The I-Love universal relation for polytropic stars under Newtonian gravity

TL;DR

This paper investigates the I-Love universal relation for polytropic stars, demonstrating its robustness in Newtonian gravity and its applicability to observational data of solar system bodies, with implications for exoplanet characterization.

Contribution

It provides a theoretical derivation of the I-Love relation for polytropic stars under Newtonian gravity and validates it against observational data, highlighting its potential for exoplanet studies.

Findings

The I-Love relation varies by 1% to 10% across different polytropic indices.

The theoretical relation aligns well with observational data of planets and moons.

It can be used to estimate stellar properties when some data is known.

Abstract

The moment of inertia and tidal deformability of idealized stars with polytropic equations of state (EOSs) are numerically calculated under both Newtonian gravity and general relativity (GR). The results explicitly confirm that the relation between the moment of inertia and tidal deformability, parameterized by the star's mass, exhibits variations of 1% to 10% for different polytropic indices in Newtonian gravity and GR, respectively. This indicates a more robust I-Love universal relation in the Newtonian framework. The theoretically derived I-Love universal relation for polytropic stars is subsequently tested against observational data for the moment of inertia and tidal deformability of the 8 planets and some moons in our solar system. The analysis reveals that the theoretical I-Love universal relation aligns well with the observational data, suggesting that it can serve as an empirical relation. Consequently, it enables the estimation of either the moment of inertia or the tidal deformability of an exoplanet if one of these quantities, along with the mass of the exoplanet, is known.