Quantitative Mapping of the Loeb Scale

Abstract: The recent discovery of a third interstellar object (ISO) 3I/ATLAS, following 1I/`Oumuamua and 2I/Borisov, has raised questions about the nature and origin of these enigmatic objects. With the Vera C. Rubin Observatory expected to discover dozens of new ISOs over the next decade, it is timely to use a classification scheme for their nature in the context of the recently proposed Loeb scale. Here, we provide a formalism for ranking ISOs quantitatively on the Loeb Scale in analogy to Sagan's formalism for mapping the Kardashev scale based on the energy output of technological civilizations.