arXiv : Scattering of scalar, electromagnetic and gravitational waves from binary systems

Annulli, Lorenzo; Bernard, Laura; Cardoso, Vitor; Blas, Diego

doi:10.1103/PhysRevD.98.084001

Article
Report number	arXiv:1809.05108 ; CERN-TH-2018-184 ; KCL-PH-TH/2018-34
Title	Scattering of scalar, electromagnetic and gravitational waves from binary systems
Author(s)	Annulli, Lorenzo (Lisbon, CENTRA) ; Bernard, Laura (Lisbon, CENTRA) ; Blas, Diego (King's Coll. London ; CERN) ; Cardoso, Vitor (Lisbon, CENTRA ; CERN)
Publication	2018-10-02
Imprint	2018-09-13
Number of pages	20
Note	19 pages, 3 figures, to appear in PRD
In:	Phys. Rev. D 98 (2018) 084001
DOI	10.1103/PhysRevD.98.084001
Subject category	hep-th ; Particle Physics - Theory ; gr-qc ; General Relativity and Cosmology
Abstract	The direct detection of gravitational waves crowns decades of efforts in the modelling of sources and of increasing detectors' sensitivity. With future third-generation Earth-based detectors or space-based observatories, gravitational-wave astronomy will be at its full bloom. Previously brushed-aside questions on environmental or other systematic effects in the generation and propagation of gravitational waves are now begging for a systematic treatment. Here, we study how electromagnetic and gravitational radiation is scattered by a binary system. Scattering cross-sections, resonances and the effect of an impinging wave on a gravitational-bound binary are worked out for the first time. The ratio between the scattered-wave amplitude and the incident wave can be of order $10^{-5}$ for known pulsars, bringing this into the realm of future gravitational-wave observatories. For currently realistic distribution of compact-object binaries, the interaction cross-section is too small to be of relevance.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2018-2025 authors (License: CC-BY-4.0)

$Total scattering cross section for a dipolar wave as a function of the external frequency. Here, $\tilde{\sigma}\equiv \sigma/(A r_\circ^2)$ is shown as a function of $\tilde{\Omega}\equiv \Omega/\omega_0$. We set $c=1$ and the two angles $\gamma=\phi_0=0$. As expected, the cross section grows unboundedly for $\Omega=2\omega_0$. For large values of $\Omega$ we recover the standard high-frequency classical result~\eqref{EMOmegainfCrossSection}.$ $Plane of the orbit with respect to the fixed observer basis $(\mathbf{P},\mathbf{Q},\mathbf{N})$. The angle $\zeta$ is the polar angle describing the motion of the reduced mass $\mu$ in the orbital plane, while $\mathbf{L}$ and $\iota$ are respectively the total angular momentum and the angle between this vector and the direction $\mathbf{N}$. The total mass is denoted $m$.$