2014/06/30 by Katerina Chatziioannou, Kent Yagi, Nicolás Yunes +1 · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · #Astrophysics #Classical mechanics #Equation of state #Gamma-ray bursts and supernovae #Gravitation #High-pressure geophysics and materials #Multipole expansion #Neutron star #Physics #Polytrope #Polytropic process #Pulsars and Gravitational Waves Research #Quadrupole #Quantum mechanics #Universality (dynamical systems) #gr-qc
paper · pdf · doi:10.1103/physrevd.90.064030
10 pages, 5 figures, published version
openalex publication_date 2014/09/17 · arxiv created 2014/09/30 · arxiv updated 2014/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The gravitational properties of astrophysical objects depend sensitively on their internal structure. In Newtonian theory, the gravitational potential of a rotating star can be fully described by an infinite number of multipole moments of its mass distribution. Recently, this infinite number of moments for uniformly-rotating stars were shown semianalytically to be expressible in terms of just the first three: the mass, the spin, and the quadrupole moment of the star. The relations between the various lower multipole moments were additionally shown to depend weakly on the equation of state, when considering neutron stars and assuming single polytropic equations of state. Here we extend this result in two ways. First, we show that the universality also holds for realistic equations of state, thus relaxing the need to use single polytropes. Second, we derive purely analytical universal relations by perturbing the equations of structure about an n=0 polytrope that reproduce semianalytic results to O(1%). We also find that the linear-order perturbation vanishes in some cases, which provides further evidence and a deeper understanding of the universality.