Initial data for binary neutron stars with adjustable eccentricity

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 e is set to zero.

Comprehensive comparison of numerical relativity and effective-one-body results to inform improvements in waveform models for binary neutron star systems

“…The density snapshots are gauge-dependent quantities, therefore, Fig To compute results for the periastron advance we consider as a representative case the setup MS1b-150100. Reliably extracting this information from NR data, as described in Appendix A, requires an additional simulation with higher eccentricity that we perform following the approach of [56,74].…”

Binary neutron stars with generic spin, eccentricity, mass ratio, and compactness: Quasi-equilibrium sequences and first evolutions

“…Other codes include the Princeton group's multigrid solver [16], BAM's multigrid solver [17], the COCAL code [18], the SpEC code's spectral solver [19,20], and our spectral code SGRID [21][22][23]. All these codes are incapable of reaching certain portions of the possible binary neutron star parameter space.…”

“…We also presented a method for generating consistent binary neutron star initial data with arbitrary eccentricity, including the possibility of reducing the eccentricity present in standard quasicircular data, in Ref. [17]. Concurrently, Ref.…”

“…Such methods can only be applied to consistent initial data if one appropriately generalizes the helical Killing vector, as was only done recently in Refs. [17,28]. Finally, there is no known way of including magnetic fields consistently in binary neutron star initial data-they are added by hand in all studies that include them.…”

New code for quasiequilibrium initial data of binary neutron stars: Corotating, irrotational, and slowly spinning systems

“…These more computationally expensive solutions are expected to respect the circularity of an orbit better than the ones coming from conformally flat initial data, which in addition seem to suppress tidal effects as the compactness of the stars increases. A conformally flat geometry can still be used to produce low eccentricity initial data if one uses ideas similar to those applied to the binary black hole problem [60], as they were implemented in [61,62].…”