Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH

¯n/ni and ñ/n versus l/(2π)
The plots for ¯n/ni and ñ/n versus l/(2π), which gives the number of
orbital revolutions. The adiabatic increase of ¯n is clearly visible in
panel 1, and the quasi-periodic nature of the variations in ñ is
portrayed in panels 2–6. These variations are governed by the
reactive 2.5PN and 3.5PN equations of motion. In the second and
third row, these contributions to ñ are plotted individually and
separated for the initial and final stages. The parameters e i t and e f
t
denote initial and final values of the time eccentricity et, while ξ i
and ξ f stand for similar values of the adimensional mean motion
ξ = GMn/c 3 . The panels are plotted for η = 0.25 and the orbital
evolution is terminated when j = √ 48.
Conversion to familiar quantities like orbital frequency f (in hertz) is
given by f ≡ n/(2π) = c 3 ξ/(2πGM) = 3.2312 × 10 4 ξ(M⊙/M). This
implies that for a compact binary with the total mass M = M⊙ and
ξ = 10 −3 , the orbital frequency will be ∼ 30 Hz.
BRI-IHP06-I – p.148/??