I am a Computer science student working on LIGO data. I have seen this well describing link

How were the solar masses and distance of the GW150914 merger event calculated from the signal?

On how to extract the masses from the data.

But I still find it a little difficult despite the good explanation. Can anyone give me a much simpler explanation on how to extract the masses from this data ?

A simple step by step solution would be really helpful

Thanks in advance

  • 2
    $\begingroup$ How exactly does your question differ from the previous one? Do you just want a from-the-ground-up tutorial on how to numerically simulate black-hole mergers in GR, and how to compare that with measured signals? That's too broad for this format. $\endgroup$ – Emilio Pisanty Feb 12 '17 at 14:22
  • $\begingroup$ I mean if theres a direct formula used which can give me a near approximation to the mass using the waveform that would be helpful as well $\endgroup$ – Rahul Aedula Feb 12 '17 at 14:26
  • $\begingroup$ Or atleast a set of operations which I have to perform on the strain data to get the masses would be fine as well . If you can just list them out no need of even explanation . Just the workflow would be fine $\endgroup$ – Rahul Aedula Feb 12 '17 at 14:28
  • $\begingroup$ The simple toy answer: You can extract it by maximizing the following quantity derived from Bayesian analysis: $(s|h(\mathbf{\theta}))-(h(\mathbf{\theta})|h(\mathbf{\theta}))$, where $s$ is the signal $\theta$ are the parameters of this waveform (e.g. chirp mass, distance, etc), $(a|b)=\int \frac{a b^*}{S_n(f)} df$ with $S_n$ being the power spectral density from the LIGO detector and $$ h(f) = \frac{1}{r}\mathcal{M}^{5/6}f^{-7/6}\exp(i\psi(f)) $$ $$ \psi(f) = 2\pi f t_c - \phi_c - \frac{\pi}{4} + \frac{3}{128}(\pi\mathcal{M}f)^{-5/3} $$ To first order approximation $\endgroup$ – Otto Feb 14 '17 at 1:48
  • $\begingroup$ Alright. how do I determine time at Coalescence and phase at Coalescence ? Is it based on the waveform ? can we find these parameters in the waveform ? $\endgroup$ – Rahul Aedula Feb 15 '17 at 0:57