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

A new approach to construct initial data for binary systems with neutron star components is introduced. The approach is a generalization of the puncture initial data method for binary black holes based on Bowen-York solutions to the momentum constraint. As with binary black holes, the method allows setting orbital configurations with direct input from post-Newtonian approximations and involves solving only the Hamiltonian constraint. The effectiveness of the method is demonstrated with evolutions of double neutron star and black hole–neutron star binaries in quasicircular orbits.

Figure 1

ADM mass $M_{\mathrm{ADM}}$ (dots), rest mass $M_0$ (triangles), and $M_{*}W$ (squares) as a function of $P/M_{*}$ for a single NS. The solid line represents a fit to $M_{\mathrm{ADM}}=M_{*}+c{P}^2$.

Figure 2

Relative differences along the $x$ axis between the TOV solution and the corresponding solution for a TOV star with momentum $P/M_{*}=0.1$. The top panel shows the relative differences $\delta \rho$ in total mass energy, and bottom panel shows those in the conformal factor $\delta \mathrm{\Phi }$.

Figure 3

Density $\rho$ profiles along the $x$ axis for a TOV star with $P/M_{*}=0.1$ at various times throughout the evolution. The profiles have been normalized to the initial central density ${\rho }_c$ and shifted to be centered at $x=0$.

Figure 4

Density $\rho$ profiles for the same case as in Fig. 3 but along the $y$ direction. Because of reflection symmetry, only half of the profile is shown. The profiles have been normalized to the initial central density ${\rho }_c$ and intersect with the point of maximum density along the $x$ axis at all times.

Figure 5

Evolution of the central density of the star in Fig. 3 normalized to the initial central value ${\rho }_c$.

Figure 6

Evolution of the central density of the spinning star model for $J/M_{*}^2$ ranging from 0 to 0.075, with densities normalized to the initial central value ${\rho }_c$.

Figure 7

Density $\rho$ profiles along the $z$ axis (rotation axis) for a TOV star with $J/M_{*}^2=0.05$ at various times throughout the evolution. The profiles have been normalized to the initial central density ${\rho }_c$.

Figure 8

Density $\rho$ profiles along the $x$ axis for the TOV star in Fig. 7.

Figure 9

Nonspinning NS binary system.

Figure 10

Amplitude (left panel) and phase (right panel) differences of the Weyl scalar ${\mathrm{\Psi }}_4$ for three different resolutions of nonspinning DNS system simulations. The resolutions in the finest grid are 0.45 km (low), 0.315 km (medium), and 0.225 km (high). The (medium–high) resolution is also presented in black rescaled with a factor of 2.49, corresponding to second-order convergence.

Figure 11

Rest-mass density snapshots from the nonspinning DNS binary evolution. Panels (a), (b), and (c) show the $xy$-plane, and panel (d) shows the $xz$-plane All densities are in units of $\mathrm{g}{\mathrm{cm}}^{-3}$, and distances are in units of $M=3.14M_{\odot }$.

Figure 12

Spinning NS binary system.

Figure 13

Rest-mass density snapshots from the spinning DNS binary evolution. Panels (a), (b), and (c) show the $xy$-plane, and panel (d) shows the $xz$-plane All densities are in units of $\mathrm{g}{\mathrm{cm}}^{-3}$, and distances are in units of $M=3.14M_{\odot }$.

Figure 14

BH-NS binary system.

Figure 15

Rest-mass density snapshots from the BHNS binary evolution. Panels (a), (b), and (c) show the $xy$-plane, and panel (d) shows the $xz$-plane All densities are in units of $\mathrm{g}{\mathrm{cm}}^{-3}$, and distances are in units of $M=3.14M_{\odot }$.