Initial data for binary neutron stars with adjustable eccentricity
arXiv:1408.4136 · doi:10.1103/PhysRevD.90.084043
Abstract
Binary neutron stars in circular orbits can be modeled as helically symmetric, i.e., stationary in a rotating frame. This symmetry gives rise to a first integral of the Euler equation, often employed for constructing equilibrium solutions via iteration. For eccentric orbits, however, the lack of helical symmetry has prevented the use of this method, and the numerical relativity community has often resorted to constructing initial data by superimposing boosted spherical stars without solving the Euler equation. The spuriously excited neutron star oscillations seen in evolutions of such data arise because such configurations lack the appropriate tidal deformations and are stationary in a linearly comoving---rather than rotating---frame. We consider eccentric configurations at apoapsis that are instantaneously stationary in a rotating frame. We extend the notion of helical symmetry to eccentric orbits, by approximating the elliptical orbit of each companion as instantaneously circular, using the ellipse's inscribed circle. The two inscribed helical symmetry vectors give rise to approximate instantaneous first integrals of the Euler equation throughout each companion. We use these integrals as the basis of a self-consistent iteration of the Einstein constraints to construct conformal thin-sandwich initial data for eccentric binaries. We find that the spurious stellar oscillations are reduced by at least an order of magnitude, compared with those found in evolutions of superposed initial data. The tidally induced oscillations, however, are physical and qualitatively similar to earlier evolutions. Finally, we show how to incorporate radial velocity due to radiation reaction in our inscribed helical symmetry vectors, which would allow one to obtain truly non-eccentric initial data when our eccentricity parameter is set to zero.
23 pages, 10 figures
References in corpus (25)
- Constraints on a phenomenologically parameterized neutron-star equation of state
- Gravitational waves from scattering of stellar-mass black holes in galactic nuclei
- The Evolution of Compact Binary Star Systems
- Calibration of Moving Puncture Simulations
- Reducing orbital eccentricity in binary black hole simulations
- Tidal effects in binary neutron star coalescence
- A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
- Reducing phase error in long numerical binary black hole evolutions with sixth order finite differencing
- Improved constrained scheme for the Einstein equations: An approach to the uniqueness issue
- Waveless Approximation Theories of Gravity
- Eccentric binary black-hole mergers: The transition from inspiral to plunge in general relativity
- Reducing eccentricity in black-hole binary evolutions with initial parameters from post-Newtonian inspiral
- Observing complete gravitational wave signals from dynamical capture binaries
- Initial data for black hole-neutron star binaries: a flexible, high-accuracy spectral method
- An introduction to relativistic hydrodynamics
- Dynamical Capture Binary Neutron Star Mergers
- Initial data for binary neutron stars with arbitrary spins
- Conformal Thin-Sandwich Solver for Generic Initial Data
- Reducing spurious gravitational radiation in binary-black-hole simulations by using conformally curved initial data
- Numerical evolution of multiple black holes with accurate initial data
- An efficient iterative method to reduce eccentricity in numerical-relativity simulations of compact binary inspiral
- Accuracy Issues for Numerical Waveforms
- Magnetohydrodynamics in stationary and axisymmetric spacetimes: a fully covariant approach
- Quasi-equilibrium models for triaxially deformed rotating compact stars
- Are different approaches to constructing initial data for binary black hole simulations of the same astrophysical situation equivalent?