I-Love-Q relations in neutron stars and their applications to astrophysics, gravitational waves, and fundamental physics

Kent Yagi, Nicolás Yunes

Research output: Contribution to journalArticlepeer-review


The exterior gravitational field of a slowly rotating neutron star can be characterized by its multipole moments, the first few being the neutron star mass, moment of inertia, and quadrupole moment to quadratic order in spin. In principle, all of these quantities depend on the neutron star's internal structure, and thus, on unknown nuclear physics at supranuclear energy densities, all of which is usually parametrized through an equation of state. We here find relations between the moment of inertia, the Love numbers and the quadrupole moment (I-Love-Q relations) that do not depend sensitively on the neutron star's internal structure. Such universality may arise for two reasons: (i) these relations depend most sensitively on the internal structure far from the core, where all realistic equations of state mostly approach each other; (ii) as the neutron star compactness increases, the I-Love-Q trio approaches that of a black hole, which does not have an internal-structure dependence. Three important consequences derive from these I-Love-Q relations. On an observational astrophysics front, the measurement of a single member of the I-Love-Q trio would automatically provide information about the other two, even when the latter may not be observationally accessible. On a gravitational-wave front, the I-Love-Q relations break the degeneracy between the quadrupole moment and the neutron star spins in binary inspiral waveforms, allowing second-generation ground-based detectors to determine the (dimensionless) averaged spin to O(10)%, given a sufficiently large signal-to-noise ratio detection. On a fundamental physics front, the I-Love-Q relations allow for tests of general relativity in the neutron star strong field that are both theory and internal-structure independent. As an example, by combining gravitational-wave and electromagnetic observations, one may constrain dynamical Chern-Simons gravity in the future by more than six orders of magnitude more stringently than Solar System and table-top constraints.

Original languageEnglish (US)
Article number023009
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number2
StatePublished - Jul 19 2013
Externally publishedYes

ASJC Scopus subject areas

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


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