Initial data for black hole–neutron star binaries: A flexible, high-accuracy spectral method

Abstract

We present a new numerical scheme to solve the initial value problem for black hole-neutron star binaries. This method takes advantage of the flexibility and fast convergence of a multidomain spectral representation of the initial data to construct high-accuracy solutions at a relatively low computational cost. We provide convergence tests of the method for both isolated neutron stars and irrotational binaries. In the second case, we show that we can resolve the small inconsistencies that are part of the quasiequilibrium formulation, and that these inconsistencies are significantly smaller than observed in previous works. The possibility of generating a wide variety of initial data is also demonstrated through two new configurations inspired by results from binary black holes. First, we show that choosing a modified Kerr-Schild conformal metric instead of a flat conformal metric allows for the construction of quasiequilibrium binaries with a spinning black hole. Second, we construct binaries in low-eccentricity orbits, which are a better approximation to astrophysical binaries than quasiequilibrium systems.

Black-hole–neutron-star mergers at realistic mass ratios: Equation of state and spin orientation effects

“…The free variables in the initial data (conformal metric, extrinsic curvature) are the weighted superposition of an isolated black hole in Kerr-Schild coordinates and of an isolated neutron star in isotropic coordinates, following the method developed by Lovelace et al [43] for binary black holes. A more detailed description of the modifications required to apply this method to black-hole-neutron-star systems is given in Foucart et al [40].…”

“…The initial data for these simulations are constructed as described in Foucart et al [40]. The constraints that Einstein's equations impose on the initial variables are solved in the extended conformal thin sandwich approximation [41], under the assumption that the system is in equilibrium in a frame rotating at angular velocity 0 and contracting with radial velocity Àv r .…”

Black hole-neutron star mergers: Effects of the orientation of the black hole spin

“…The system of elliptic equations is solved using the spectral elliptic solver SPELLS developed by the Cornell-Caltech collaboration [19], and initially used to construct initial data for binary black hole systems by Pfeiffer et al [18,20]. A detailed presentation of the methods used for the construction of BHNS initial data was given in Foucart et al [21]. Here, we limit ourselves to a brief summary plus a description of the changes made to accommodate the possibility of arbitrary spin orientation.…”

“…One known effect of the quasi-circular approximation is that the binary will have a nonzero eccentricity. The eccentricity can be decreased by modifying the initial values ofȧ 0 and Ω rot [24] (see also [21] for an application of that method to BHNS binaries) as long as the initial eccentricity and orbital phase can be accurately measured. Here, we only apply this technique when the spin of the BH is aligned with the orbital angular momentum of the binary.…”

Bowen-York-type initial data for binaries with neutron stars

“…The conformal thin sandwich approach requires solving a set of five elliptic equations for the conformal factor, lapse function and shift vector [12][13][14]. Many groups have used the Lorene code from the Meudon group [15,16] for this purpose, and other groups have developed their own infrastructure [17][18][19][20][21][22][23].…”