Toward Realistic and Practical No-Hair Relations for Neutron Stars in the Non-Relativistic Limit

Abstract

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 semi-analytically 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 semi-analytic results to $\mathcal{O}(1\%)$. We also find that the linear-order perturbation vanishes in some cases, which provides further evidence and a deeper understanding of the universality.

10 pages, 5 figures, published version

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• Multipole moments in scalar-tensor theory of gravity
• Unveiling the universality of I-Love-Q relations
• Relating Follicly-Challenged Compact Stars to Bald Black Holes
• Non-radial oscillations and global stellar properties of anisotropic compact stars using realistic equations of state
• Assessing equation of state-independent relations for neutron stars with nonparametric models
• Universal Relations for rapidly rotating neutron stars using supervised machine-learning techniques
• Quasi-universal relations in the context of future neutron star detections
• Perturbative solution to the Lane-Emden equation: An eigenvalue approach
• Tests of Classical Gravity with Radio Pulsars
• I-Love irrotationally
• Equation-of-State Independent Relations in Rapidly Rotating Hybrid Stars