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arXiv · 0906.0096

Relativistic tidal properties of neutron stars

Thibault Damour·Alessandro Nagar
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Abstract

We study the various linear responses of neutron stars to external relativistic tidal fields. We focus on three different tidal responses, associated to three different tidal coefficients: (i) a gravito-electric-type coefficient Gμ_\ell=[length]^{2\ell+1} measuring the \ell^{th}-order mass multipolar moment GM_{a_1... a_\ell} induced in a star by an external \ell^{th}-order gravito-electric tidal field G_{a_1... a_\ell}; (ii) a gravito-magnetic-type coefficient Gσ_\ell=[length]^{2\ell+1} measuring the \ell^{th} spin multipole moment G S_{a_1... a_\ell} induced in a star by an external \ell^{th}-order gravito-magnetic tidal field H_{a_1... a_\ell}; and (iii) a dimensionless ``shape'' Love number h_\ell measuring the distortion of the shape of the surface of a star by an external \ell^{th}-order gravito-electric tidal field. All the dimensionless tidal coefficients Gμ_\ell/R^{2\ell+1}, Gσ_ł/R^{2\ell+1} and h_\ell (where R is the radius of the star) are found to have a strong sensitivity to the value of the star's ``compactness'' c\equiv GM/(c_0^2 R) (where we indicate by c_0 the speed of light). In particular, Gμ_ł/R^{2ł+1}\sim k_\ell is found to strongly decrease, as c increases, down to a zero value as c is formally extended to the ``black-hole (BH) limit'' c^{BH}=1/2. The shape Love number h_\ell is also found to significantly decrease as c increases, though it does not vanish in the formal limit c\to c^{BH}. The formal vanishing of μ_\ell and σ_\ell as c\to c^{BH} is a consequence of the no-hair properties of black holes; this suggests, but in no way proves, that the effective action describing the gravitational interactions of black holes may not need to be augmented by nonminimal worldline couplings.

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Thibault Damour, Alessandro Nagar. 2009-12-03. Relativistic tidal properties of neutron stars. https://doi.org/10.1103/physrevd.80.084035

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