Why I-Love-Q: Explaining why universality emerges in compact objects

Kent Yagi, Leo C. Stein, George Pappas, Nicolás Yunes, and Theocharis A. Apostolatos
Phys. Rev. D 90, 063010 – Published 23 September 2014

Abstract

Black holes are said to have no hair because all of their multipole moments can be expressed in terms of just their mass, charge and spin angular momentum. The recent discovery of approximately equation-of-state-independent relations among certain multipole moments in neutron stars suggests that they are also approximately bald. We here explore the yet unknown origin for this universality. First, we investigate which region of the neutron star’s interior and of the equation of state is most responsible for the universality. We find that the universal relation between the moment of inertia and the quadrupole moment is dominated by the star’s outer core, a shell of width 50%–95% of the total radius, which corresponds to the density range 10141015g/cm3. In this range, realistic neutron star equations of state are not sufficiently similar to each other to explain the universality observed. Second, we study the impact on the universality of approximating stellar isodensity contours as self-similar ellipsoids. An analytical calculation in the nonrelativistic limit reveals that the shape of the ellipsoids per se does not affect the universal relations much, but relaxing the self-similarity assumption can completely destroy it. Third, we investigate the eccentricity profiles of rotating relativistic stars and find that the stellar eccentricity is roughly constant, with variations of roughly 20%–30% in the region that matters to the universal relations. Fourth, we repeat the above analysis for differentially rotating, noncompact, regular stars and find that this time the eccentricity is not constant, with variations that easily exceed 100%, and moreover universality is lost. These findings suggest that universality arises as an emergent approximate symmetry: as one flows in the stellar-structure phase space from noncompact star region to the relativistic star region, the eccentricity variation inside stars decreases, leading to approximate self-similarity in their isodensity contours, which then leads to the universal behavior observed in their exterior multipole moments.

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  • Received 29 June 2014

DOI:https://doi.org/10.1103/PhysRevD.90.063010

© 2014 American Physical Society

Authors & Affiliations

Kent Yagi1, Leo C. Stein2, George Pappas3, Nicolás Yunes1, and Theocharis A. Apostolatos4

  • 1Department of Physics, Montana State University, Bozeman, Montana 59717, USA
  • 2Center for Radiophysics and Space Research, Cornell University, Ithaca, New York 14853 USA
  • 3School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
  • 4Department of Physics, Section of Astrophysics, Astronomy and Mechanics, University of Athens, Panepistimiopolis Zografos GR15783, Athens, Greece

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Issue

Vol. 90, Iss. 6 — 15 September 2014

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