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

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, all of which is usually parameterized 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 NS compactness increases, the I-Love-Q trio approaches that of a BH, 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 6 orders of magnitude more stringently than Solar System and table-top constraints.

Application of the Ghosh & Lamb Relation to the Spin-up/down Behavior in the X-ray Binary Pulsar 4U 1626–67

“…There, the pair of dashed lines indicate statistical 68% (χ 2 increment ∆χ 2 < 2.3 for 2 degrees of freedom) confidence limits, calculated by adding 5.5% systematic errors to the individual flux measurements [2]. The M-R relations from representative EOSs [SLy [14], APR [15] and Shen ( [16]; [17]) presented in Yagi and Yunes (2013)] are also shown.…”

Neutron stars, ungravity, and the I-Love-Q relations

“…Deformation due to rotation and tidal forces of the NS is the same in the Newtonian limit [14,48]. We keep this feature in the presence of UG, that is, λ * , rot = λ * , tid , and consider the rotational deformations in this work rather than solving differential equations as has been done in Ref.…”

“…We keep this feature in the presence of UG, that is, λ * , rot = λ * , tid , and consider the rotational deformations in this work rather than solving differential equations as has been done in Ref. [14]. In the Newtonian limit, for a spheroid shaped NS rotating around the z axis, the quadrupole moment tensor reads [49] …”

“…In the next subsections we analytically present the UG I-Love-Q relations, i.e., C * 's, in the Newtonian limit for n = 0 and n = 1 polytropes and compare them to the ordinary ones, i.e., C's [14].…”

“…therein). By combining the universal I-Love-Q relations with the information from gravitational wave measurements of binary pulsars (advanced LIGO [11], Virgo [12], and KAGRA [13]), one can get a unique, model-independent and internal-structure independent test of General Relativity [9,14] and obtain information on the EoS [15,16]. Regarding the universality of the I-Love-Q relations, it is also interesting to examine gravity models for which the dynamic features of NSs are altered.…”