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Nonspherical Perturbations of 3D Boson Stars

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Nonspherical Perturbations : scalar field pert = epsilon x Y_lm

We investigate the evolution of boson stars under `pure' nonspherical perturbations that are proportional to spherical harmonics. Under such perturbations it is anticipated that equilibrium boson star configurations will be stable (even for configurations that are unstable or critical in nature with respect to spherical perturbations). This is due to the results of [Yoshida, Eriguchi and Futamase, 1994] in which quasinormal modes frequencies with both real and imaginary parts are found to exist for various models of boson stars. We perform waveform extractions for l=2 Zerilli functions and the Newman-Penrose scalar Psi4 for nonspherical perturbations applied to several equilibrium configurations.

Quasinormal Modes of l=2 for a Stable Boson Star of central density 0.1414 [Yoshida, Eriguchi and Futamase, 1994]
Mode Re[frequency] Im[frequency]
1 1.9823 0.099616
2 2.0197 0.10009
3 2.0703 0.1083
4 2.1159 0.11529
5 2.1663 0.11872
6 2.2173 0.1238
7 2.269 0.12699
8 2.3223 0.13047
9 2.3756 0.13333
10 2.4301 0.13562
11 2.4848 0.1377
12 2.5406 0.13923

Scalar field pert = 0.01 Y_20



Mode Contribution
1 0.000388
2 0.000380
3 0.0016
4 0.02527
5 0.1238
6 0.3415
7 0.510
8 0.5709
9 0.464
10 0.241
11 0.0837
12 0.00887

Scalar field pert = 0.01 Y_20 + 0.01 Y_22

Nonspherical Perturbations : "spherical pert" weighted on the z axis

Non-spherical Perturbations : numerical resolution perturbations on spherical stars

Figure 1
Model Grid Size Resolution
Stable star 128x128x124 dx=0.5,dy=0.5,dz=0.516
Critical star 128x128x124 dx=0.4,dy=0.4,dz=0.416
Unstable star 128x128x124 dx=0.4,dy=0.4,dz=0.416
Figure 2
Perturbation Type Grid Size Resolution
Axisymmetric 128x128x124 dx=0.4,dy=0.4,dz=0.416
Nonaxisymmetric 128x126x124 dx=0.4,dy=0.408,dz=0.416

Convergence of the IVP Solver


We consider a stable branch boson star with central field density 0.1414. The stable star is perturbed by taking a spherically perturbed configuration (of size which adds 7% to the mass of the star) and weighting the configuration preferentially in the z direction, creating a nonspherical perturbation. An approximate solution to the Hamiltonian constraint equation is obtained from the Initial Value Problem solver after providing the nonspherical configuration as input.