The manner in which gas accretes and orbits within circumnuclear rings has direct implications for the star formation process. In particular, gas may be compressed and shocked at the inflow points, resulting in bursts of star formation at these locations. Afterwards the gas and young stars move together through the ring. In addition, star formation may occur throughout the ring, if and when the gas reaches sufficient density to collapse under gravity. These two scenarios for star formation in rings are often referred to as the `pearls on a string and `popcorn paradigms. In this paper, we use new Herschel PACS observations, obtained as part of the KINGFISH Open Time Key Program, along with archival Spitzer and ground-based observations from the SINGS Legacy project, to investigate the heating and cooling of the interstellar medium in the nearby star-forming ring galaxy, NGC4736. By comparing spatially resolved estimates of the stellar FUV flux available for heating, with the gas and dust cooling derived from the FIR continuum and line emission, we show that while star formation is indeed dominant at the inflow points in NGC 4736, additional star formation is needed to balance the gas heating and cooling throughout the ring. This additional component most likely arises from the general increase in gas density in the ring over its lifetime. Our data provide strong evidence, therefore, for a combination of the two paradigms for star formation in the ring in NGC4736.
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