Newtonian I-Love-Q relations: An enthalpy-based approach

Abstract

We present a pedagogical introduction to the I-Love-Q relations within Newtonian gravity using an enthalpy-based formulation of stellar structure. Introducing the specific enthalpy converts Euler's equation into a first integral of hydrostatic equilibrium and recasts the equation of state as a relation between the mass density and the enthalpy. Together with Poisson's equation, these relations provide a unified description of spherical equilibrium and deformations induced by rotation and tides. We illustrate the formalism with polytropic equations of state and a relativistic free Fermi gas. In Newtonian gravity, slow uniform rotation and a weak tidal field excite the same linear quadrupolar response, yielding the exact identity ${\bar{I}}^2\bar{Q}/\bar{\lambda }\equiv 1$ for the dimensionless (``bar'') observables---independently of the equation of state. This exact identity is distinguished from the approximate universality of the pairwise I-Love-Q relations, whose residual dependence on stellar structure is illustrated by the models considered in this work.

arXiv comment13 pages, 3 figures Submitted to European Journal of Physics