Nonspherical Perturbations of 3D Boson Stars

Stable Boson Star (164^3 grid, .375 resolution)

Zerilli and Psi4 waveforms and modefits with the 12 quasinormal modes listed in Yoshida, Eriguchi and Futamase, 1994. We observe excellent agreement between these gravitational waveforms and modefits. See plot of coefficients at the bottom of the page for the contributions from each mode.

Strength of l=4 Zerilli Functions

For a perturbation proportional to the Y_20 spherical harmonic, we observe nonzero (l=2, m=0); (l=4, m=0) and (l=4, m=4) Zerilli signals. The strength of the l=4 Zerilli waveforms is roughly 20% of that of the (l=2, m=0) waveform. Consequently, the l=4 waveforms will not have a significant contribution to the energy emitted in gravitational waves.
Note: We don't understand why we get a significant signal for (l=4,m=4). In contrast, we observe the (l=4, m=2) signal to be totally insignificant. The perturbation (~m=0 harmonic) has no Phi dependence, while m=4 has a Exp[4*Phi] dependence (See a basic table with spherical harmonics).

Critical Star (164^3 grid, .25 resolution)

The critical and unstable systems are more dynamical after the placement of the perturbation. Consequently, the waveforms display a more complex precursor before ringing down in an exponentially decaying region. For the same relative perturbation ~ 0.01 Y_20 * scalar_field, the waveforms for the critical and unstable stars are larger than for the stable configuration.

Unstable Star (164^3 grid, .25 resolution)

Migration Attempt- large perturbation that takes away mass from a critical star (164^3 grid, .3 resoltution)

Under a large perturbation ~ -0.1 Y_20, the critical configuration oscillates and the central field density becomes spherically symmetric at late times. At the end of this run the star does not show signs of collapsing to a black hole. The second plots shows that the star tending to become spherically symmetric after a short time (even under this very large perturbation).

Note: This is just a first try that shows positive signs. Much Longer runs will be needed for a complete migration.

Coefficients of individual QNM's within modefits

We observe a spread of modes present within the gravitational wave signals. For our Y_lm perturbations we see insignificant contributions from the n=1,2,3 or n>11 QNM. We would need to understand the toy model for boson stars to come up with an explanation.

The last two tables show the difference in coefficients of QNMs from two perturbations weighted at different radial location. The coefficients of the perturbation weighted away from the origin possibly shows a slight shift towards lower modes.