Tidal deformation of a slowly rotating material body: Interior metric and Love numbers

Landry, Philippe

doi:10.1103/physrevd.95.124058

Cited by 40 publications

(68 citation statements)

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“…Generalizations to spinning bodies (beyond the scope of this work) have subsequently been given in Refs. [29][30][31][32].…”

Section: Previous Workmentioning

confidence: 99%

On the ambiguity in relativistic tidal deformability

Gralla

2018

Class. Quantum Grav.

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Abstract. The LIGO collaboration recently reported the first gravitational-wave constraints on the tidal deformability of neutron stars. I discuss an inherent ambiguity in the notion of relativistic tidal deformability that, while too small to affect the present measurement, may become important in the future. I propose a new way to understand the ambiguity and discuss future prospects for reliably linking observed gravitational waveforms to compact object microphysics.

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“…Generalizations to spinning bodies (beyond the scope of this work) have subsequently been given in Refs. [29][30][31][32].…”

Section: Previous Workmentioning

confidence: 99%

On the ambiguity in relativistic tidal deformability

Gralla

2018

Class. Quantum Grav.

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“…These were computed independently in 2009 by Binnington and Poisson [2] (hereafter, BP) and by Damour and Nagar [1] (hereafter, DN) by considering axial perturbations of a perfect-fluid star in general relativity (see also [26] for an earlier study by Favata in the context of post-Newtnonian theory). These perturbations can be reduced to a single second-order master equation; however, it has been previously noted that the master equation of BP and that of * paolo.pani@roma1.infn.it † leonardo.gualtieri@roma1.infn.it ‡ tiziano.abdelsalhin@roma1.infn.it § fjimenez@na.infn.it 1 When the object is spinning, angular momentum gives rise to spin-tidal coupling and to a new class of rotational TLNs [3,9,10,19,20]. In this note we focus on static objects so we shall not consider the rotational TLNs.…”

Section: Introductionmentioning

confidence: 99%

Magnetic tidal Love numbers clarified

et al. 2018

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In this brief note, we clarify certain aspects related to the magnetic (i.e., odd parity or axial) tidal Love numbers of a star in general relativity. Magnetic tidal deformations of a compact star had been computed in 2009 independently by Damour and Nagar [1] and by Binnington and Poisson [2]. More recently, Landry and Poisson [3] showed that the magnetic tidal Love numbers depend on the assumptions made on the fluid, in particular they are different (and of opposite sign) if the fluid is assumed to be in static equilibrium or if it is irrotational. We show that the zero-frequency limit of the Regge-Wheeler equation forces the fluid to be irrotational. For this reason, the results of Damour and Nagar are equivalent to those of Landry and Poisson for an irrotational fluid, and are expected to be the most appropriate to describe realistic configurations.

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“…The n = 1 polytrope results presented in Ref. [26] are also incompatible with our independent post-Newtonian calculation.The octupole rotational-tidal Love numbers have been calculated for polytropes by Landry [28], and for realistic-EoS NSs in the static fluid state by Pani, Gualtieri and Ferrari [26]. In Sec.…”

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confidence: 99%

“…Our models are chosen to be compatible with the maximum observed NS mass of approximately 2M [35,36], and they also respect the causal bound on the sound speed. We find that 1 Note that we redefine this scaled Love number relative to Landry and Poisson [27,28]: f o [here] ≡ f o [LP] + 5 3 k el 2 (see Sec. III F).…”

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confidence: 99%

Extended I-Love relations for slowly rotating neutron stars

et al. 2018

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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 ...

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Tidal deformation of a slowly rotating material body: Interior metric and Love numbers

Cited by 40 publications

References 40 publications

On the ambiguity in relativistic tidal deformability

On the ambiguity in relativistic tidal deformability

Magnetic tidal Love numbers clarified

Extended I-Love relations for slowly rotating neutron stars

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