Gravitomagnetic tidal currents in rotating neutron stars

Abstract

It was recently revealed that a rotating compact body responds dynamically when it is subjected to a gravitomagnetic tidal field, even when this field is idealized as time-independent. The dynamical response is characterized by time-changing internal currents, and it was suspected to originate from zero-frequency g-modes and r-modes driven by the tidal forces. In this paper we provide additional insights into the phenomenon by examining the tidal response of a rotating body within the framework of post-Newtonian gravity. This approach allows us to develop an intuitive picture for the phenomenon, which relies on the close analogy between post-Newtonian gravity and Maxwell's theory of electromagnetism. In this picture, the coupling between the gravitomagnetic tidal field and the body's rotational velocity is naturally expected to produce an unbalanced Lorentz-like force within the body, and it is this force that is responsible for the tidal currents. The simplicity of the fluid equations in the post-Newtonian setting allows us to provide a complete description of the zero-frequency modes and demonstrate their precise role in the establishment of the tidal currents. We estimate the amplitude of these currents, and find that for neutron-star binaries of relevance to LIGO, the scale of the velocity perturbation is measured in kilometers per second when the rotation period is comparable to 100 milliseconds. This estimate indicates that the tidal currents may have a significant impact on the physics of neutron stars near merger.Comment: 24 pages, 3 figures, final version to be published in Physical Review

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

“…at the equator. This figure differs only by a factor of σ from the post-Newtonian order-of-magnitude estimate of Poisson and Doucot [6].…”

“…As argued in Paper II, and shown convincingly by the post-Newtonian analysis of Ref. [6], the dynamical velocity perturbations represent time-varying internal currents which are driven by the zero-frequency modes of the fluid when the gravitomagnetic tidal field is allowed to couple to the body's spin. In this subsection, I calculate the amplitude of these currents at the equator of a neutron star in a binary system of relevance to LIGO.…”

“…They scale with the body's compactness like F o ∼ f o (R/M ) 5 and K o ∼ k o (R/M ) 5 ; the scaling of F o was foreseen in Paper I, and the scaling of K o was predicted by Ref. [6]. The dimensionless rotational-tidal Love numbers f o and k o are plotted as a function of compactness in Fig.…”

Extended I-Love relations for slowly rotating neutron stars

“…A post-Newtonian calculation of gravitomagnetic rotational-tidal deformations was performed by Poisson and Douçot in Ref. [61]. However, the authors were interested in effects other than the specific value of the gravitomagnetic rotational-tidal Love number k o , and consequently they only computed k o for the special case of an n = 1 polytrope.…”

Computer algebra in gravity research

“…Poisson and Douçot ( 2017 ) studied tidal currents in rotating neutron stars in a post-Newtonian setting. Poisson has said that the use of GRtensorIII was essential in the work.…”