How did they found that the gravitational waves where emitted at redshift $z=0.09$?
I understand the measurement of redshift for an electromagnetic wave where we have measured in a lab various transitions and therefore we can make a comparison with the wavelength we receive.
But how can they manage to get the redshift for the emitter of gravitational waves, since we have no reference?
As stated in the LIGO discovery paper (pdf), the event is placed at $410^{+160}_{-180}\ \mathrm{Mpc}$ luminosity distance, equivalent to a redshift of $z = 0.09^{+0.03}_{-0.04}$. This gives a clue as to how one measures the distance for this event.
If we know how intrinsically luminous an object (like a star, or a supernova) is, we can compare this to how bright it seems and recover a distance via the standard inverse-square law. The distance we get is by definition the luminosity distance. For this detection, the same principle applies, since the simulations predict the intrinsic strength of the signal.
Actually, we also can leverage frequency information. Again, we have numerical simulations that predict waveforms, and the waveform itself will be redshifted in the same way as any other signal propagating at the speed of light.
In practice, one takes the entire waveform and a bank of numerical simulations, and does a statistical analysis to see how well the signal matches models, and what self-consistent distance/redshift make it fit. This is detailed in Veitch et al. 2015 Phys. Rev. D 91 042003.
Note there is some degeneracy with inclinations. The detectors are not monopole antennae, but at least with two of them we can sort of localize the source on the sky to figure out what fraction of the power is actually absorbed. A more stubborn degeneracy lies in the orientation of the astrophysical system with respect to our line of sight. Since gravitational waves are (at least) quadrupolar in order, an edge-on system nearby will be hard to distinguish from a face-on system further away. This is at least part of the reason for the large uncertainties.
To be precise, LIGO didn't measure the redshift. As explained in the introduction this supporting document from the LIGO team, "Properties of the binary black hole merger GW150914", the observables conspire such that no direct information on the redshift is available, as your intuition suggested.
However, analysis of the detected signal amplitude and waveform, in comparison with models, does give the absolute luminosity distance of approximately 410 Mpc, or 1.34 billion light years.
To get a redshift, a specific cosmological model must be assumed. LIGO used the latest and greatest from the Planck experiment: a flat $\Lambda CDM$ universe with Hubble constant $H_0 = 67.9$ km/s/Mpc ($H_0^{-1}c=4415$ Mpc) and matter density parameter $\Omega_m=0.306$.
One naively calculates a redshift of $410/4415=0.093$, which is pretty close to the quoted result because the redshift is small. An accurate calculation reduces the value a bit to $0.088$; see Figure 11 of Chapter 3 and accompanying text of Syksy Rasanen's notes, available here.
This is jroberts who asked the question 2 days ago about measuring the redshift of the LIGO events. My question appears to have precipitated this question.
I would like to pose a highschool answer to "Can we measure distance to LIGO gravity wave events using redshift?" since this is more general and inclusive than the question posed above.
The answer appears to be no. Where as we have used many tools including: 1 Laser time measurements to measure the moon's distance (thanks to unique reflectors placed during the Apollo missions. 2. Trigonometric parallax using as baseline, the diameter of earth's orbit, to measure distance to nearby stars, 3. Cephied variable stars, using their period:luminosity ratio to measure distances out to nearby galaxies. 4. "Standard candle" galaxies to estimate even greater distances, and 5. Redshifts of emission or absorption lines, when correlated with other distance measurements, to yield the greatest distances, keeping in mind that these red shifts are due to TWO parameters 1 velocity of recession and 2. expansion of space-time (incidentally many ca. 1970 astronomy texts left out the latter eg Abell's Astronomy.)
The LIGO events are seeing an event sortalike the pneumatic shock wave from an explosion of TNT, however, the shock waves are gravity waves which are distorting spacetime.
Does this sound useful to anyone?
