GW1 - Sources of Gravitational Waves |
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Speaker |
Soares, Ivano Damiao |
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Coauthors |
Aranha, Rafael F.; Soares, Ivano Damiao; Tonini, Eduardo V. |
| Talk Title |
Gravitational Wave Luminosity and Net Momentum Flux in Head-on Mergers of Black Holes: Radiative Patterns and Mode-Mixing |
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Abstract |
We show that gravitational wave radiative patterns from a point test particle falling radially into a Schwarzschild black hole, as derived by Davis, Ruffini, Press and Price (Phys. Rev. Lett. 27, 1466 (1971)), are present in the nonlinear regime of head-on mergers of black holes. In the Bondi-Sachs characteristic formulation we express the gravitational wave (gw) luminosity and the net momentum flux in terms of the "news" functions. We evaluate the $(-2)$-spin-weighted multipole decomposition of these quantities via exact expressions valid in the nonlinear regime and defined at the future null infinity. Our treatment uses Robinson-Trautman dynamics, with characteristic initial data corresponding to the head-on merger of two black holes. We consider mass ratios in the range $0.01 \leq \alpha \leq 1 $. We obtain the exponential decay with $\ell$ of the total energy contributed by each multipole $\ell$, with an accurate linear correlation in the log-linear plot of the points up to $\alpha \simeq 0.7$. Above this mass ratio the contribution of the odd modes to the energy decreases faster than that of the even modes, leading to the breaking of the linear correlation; for $\alpha=1$ the energy in all odd modes is zero. The dominant contribution to the total radiated energy comes from the quadrupole mode $\ell=2$ corresponding to about $\simeq 84\%$ for small mass ratios, up to $\simeq 99.8\%$ for the limit mass ratio $\alpha=1$. The total rescaled radiated energy $E^{\rm total}_W/m_0 \alpha^2$ decreases linearly with decreasing $\alpha$, yielding for the point particle limit $\alpha \rightarrow 0$ the value $\simeq 0.0484$, about five times larger than the result of Davis et al.\cite{davis}. The mode decomposition of the net momentum flux and of the associated gravitational wave impulses results in an adjacent-even-odd mode-mixing pattern. The impulses contributed by each $(\ell,\ell+1)$ mixed mode satisfy accurately the exponential decay with $\ell$, for the whole mass ratio domain considered, $0.01 \leq \alpha < 1$. The $(2,3)$ mode contributions to the total impulses are dominant. The mode-mixing effect can also be seen in the decomposition of the net kick velocity imparted to the system by the gravitational wave emission. The mixed mode impulses reach a maximum at $\alpha \simeq 0.7$; for $\alpha > 0.7$ the impulses decrease and are zero in the equal mass case, due to the decrease to zero of the odd modes of the "news". |
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