Just like the frequency of a musical note can tell us about the size of the instrument, the frequency of a gravitational wave
signal can tell us about the size of binary black holes. Each cycle of a gravitational wave signals corresponds to
one half orbit of a binary black hole. You can see this in the video - a gravitational wave "crest" leaves the system each time
a black hole passes by. So, the period of the gravitational wave signal is always half the period of the binary orbit:
2 * TGW
The plots show the same simulated signal for a binary black merger, in the time domain (above) and time-frequency domain (bottom). As the black holes
get closer, they orbit faster, so the frequency goes up near the merger time (the black holes merger near time 1.7 s).
Use the time-frequency plot (spectrogram) to estimate the orbital radius just before merger:
- Using the plots at right to estimate the gravitational wave period near merger. [Hint: What's the highest frequency in the spectrogram?]
- Calcuate the orbital period. This is twice the gravitational wave period.
- Near merger, black holes always move really, really fast - around 108 m/s. This is around 1/3 the speed of light (!!). Use this
velocity to estimate the orbital radius of the black holes [Hint: distance = rate X time].
- Is the radius you calculated closer to the size of a car, a city, a planet, or a star? Imagine an object this size, spinning around
100 times per second. What would it look like?
Now that you know the orbital radius, you can also estimate the black hole mass:
- The orbital radius near merger can be related to the black hole mass using the "ISCO" radius, rISCO = 6GM / c2.
Assuming the orbital radius you calculated is the ISCO radius, estimate the mass of these black holes. G is Newton's constant,
c is the speed of light.
- Divide your answer by the mass of our sun to estimate the mass in units of "solar masses".
- The masses used to generate this signal are similar to parameters for GW150914 (well ... within a factor of 2). Take a look at
the real GW150914 data. You can see the masses
by clicking "show parameters". How do the spectrograms and masses of GW150914 compare with what you did here?