies with rings, three of which are duplicates from our sample. With these data, we examine what role a bar may play in the star formation process in rings. Compared to barred ringed galaxies, we find that the inner ring SFRs and H{alpha}+[N ii] equivalent widths in nonbarred ringed galaxies show a similar range and trend with absolute blue magnitude, revised Hubble type, and other parameters. On the whole, the star formation properties of inner rings, excluding the distribution of H ii regions, are independent of the ring shapes and the bar strength in our small samples. We confirm that the deprojected axis ratios of inner rings correlate with maximum relative gravitational force Q_g; however, if we consider all rings, a better correlation is found when local bar forcing at the radius of the ring, Q_r, is used. Individual cases are described and other correlations are discussed. By studying the physical properties of these galaxies, we hope to gain a better understanding of their placement in the scheme of the Hubble sequence and how they formed rings without the driving force of a bar.
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