THE ORIGIN OF THE FAR-INFRARED LUMINOSITY WITHIN THE SPIRAL GALAXY NGC-6946

High resolution, 45'', measurements of the 160 mum and Halpha luminosity have been examined at 158 locations within the spiral galaxy NGC 6946 in order to elucidate the origin of the far luminosity. After correcting the Halpha luminosity for extinction and extrapolating the 160 mum luminosity to a 40-1000 mum far infrared luminosity we find that the far infrared luminosity is comparable to that expected from the O and B stars which are required to ionize the hydrogen ps. The results show that the far infrared luminosity is in quantitative agreement with that expected from O and B stars at all locations within NGC 6946. Further, the IRAS HiRes 60 and 100 mum images of NGC 6946 indicate that the temperature of the dust primarily responsible for the far infrared luminosity is approximately 33 K (lambda-1) and similar to that expected for H II regions over the entire star-forming disk. The mass of dust required to radiate the 60 and 100 mum emission, measured for NGC 6946 by IRAS, is about a factor of 10 lower than the dust content of NGC 6946 estimated from the atomic and molecular gas masses and a Galactic gas/dust mass ratio. The most plausible explanation for the discrepancy is that the majority (approximately 90%) of the dust within NGC 6946 is radiating at wavelengths longward of 100 mum, and must therefore be cooler than the approximately 33 K dust that dominates the emission measured by IRAS. The 170 and 160 mum measurements of NGC 6946, obtained by Smith (1984) and Engargiola [ApJ, 76, 875 (1991)], provide independent support for large quantities of cold dust, as both the 160 and 170 mum flux measurements are significantly higher than would be expected if all the dust in NGC 6946 were radiating at the same temperature as that measured by IRAS. The mass of warm dust is used to constrain the mass of dust that radiates at wavelengths longward of 100 mum, and the shape of the far infrared spectral energy distribution is used to constrain the temperature of the dust. The observations require the bulk, approximately 90%, of the dust mass within NGC 6946 to be cold with a temperature less-than-or-equal-to 17 K. It has long been known that molecular gas dominates the interstellar medium within NGC 6946 and the temperature derived for the dust is consistent with that expected for molecular clouds. The far infrared luminosity of NGC 6946 is dominated by thermal emission from warm, approximately 33 K, dust even though most (approximately 90%) of the dust mass within NGC 6946 is much colder with a temperature of approximately 17 K. The ability for a small mass of warm dust to dominate the luminosity of significantly greater quantities of colder dust arises as a natural consequence of the strong temperature dependence of thermal emission.