Extended I-Love relations for slowly rotating neutron stars

Abstract

Observations of gravitational waves from inspiralling neutron star binaries-such as GW170817can be used to constrain the nuclear equation of state by placing bounds on stellar tidal deformability. For slowly rotating neutron stars, the response to a weak quadrupolar tidal field is characterized by four internal-structure-dependent constants called "Love numbers". The tidal Love numbers k el 2 and k mag 2 measure the tides raised by the gravitoelectric and gravitomagnetic components of the applied field, and the rotational-tidal Love numbers f o and k o measure those raised by couplings between the applied field and the neutron star spin. In this work we compute these four Love numbers for perfect fluid neutron stars with realistic equations of state. We discover (nearly) equation-of-state independent relations between the rotational-tidal Love numbers and the moment of inertia, thereby extending the scope of I-Love-Q universality. We find that similar relations hold among the tidal and rotational-tidal Love numbers. These relations extend the applications of I-Love universality in gravitational-wave astronomy. As our findings differ from those reported in the literature, we derive general formulas for the rotational-tidal Love numbers in post-Newtonian theory and confirm numerically that they agree with our general-relativistic computations in the weak-field limit. * jgagn129@uottawa.ca † stephen.green@aei.mpg.deThe scaled Love numbers are the quantities that enter into the universality relations [30], whereas the genuine Love numbers remain finite and nonzero in the zero-compactness limit, GM/c 2 R → 0 [27].Section II is devoted to justifying our restriction to quadrupolar applied tides. We show how the various tidal fields and Love numbers appear in the metric and we identify some of their physical effects. Supposing the tidal fields are sourced by a binary companion, we estimate the size of each term, and we argue that higher multipole terms make a smaller contribution to the metric. We note, however, that the higher-terms could still contribute significantly to the waveform itself, and this should be investigated in future work.A complete analysis of the deformation of a slowly rotating body subject to a quadrupolar tidal field was carried out by 31], and separately by Pani, Gualtieri, Maselli and Ferrari [26,32], who also investigated the effect of an octupolar tidal field and worked to second order in spin. The two frameworks differ primarily in their assumptions about the fluid state: Pani, Gualtieri and Ferrari hold the fluid completely static [26], while Landry and Poisson allow it to develop tidal currents [10] in accordance with the circulation theorem of relativistic hydrodynamics [33]. Because these fluid motions are vorticity-free in a nonrotating star, the latter state has been termed irrotational. The static state is incompatible with the Einstein equation except in axisymmetry [29]. In this work we follow the framework of Landry and Poisson, which we review in Sec. III.In Sec. IV, we compute the ...

Impact of high-order tidal terms on binary neutron-star waveforms

“…Our results agree with those of Ref. [37] and with the revised ones in Ref. [44] in the relevant regimes [71].…”

“…However, there exist some approximate EoSindependent relations, Σ i = Σ i (Λ i ), that connect the magnetic TLNs to the standard electric TLNs [44]. Notice that the magnetic TLNs depend on the properties of the fluid [34,37,70]. In particular, the magnetic TLNs for irrotational fluids or for static fluids have the opposite sign and the quasiuniversal relation also depends on the fluid properties.…”

Magnetic tidal Love numbers clarified

“…In particular, the static and irrotational magnetic TLNs satisfy two different approximately-universal relations, as discussed in Refs. [18,20], where some fits for such relations are pro-vided in both cases.…”

“…Meanwhile, in 2013 Yagi [21] used the result of DN to compute the effect of the magnetic TLNs in the waveform and to compute some quasi-universal relations [27,28] among TLNs of different parity and different multipole moments. In 2015, Landry and Poisson (hereafter, LP) discovered [3] that the magnetic TLNs depend on the properties of the fluid (see also [20,29]). In particular, they found that the magnetic TLNs for irrotational fluids or for static fluids are different and have the opposite sign.…”

“…In particular, they found that the magnetic TLNs for irrotational fluids or for static fluids are different and have the opposite sign. Consequently, the quasi-universal relations involving magnetic TLNs also depend on the fluid properties [18,20,30]. Thus, at the present stage we are left with three different types of magnetic TLNs: those computed by DN, those computed by BP, and those computed by LP for irrotational fluids.…”