Constraints on the astrophysical environment of binaries with gravitational-wave observations

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Table 1

Corrections to the GW phase in the Fourier space computed within the stationary phase approximation for a quasi-circular binary (see Eq. (12)).

Mechanism	γ_{(β = 0)}	κ₀	γ_{(β = 1)}	κ₁
Gravitational pull	2	1	4/3	1
Gravitational drag	11/3	− η⁻³(1 − 3η)π^−11∕3	3	− η^−16∕5(1 − 3η)π⁻³
Accretion – Bondi	11/3	− η⁻³(1 − 3η)π^−11∕3	3	− η^−16∕5(1 − 3η)π⁻³
Accretion – collisionless	3	− η⁻¹π⁻³	7/3	− η^−6∕5π^−7∕3

Notes. The binary moves in a mediumof density , and it is subjected to accretion, gravitational forces from the matter distribution (assumed to be centered at the binary’s center of mass), and to gravitational drag. Results refer to β = (0, 1) and to collisionless and Bondi accretion, respectively.

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