Evolving spherical boson stars on a 3D Cartesian grid

Abstract

A code to evolve boson stars in 3D is presented as the starting point for the evolution of scalar field systems with arbitrary symmetries. It was possible to reproduce the known results related to perturbations discovered with 1D numerical codes in the past, which include evolution of stable and unstable equilibrium configurations. In addition, the apparent and event horizons masses of a collapsing boson star are shown for the first time. The present code is expected to be useful at evolving possible sources of gravitational waves related to scalar field objects and to handle toy models of systems perturbed with scalar fields in 3D.

Evolution of 3D boson stars with waveform extraction

“…The simulations shown here are performed using the fully general 3D simulation code presented in [20], which is based on the Cactus Computational Toolkit [21]. The existence of the rapidly damping quasinormal modes predicted by Yoshida et al is confirmed numerically.…”

“…In the continuum limit, one should observe only the high frequency oscillations. Reference [20] has shown that the amplitude of the radial oscillation converges toward zero as the resolution is improved and that in the spherical case no high frequency oscillations appear. For this run at a resolution of x = y = z = 0.375, the maximum of the metric has risen only from about g rr max = 1.166 to g rr max = 1.170.…”

“…In this case a uniformly weighted perturbation proportional to a linear combination of Y 20 and Y 22 (amplitudes 20 = 0.032 and 22 = 0.026, respectively) was applied. Figure 6(a) presents the extracted Zerilli = 2 (both m = 0 and m = 2) waveforms for a stable star (model 1, 20 = 0.032. Although no explicit radial perturbation was applied, numerical perturbations due to grid discretization (resolution x = y = z = 0.375) impose a slight radial perturbation on the system.…”

“…The weighted perturbation was centred at a radius of R p = 3.025, which is about half the 95% radius of the star. This was a pure Y 20 perturbation with 20 = 0.016 in equation (17). The data were then passed through the IVP and the evolution was tracked using the 3D code.…”

“…The nonspherical perturbations for the systems are parametrized by 20 = 0.128 and 22 = 0.104 (using equation (17)). The first simulation, denoted Run 1, has a radial amplification of µ = 1.01 while the second, denoted Run 2, has a radial amplification of µ = 1.03.…”