1202.3565 (Donato Bini et al.)

Effective action approach to higher-order relativistic tidal
interactions in binary systems and their effective one body description    [PDF]

Donato Bini, Thibault Damour, Guillaume Faye

The gravitational-wave signal from inspiralling neutron-star--neutron-star
(or black-hole--neutron-star) binaries will be influenced by tidal coupling in
the system. An important science goal in the gravitational-wave detection of
these systems is to obtain information about the equation of state of neutron
star matter via the measurement of the tidal polarizability parameters of
neutron stars. To extract this piece of information will require to have
accurate analytical descriptions of both the motion and the radiation of
tidally interacting binaries. We improve the analytical description of the late
inspiral dynamics by computing the next-to-next-to-leading order relativistic
correction to the tidal interaction energy. Our calculation is based on an
effective-action approach to tidal interactions, and on its transcription
within the effective-one-body formalism. We find that second-order relativistic
effects (quadratic in the relativistic gravitational potential $u=G(m_1
+m_2)/(c^2 r)$) significantly increase the effective tidal polarizability of
neutron stars by a distance-dependent amplification factor of the form $1 +
\alpha_1 \, u + \alpha_2 \, u^2 +...$ where, say for an equal-mass binary,
$\alpha_1=5/4=1.25$ (as previously known) and $\alpha_2=85/14\simeq6.07143$ (as
determined here for the first time). We argue that higher-order relativistic
effects will lead to further amplification, and we suggest a Pad\'e-type way of
resumming them. We recommend to test our results by comparing
resolution-extrapolated numerical simulations of inspiralling-binary neutron
stars to their effective one body description.

View original: http://arxiv.org/abs/1202.3565