Toward realistic and practical no-hair relations for neutron stars in the nonrelativistic limit

Katerina Chatziioannou, Kent Yagi, Nicolás Yunes

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number064030
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number6
StatePublished - Sep 17 2014
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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