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

  • Context: Graduate 
  • Thread starter Thread starter ergospherical
  • Start date Start date
  • Tags Tags
    Waveform
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
1 reply · 2K views
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?
 
Physics news on Phys.org
(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).
 
Reply
  • Informative
  • Like
Likes   Reactions: berkeman and ergospherical