WOLFRAM|DEMONSTRATIONS PROJECT

Gravitational Waves from Non-precessing Spinning Binary Black Hole Coalescence

​
m
1
(​
M
⊙
​)
m
2
(​
M
⊙
​)
χ
1
χ
2
distance (Mpc)
This Demonstration shows the Fourier amplitude of the gravitational wave from the coalescence of two non-precessing spinning black holes. The inspiral region is shown in red, the merger is shown in green, and the ringdown is shown in blue. The amplitude spectral density (ASD) for initial Laser Interferometer Gravitational-Wave Observatory (LIGO) design is shown as a dashed line. The ASD for advanced LIGO is shown as a dot-dashed line.
You can change the component mass parameters
m
1
and
m
2
(
M
⊙
represents the mass of the Sun) and the dimensionless spin parameters
χ
1
and
χ
2
for the two black holes to see changes in the waveform amplitude as well as the position of the spectrum. When the total mass of the binary black hole system is increased, the spectrum shifts toward a lower frequency. By keeping the mass parameter fixed when you change the spin parameters, the spectrum shifts toward higher frequency. This effect is called the orbital hang-up effect.
By changing the mass and spin parameters, you can also see the change in the merger frequency (
f
merge
) and ringdown frequency

f
ringdown
). By taking the ratio of the waveform spectra (which in this Demonstration is multiplied by
f
for ease of calculation) to the ASD, you can estimate the signal-to-noise ratio of the waveform for either initial LIGO or advanced LIGO sensitivity. The waveform amplitude varies inversely with the distance of the binary black holes. You can change the distance and see how the waveform amplitude scales.