I-Love-Q Relations in Neutron Stars and their Applications to Astrophysics, Gravitational Waves and Fundamental Physics (1303.1528v3)

Abstract: 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 supra-nuclear energy densities. 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. 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 $\mathcal{O}(10)%$, 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 6 orders of magnitude more stringently than Solar System and table-top constraints.

• The paper demonstrates that the I-Love-Q relations exhibit universality, reducing dependence on the neutron star's equation of state.
• The paper shows that these relations enable astronomers to infer hard-to-measure parameters from observations, such as gravitational wave signals.
• The paper suggests that any deviations from these universal relations may indicate new physics beyond general relativity.

Analysis of I-Love-Q Relations in Neutron Stars

The paper conducted by Yagi and Yunes explores the properties of neutron stars (NSs) by examining the I-Love-Q relations, which connect the moment of inertia (I), the tidal Love numbers (Love), and the quadrupole moment (Q). The essential finding of this work is that these relationships do not depend heavily on the NS's internal structure, a property known as universality. This result holds over a range of plausible equations of state (EoS) governing the NS matter at supra-nuclear densities. This universality potentially arises because the relations depend significantly either on the NS's outer layers or resemble the behavior of black holes (BHs) at high compactness, which lack internal-structure dependence due to the no-hair theorem.

Main Findings and Implications

1. Universal Relations: The I-Love-Q relations are found to be almost independent of the EoS, indicating that once one of these parameters is measured, the others can be inferred without precise knowledge of the internal physics of the NS. This universality is robust for slowly-rotating NSs, i.e., systems where differential rotation and fast spins are not significant.
2. Applications in Observational Astrophysics: By utilizing the I-Love-Q relations, astronomers can infer properties of NSs that are difficult to measure directly. For example, if the moment of inertia is measured in a binary pulsar system, the quadrupole moment and Love number can be deduced. This is particularly useful in the paper of systems where direct measurements are challenging.
3. Gravitational Waves: In the arena of gravitational wave (GW) astrophysics, the I-Love-Q relations help break the degeneracy between spin-induced effects and the quadrupole moment in the waveform of binary NS mergers. This could enhance the capacity of GW detectors like LIGO to determine the spin parameters of colliding NSs, thus providing indirect but vital information about their internal structure.
4. Tests of General Relativity and Beyond: The ability to measure I and Love independently offers a means to test GR in the strong-field regime. Deviations from the predicted I-Love-Q relations could signal new physics beyond GR. For example, the paper outlines how such measurements could constrain alternative theories, like dynamical Chern-Simons gravity, beyond existing Solar System tests.

Theoretical and Future Directions

The implications of these findings are multi-faceted. They open avenues for testing fundamental physics using astrophysical observations, provide deeper insights into the structure of ultra-dense matter, and enhance our capacity to paper cosmic phenomena through GWs. The research encourages further investigation into rapidly rotating and potentially differentially rotating NSs, as well as the impact of magnetic fields and thermal effects on these relations. Future theoretical studies could also extend these techniques to explore the impacts of non-standard fields or exotic particles interacting with neutron stars, potentially leading to novel constraints on beyond-Standard Model physics.

In conclusion, Yagi and Yunes have presented a rigorous investigation into the physical properties of neutron stars, revealing a remarkable universality in the I-Love-Q relations. This work not only enhances our understanding of neutron stars but also further establishes them as critical laboratories for testing the laws of physics under the most extreme conditions observable in the universe. Such universality might be the key to unlocking new insights into the fundamental nature of gravity and the behavior of matter at ultrahigh densities.