Gravitational scattering of solitonic boson stars: Analytics vs Numerics

Abstract

We study the scattering of boson-star binaries, taking into account three effects: point-mass gravitational, tidal, and short-range scalar-field interactions. We compare analytic results to the scattering angle extracted from four sequences of numerical-relativity simulations at fixed energy and varying impact parameter. The very good agreement exhibits the attractive (repulsive) effect of in-phase (out-of-phase) binaries, wich dominates at small impact parameters. We thus obtain the first effective-one-body potential, central for the construction of analytic gravitational-wave templates.

Figures (4)

• Figure 1: Feynman diagrams needed for the computation of the scalar field effective action up to $\mathcal{O}\left( G c_A c_B\right)$. The dashed (wavy) line represents the scalar (graviton) propagator.
• Figure 2: Scattering angle comparison between the NR data (filled circles) and the EOB-resummed, PM based analytical prediction (AR; solid lines) for equal-mass, non-spinning boson star configurations for various rescaled initial angular momentum ($j =J/(G m_1 m_2)$).
• Figure 3: Fractional differences $\Delta\chi/\chi_{\rm NR} = (\chi_{\rm AR}-\chi_{\rm NR})/\chi_{\rm NR}$ of analytical results (including both the tidal and scalar interactions) with respect to the numerical results.
• Figure 4: Difference $\Delta \chi=\chi^{\rm AR} - \chi^{\rm NR}$ between the analytic and NR values of the scattering angle for BS$\rm{\overline{BS}}$ binaries with initial energy given by Eq. (\ref{['eq:Einc']}) with $c_V=1$, $c_V=1.37$ and $c_V=1.5$. The error bars ($\sigma$) correspond to the NR results presented in Table \ref{['tab:initData']}.