The Physical and Mathematical Meaning of Temperature and Its Implications for Astronomy

Temperatures reported for astronomical objects are commonly extreme, and all are ascertained indirectly, using spectroscopy. However, narrow spectral peaks record microscopic behavior (transitions), whereas temperature is a macroscopic (bulk) feature of an object. Using macroscopic theories of heat, light, and their transport, we show that temperature is best defined in terms of the radiant flux of an object (Stefan–Boltzmann law)—including that from large gas bodies—because this flux defines which objects are hotter or colder, and because relevance to mathematical order is the essential attribute of any measurable quantity. Laboratory examples further show that spectroscopic determinations of temperature require the following: (1) use of a large spectral range relevant to that temperature; (2) observation of the unique peak shape characteristic of thermal emissions; (3) accounting for reflections at surfaces; and, most importantly, (4) that conditions are optically thick, a condition fostered by large object size and high temperatures. Temperature of monatomic gas is accurately described by classical kinetic theory because molecular translations are unaffected by electron dynamics. Inelastic molecular collisions provide continuous thermal emissions under optically thick conditions attained in immense astronomical environments. We show how thermal and non-thermal spectroscopic features can be distinguished. Our findings are applied to star-forming regions, intergalactic media, lightning, the Sun’s surface and the corona. Our results resolve long-standing problems regarding heat sources.