# Gravitational wave redshifts and LIGO [duplicate]

When I heard about the LIGO gravitational wave detection, I wondered if the distance to the event was determined by the inverse square law of radiation and/or by measured red shifts. Which is/are the case? A previous answer to the nature of the redshifts of gravitational waves implies that the original frequency is unknown and therefore the red shift is also unknown. I further wonder how the computations of the masses of the two stars can be so precise, but the gravitational waves' frequencies not be.

I am an amateur astronomer, and past planetarium director, and not versed in relativistic gravity theory. I have hunted for an answer since February, even e mailing Kip Thorne, whose book "Gravitation" I own.

Regarding critique as a duplicate: I am accustomed to asking the distance to an object, by asking the redshift, esp. for distances too far for Cephiad variables to be visible. Perhaps the question is dumb, but no one has inquired about the possibility of directly measuring redshift of this event. Therefore, I think this question is somewhat unique. From the comments I gather that LIGO events can never have their redshifts directly measured.

## marked as duplicate by Rob Jeffries, John Rennie gravity StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Dec 8 '16 at 9:28

• Possible duplicate of Redshift of merging black holes – Rob Jeffries Dec 8 '16 at 7:37
• – Rob Jeffries Dec 8 '16 at 7:43
• The question definitely isn't dumb, it's a good question --- but is still a duplicate, and the answers (especially the one by @ArtBrown) completely answer your question. – DilithiumMatrix Dec 9 '16 at 15:45
• I would just like to thank all that answered my query. As mentioned, I have been searching many sites for an answer for almost one year, and had LIGO in LA, been open to the public when I drove by it last March, I would have sought an answer there too. It is a privilege to obtain responses from such learned people. – j roberts Dec 12 '16 at 16:20
• Please also note that the previous answer, and question, for which this is labeled a duplicate, did not answer fully the distance, or luminosity distance, in any significant way. The issue was determining the inherent luminosity, which is no easy task (like other astrophysical distance measurements, inherent luminosity has to be estimated from some modeled and understood physics). Here it was derived from 1)the waveform which gave freq and freq dot that gave the chirp mass, and 2) from detailed numerical calculations of merging BHs. These led to the 3 solar mass luminosity – Bob Bee Dec 18 '16 at 20:50

DilithiumMatrix has it right. A few more points and a couple references you can read and understand that describes the first black hole merger and some of the key findings. Not that hard, little math, good figures.

The measurements allows you to determine the chirp mass and the masses of initial black holes, and the final one, to some accuracy. The difference for that so called 091415 event (the date observed) between end and starting masses was 3 solar masses, which therefore is the amount of energy radiated as gravitational waves. From that and the times for the merger (most of the radiation is emitted in the last few orbits and as they merge, and it's been modeled pretty accurately so from the total energy one can estimate the peak power of and actually the amplitude of the waveform emitted) one can get the emitted power over the approximately 1/4 sec that most of it was emitted. From that emitted power, i.e., its inherent luminosity, and comparing it to the detected power, one can get the propagation loss and assuming 1/$R^2$ propagation one gets the distance R. that is the so called luminosity distance, which was 1.3 billion light years. From that one estimates the cosmological redshift, it was about 0.09.

The first reference is an interesting read, see it at http://www.ligo.org/science/Publication-GW150914/index.php. A good intro.

Their published professional papers were multiple, but the first one summarized everything important and you can get a sense of the uncertainties (for instance the initial masses were more uncertain, but the mass differences of the final black hole and the initial two is more accurate and is where they got the 3 solar masses approx). It is not a hard read, and also interesting, at https://dcc.ligo.org/public/0122/P150914/014/LIGO-P150914_Detection_of_GW150914.pdf

It is interesting to note that the peak power emitted in gravitational radiation, about 3 solar masses in a quarter second or so, was more power than the total instantaneous power emitted from light from all the stars in the observable universe, for that short period of time.

The LIGO team believes they will get more accurate numbers for the masses, in,causing the initial masses, if they can see more of the whole merger process - they only saw seconds of it. I believe they saw more in the second observation a few months later.

Another couple interesting points is that they were not able to pin down the exact location where the sources were, they were doing basically time difference of arrival and only had two independent measurements. With more LIGOs around the world they'll locate much better, and they try to compare to optical or other radio or X Ray observations around it, for more astronomical correlations.

• You are quite welcome John. BTW, the LIGO papaers for the detection are quite nice and not hard. They discuss a lot of the methodology and physics. Google LIGO black hole merger – Bob Bee Dec 9 '16 at 4:42

The frequency evolution of the signal can be determined very precisely. Based on the rate of change of the frequency the 'chirp-mass' is uniquely determined (to some accuracy). The 'chirp-mass' also determines the intrinsic amplitude of the gravitational wave event. Comparing the intrinsic amplitude with the observed amplitude then determines the distance (note the 'strain' is inversely proportional to the distance, not the distance squared).

• Many thanks. ...So I gather that the redshift could not be measured? – j roberts Dec 8 '16 at 3:44
• @jroberts the redshift is determined indirectly... the redshift as it effects the frequency cannot be disentangled from determining the mass. The distance which is measured, however, is the luminosity distance---so it can be used to calculate the redshift based on some cosmological model. – DilithiumMatrix Dec 8 '16 at 4:29