What is the Expression for the Waveform of an In-Spiralling Compact Binary?

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In summary, the paper presents an expression for the waveform from an in-spiralling compact binary, which involves a set of angles describing the position and orientation of the binary, a chirp mass, the wave frequency, and the phase. The derivation of this expression is not explicitly stated in the paper, but references point to a book for further details. The function Q is also mentioned in the paper, with further explanation provided in an earlier paper and Kip Thorne's book.
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ergospherical
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This paper gives the following expression for the waveform from an in-spiralling compact binary:\begin{align*}
h(t;\boldsymbol{\theta}) = \frac{1}{r} Q(\boldsymbol{\phi}) \mathcal{M}(\pi \mathcal{M} F)^{2/3} \cos \Phi(t)
\end{align*}where
  • ##\boldsymbol{\phi} = (\theta, \varphi, \psi, \iota)## is a set of angles describing position & orientation of binary
  • ##\mathcal{M} \equiv \mu^{3/5} M^{2/5}## is the chirp mass
  • ##F(t)## is the wave frequency & ##\Phi(t) \equiv 2\pi \int F(t) dt## is the phase
I've been trying to find a derivation of this guy for quite a while, with no luck. The references lead to the book "300 years of Gravitation", which I'd have to wait until tomorrow to have a look at.

Also, what's the function ##Q## explicitly?
 
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(Disclaimer: I am not an expert in this area.) That paper cites an earlier paper (also found on arxiv here), where equation 15 is comparable to OP. The earlier paper points to Kip Thorne's book for the derivation, but also apparently goes into detail about the definition of Q in section IV (edit: see equation 66).
 
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FAQ: What is the Expression for the Waveform of an In-Spiralling Compact Binary?

What is a compact binary?

A compact binary is a system of two stars that are orbiting each other very closely, with a combined mass that is significantly larger than that of our sun.

What does "in-spiralling" mean in the context of a compact binary?

In-spiralling refers to the gradual decrease in the orbital distance between the two stars in a compact binary as they emit gravitational waves and lose energy, causing them to spiral towards each other.

What is the expression for the waveform of an in-spiralling compact binary?

The waveform of an in-spiralling compact binary can be described by the Einstein quadrupole formula, which is a mathematical expression that relates the gravitational wave strain to the masses and orbital parameters of the binary system.

How does the waveform of an in-spiralling compact binary change over time?

The waveform of an in-spiralling compact binary starts as a low frequency signal with a small amplitude, and as the binary gets closer together, the frequency increases and the amplitude becomes larger until the two stars eventually merge.

Why is the study of in-spiralling compact binaries important?

Studying in-spiralling compact binaries can provide valuable information about the properties of gravity and the nature of space-time. It can also help us better understand the formation and evolution of galaxies and the universe as a whole.

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