Gravitational Waves Inspiral time period

Hi All,

As I understand, before the merger of two binary black holes, there is a period called Inspiral. The gravitational waves are generated during this period itself and currently, we could measure the spike in strain energy when they get merged to confirm the event. (Reference:, Section 2.2.2 and figure 6)

Hence, my query here is,

  • Is it possible to find out the inspiral time period and its corresponding strain values for each of the confirmed 90 gravitational waves (which have been detected so far)?

Could you please help me with this?


Hello Gopinath,

Yes, you’re correct about the inspiral phase prior to merger. However, the LIGO and Virgo detectors don’t use the gravitational waves from the merger to confirm the detection, but rather search for the entire signal, including the inspiral. Of course, they are only able to measure the very end of the inspiral, since the earlier parts are too low frequency–the detectors’ sensitive band starts around 20 Hz. For low-mass binary black holes, such as GW151226 (and even more so for binary neutron stars like GW170817), one detects the signal primarily using the inspiral–the merger phase is at sufficiently high frequency that it falls in a less sensitive portion of the detectors and thus does not contribute as much as it does for heavier binaries like GW150914.

However, even for binary neutron stars, the signal in the detectors’ sensitive band only lasts for a few minutes, while in most formation scenarios, the black holes or neutron stars have been slowly inspiralling due to emitting gravitational radiation for billions of years–see, e.g., Fig. 1 in each of these two papers for some example formation scenarios for GW150914. If you are interested in how long it takes the binary to inspiral from an early time, then see, e.g., Sec. 3.1.4 in this review and the classic paper by Peters they reference.

However, I presume that you are interested instead just in the portion of the inspiral in the detectors’ sensitive band. Here there are not results already available in the literature, but if you are just interested in a rough estimate, there are plots of representative waveforms for all events through GWTC-2 starting from 20 Hz (except for cases where one mass is 5 solar masses or less, where they start at 70 Hz) here. You can also make plots of nonspinning waveforms from 30 Hz using this app.

If you need something more accurate, then you will need to start from the posterior samples for the binary’s parameters (available from the Gravitational Wave Open Science Center) and generate a probability distribution of waveforms (or the waveform for some point estimate like the maximum likelihood or maximum a posteriori values) using the same waveform model used to obtain the posterior samples (see here for instructions, though beware inverse Fourier transform artifacts if you plot a natively frequency-domain waveform in the time domain, like IMRPhenomD in the example).

I hope that this helps.