Keywords
moment of inertia
Lane-Emden equation
mass-radius diagrams
polytropic index
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Abstract
Newtonian polytropes are fundamental models in astrophysics that can represent self-gravitating systems such as stars and certain compact objects. Despite their popularity, however, it is striking that very little has been discussed in the literature about their moment of inertia. In this context, here, we aimed to analyze some integral and structural properties of Newtonian polytropes, with special emphasis on their moment of inertia. For this purpose, we studied the Lane-Emden equation and present both analytical and numerical solutions for different values of the polytropic index n. We also provide mass-radius diagrams and calculate the moment of inertia for various configurations. We found that the normalized moment of inertia I/MR2, as a function of the polytropic index n, follows a polynomial of the fourth order.
References
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