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

  • Thread starter Thread starter ergospherical
  • Start date Start date
  • Tags Tags
    Waveform
Click For Summary
The discussion centers on the expression for the waveform of an in-spiralling compact binary, given as h(t;θ) = (1/r) Q(φ) M(π M F)^(2/3) cos Φ(t). Key components include the set of angles φ that describe the binary's position and orientation, the chirp mass defined as M = μ^(3/5) M^(2/5), and the wave frequency F(t) with phase Φ(t) = 2π ∫ F(t) dt. Participants express difficulty in finding a derivation for this expression, with references pointing to "300 years of Gravitation" and Kip Thorne's work for further details. There is also a query about the explicit function Q, which is discussed in an earlier paper linked in the thread. The conversation highlights the complexity of deriving and understanding the waveform expression in the context of gravitational wave research.
ergospherical
Science Advisor
Homework Helper
Education Advisor
Insights Author
Messages
1,100
Reaction score
1,387
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).
 
  • Informative
  • Like
Likes berkeman and ergospherical
MOVING CLOCKS In this section, we show that clocks moving at high speeds run slowly. We construct a clock, called a light clock, using a stick of proper lenght ##L_0##, and two mirrors. The two mirrors face each other, and a pulse of light bounces back and forth betweem them. Each time the light pulse strikes one of the mirrors, say the lower mirror, the clock is said to tick. Between successive ticks the light pulse travels a distance ##2L_0## in the proper reference of frame of the clock...

Similar threads

  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 16 ·
Replies
16
Views
4K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 36 ·
2
Replies
36
Views
5K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 21 ·
Replies
21
Views
2K