3
$\begingroup$

In answers to previous questions about (see, especially, this one) the LIGO detections it is stated that LIGO is unable to determine redshift, only luminosity distance. This is made clear in the papers. They do not provide a similar caveat to the mass/energy estimates, though. Schematically, because I don't know the equations, black hole mass determines orbital period and inspiral rate. Thus, the mass determines the frequency of the wave produced. The waves get redshifted in transit to Earth. So how is it that their mass estimates are not, in some way, redshift dependent? Are they some kind of "comoving mass" (mass multiplied by some factors of $1+z$), or are they true rest frame masses?

Put another way: what are the details of how they go from waveform to binary parameters and luminosity distance, with particular attention to where the redshift dependence cancels?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
2
$\begingroup$

The final waveform visible in the detector depends on, 1) Intrinsic parameters: 2 Masses, 6 Spins 2) Extrinsic Parameters: Declination, Right Ascension, Luminosity distance, Orbital inclination, polarization and coalescence phase.

There are 3 degeneracies i.e. two different values will produce the same waveform 1) Luminosity distance - observed mass: A source mass Ms will be seen as Ms*(1+z) in the detectors. With detector noise in the observed waveform you cant tell what is the right combination ? Off-course the more you go away in z from true value you will also go away in waveform amplitude. 2) Inclination angle-luminosity distance: You cant tell if binary is poorly aligned and clode or nicely aligned(face-on) and far away. The waveform is the same 3) Partial degeneracy in spin-mass ratio: There is a partial degeneracy because a no-spin+high mass ratio (low_mass/high_mass components) will produce the same waveform as as high-spin+low mass ratio.

Now you create this mammoth parameter-space covered by these 9 parameters and see where does you match of generated waveform matches best with the observed waveform.

With 2-detectors its a real pain in the neck. With 3-detectors at least you can localize and get good initial numbers for sky-location (Ra, dec).

Improve this answer
$\endgroup$
2
  • $\begingroup$ From the sounds of 1, I'm right to think that they observe a comoving mass, and finding the rest frame (true) mass requires using the luminosity distance to find the redshift to rescale the mass. Is that a fair way to characterize it? I ask because I'm interested in the possibility of using these events as standard candle events that, once we can find the galaxies they're happening in and get spectroscopic redshifts, will allow an independent probe of cosmology. $\endgroup$
    – Sean E. Lake
    Commented Jun 26, 2017 at 21:33
  • 1
    $\begingroup$ Yes you are right. We call it detector frame mass instead of comoving mass. Some work has gone into using gw signatures as standard cards unfortunately degeneracies prohibit it. So in the end it is mostly attempting to break degeneracies. Then mergers are great candles. $\endgroup$
    – user2555272
    Commented Jun 27, 2017 at 8:02

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.