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Multipole Love relations

Kent Yagi*

  • Department of Physics, Montana State University, Bozeman, Montana 59717, USA

  • *kyagi@physics.montana.edu
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Phys. Rev. D 89, 043011 – Published 20 February, 2014Errata Phys. Rev. D 96, 129904 (2017); Phys. Rev. D 97, 129901 (2018)

DOI: https://doi.org/10.1103/PhysRevD.89.043011

Abstract

Gravitational-wave observations in the near future may allow us to measure tidal deformabilities of neutron stars, which leads us to the understanding of physics at nuclear density. In principle, the gravitational waveform depends on various tidal parameters, which correlate strongly. Therefore, it would be useful if one can express such tidal parameters with a single parameter. Here, we report on universal relations among various ℓth (dimensionless) electric, magnetic, and shape tidal deformabilities in neutron stars and quark stars that do not depend sensitively on the equation of state. Such relations allow us to break the degeneracy among the tidal parameters. In this paper, we focus on gravitational waves from nonspinning neutron-star binary inspirals. We first derive the leading contribution of the ℓth electric and ℓ=2 magnetic tidal deformabilities to the gravitational-wave phase, which enters at 2ℓ+1 and 6 post-Newtonian orders relative to the leading Newtonian one, respectively. We then calculate the useful number of gravitational-wave cycles and show that not only the ℓ=2 but also ℓ=3 electric tidal deformabilities are important for parameter estimation with third-generation gravitational-wave detectors such as LIGO III and Einstein Telescope. Although the correlation between the ℓ=2 and ℓ=3 electric tidal deformabilities deteriorate the measurement accuracy of the former deformability parameter, one can increase its measurement accuracy significantly by using the universal relation. We provide a fitting formula for the LIGO III noise curve in the appendixes.

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Errata

Erratum: Multipole Love relations [Phys. Rev. D 89, 043011 (2014)]

Kent Yagi
Phys. Rev. D 96, 129904 (2017)

Erratum: Multipole Love relations [Phys. Rev. D 89, 043011 (2014)]

Kent Yagi
Phys. Rev. D 97, 129901 (2018)

Article Text

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Phys. Rev. D 89, 043011– Published 20 February, 2014
  • Received 4 November 2013

© 2014 American Physical Society

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