Initial data for binary neutron stars with adjustable eccentricity

摘要

Binary neutron stars in circular orbits can be modeled as helicallysymmetric, i.e., stationary in a rotating frame. This symmetry gives rise to afirst integral of the Euler equation, often employed for constructingequilibrium solutions via iteration. For eccentric orbits, however, the lack ofhelical symmetry has prevented the use of this method, and the numericalrelativity community has often resorted to constructing initial data bysuperimposing boosted spherical stars without solving the Euler equation. Thespuriously excited neutron star oscillations seen in evolutions of such dataarise because such configurations lack the appropriate tidal deformations andare stationary in a linearly comoving---rather than rotating---frame. Weconsider eccentric configurations at apoapsis that are instantaneouslystationary in a rotating frame. We extend the notion of helical symmetry toeccentric orbits, by approximating the elliptical orbit of each companion asinstantaneously circular, using the ellipse's inscribed circle. The twoinscribed helical symmetry vectors give rise to approximate instantaneous firstintegrals of the Euler equation throughout each companion. We use theseintegrals as the basis of a self-consistent iteration of the Einsteinconstraints to construct conformal thin-sandwich initial data for eccentricbinaries. We find that the spurious stellar oscillations are reduced by atleast an order of magnitude, compared with those found in evolutions ofsuperposed initial data. The tidally induced oscillations, however, arephysical and qualitatively similar to earlier evolutions. Finally, we show howto incorporate radial velocity due to radiation reaction in our inscribedhelical symmetry vectors, which would allow one to obtain truly non-eccentricinitial data when our eccentricity parameter $e$ is set to zero.