I-Love relations for incompressible stars and realistic stars

Abstract

In spite of the diversity in the equations of state of nuclear matter, the recently discovered I-Love-Q relations [Yagi and Yunes, Science 341, 365 (2013)], which relate the moment of inertia, tidal Love number (deformability) and the spin-induced quadrupole moment of compact stars, hold for various kinds of realistic neutron stars and quark stars. While the physical origin of such universality is still a current issue, the observation that the I-Love-Q relations of incompressible stars can well approximate those of realistic compact stars hints at a new direction to approach the problem. In this paper, by establishing recursive post-Minkowskian expansion for the moment of inertia and the tidal deformability of incompressible stars, we analytically derive the I-Love relation for incompressible stars and show that the so obtained formula can be used to accurately predict the behavior of realistic compact stars from the Newtonian limit to the maximum mass limit.PACS numbers: 04.40. Dg, 04.25.Nx, 97.60.Gb, 95.30.Sf I. INTRODUCTIONRecently, Yagi and Yunes [1, 2] have discovered the so called "I-Love-Q universal relations" prevailing in compact stars, including both neutron stars (NSs) or quark stars (QSs). In such relations, the moment of inertia I, the quadrupole tidal Love number λ (or, more precisely, tidal deformability [3,4]), and the spin-induced quadrupole moment Q of compact stars are expressed in terms of one another, with the stellar mass M playing the role of a scaling parameter. Soon after the discovery of Yagi and Yunes [1,2], the I-Love-Q relations were generalized to several other cases, including binary systems with strong dynamical tidal field [5], magnetized NSs with sufficiently high rotation rates [6], rapidly-rotating stars [7,8], and higher-order multipole moments induced by either tidal forces or rotation [4,9,10].These relations are useful for several reasons [1,2]. First, they provide a link directly connecting the I-Love-Q triplet. Once the mass of a compact star is known, each one of of I, λ and Q can lead to the determination of the other two. Second, in the analysis of gravitational wave signals emitted during the late stages of NS-NS binary mergers, they can break the degeneracy between the contributions due to the quadrupole moment and the spin and hence enable more accurate measurement of the averaged spin of the system [1,2,11,12]. Third, they can identify the validity of other modified gravity theories such as the Chern-Simons gravity and the Eddington-inspired Born-Infeld (EiBI) gravity [1,2,13,14].On the other hand, the emergence of the I-Love-Q relations is also interesting from theoretical point of view. As is well known, the physical characteristics of NSs (or QSs), including mass, radius, and moment of inertia, are usually obscured by various uncertainties in the equation of state (EOS) of nuclear matter (or quark matter). In fact, nuclear physicists have been using different characteristics (e.g., the mass-radius relation, the maximum mass and gravitational wave spectrum) ...

Tidal Love numbers and moment–Love relations of polytropic stars

“…Therefore, these relations can be considered as universal only for sufficiently stiff stars. Thus, our analytical form of the I-Love relation (or the multipolar moment-Love relations) further supports the proposal reported in Sham et al (2015); Chan et al (2015Chan et al ( , 2016.…”

“…Its physical origin is certainly an interesting issue. It has been observed and proved in the cases of the modified Tolman model and self-bound stars, which both possess non-zero surface mass density, that the I-Love relation is stationary in the incompressible limit (Chan et al 2014;Sham et al 2015;Chan et al 2015Chan et al , 2016. Along a similar line of thought, using our perturbation solutions to the tidal Love numbers and the mass moments, we have established in the present paper that the I-Love relation is stationary with respect to arbitrary density changes in the incompressible limit, and generalised the stationarity to cases where l 2 (see Section 8.2).…”

“…Yagi & Yunes (2013a) attempted to attribute these universal relations of compact stars to the no-hair theorem, which states that black holes do not have interior structure, in the black hole limit. On the other hand, several studies (Sham et al 2015;Chan et al 2014Chan et al , 2015Chan et al , 2016 indicate that the I-Love-Q relations indeed originate from the facts that (i) compact stars (including both NSs and QSs) are stiff enough to be considered as incompressible during tidal deformation, and (ii) the I-Love-Q relations are stationary and remarkably flat around the incompressible limit. As a matter of fact, the I-Love-Q relations still prevail in the Newtonian limit and their accuracies were found to worsen towards the high compactness regime (Sham et al 2015;Chan et al 2015Chan et al , 2016.…”

Universal Relations and Alternative Gravity Theories

“…(2) Testing the validity of the I-Love-Q relations offers another possibility for testing the equation of state. As it has been demonstrated [32][33][34], the universality of the I-Love-Q relations comes from properties of the equation of state that are related to the fact that the equation of state for compact objects is close to being incompressible. Deviations from being incompressible would change the different relations and in principle could also introduce some spin dependence.…”

Non-validity of I–Love–Q Relations for Hot White Dwarf Stars

“…The I-Love-Q and I-Love relations, respectively, were investigated for incompressible and realistic stars; it was shown that the EoS-independent behaviour of the I-Love-Q relation can be attributed to its incompressible limit (Sham et al 2015;Chan et al 2015). Moreover, these relations were also calculated by Pani (2015) for exotic objects such as thin-shell gravastars at zero temperature, without assessing their validity.…”