Why Masses of Binary Black Hole Mergers Are Overestimated?^†

Round 1

Reviewer 1 Report

The article deals with gravitational radiation arising from the fusion of two black holes. The authors propose that gravitational redshift should be taken into account after the melting process of black holes. The idea seems to be quite reasonable, but the article does not make it clear whether the contribution of the source is more relevant than the contribution of the gravitational field at the measurement site, such as Earth. In addition, the metric resulting from the coalescence of two black holes is accessible through numerical simulations. This raises the question whether the estimate of equation (4) is really relevant.

Author Response

See the enclosed file.

Author Response File: Author Response.pdf

Reviewer 2 Report

The main claim of the paper is that masses of merging binary BHs inferred from GW signals are overestimated because the gravitational redshift is overestimated. The authors also present a number of other reasons, supporting in their opinion this claim. 

The paper reveals a deep misunderstanding of the theory and practice behind this field of research. In fact the paper is a mixture of right and wrong statements. 
The authors would get the answers to their critical questions regarding first detection paper consulting rich literature e.g. Michele Maggiore "Gravitational waves: vol 1 and vol 2". I will not address the completness and depth of presentation in the paper [1], but a single paper without reference to the huge background of theoretical work standing behind cannot fully justify claims invalidating its findings. 

The main misunderstanding is that the authors treat GWs emitted from the binary system in the same way as e.g. the photons emitted from the accretion disk close to the BHs horizon. In fact what is relevant here is the fact that the GW is emitted form the system as a whole - its coherent motions during the inspiral phase. 
Therefore, the large gravitational redshift near the horizons of the BHs is not an issue here. Moreover, there is a misunderstanding in saying that since before the binary BHs were moving with velocities close to the speed of light - the Doppler effect would be pronounced. The Doppler effect should be included if significant relative motion between the coalescing system as a whole and the observer was demonstrated. One should bear in mind that what we are talking about is the GW in the far radiation zone. 

It is true that two body problem has no exact solution in the GR - GW community is fully aware of this, and post newtonian formalism has its well defined range of application. One should stress however that the inference of the chirp mass and the distance (because of inclusion of the cosmological redshift - they are the redshifted chirp mass and the luminosity distance) relies on the analysis of inspiral phase before the merger when the post newtonian formalism works well. It turns out that mesurements of the frequency f and its drift f^dot (the chirp) allow such measurements. By the way the equation (5) is well known to and used by GW community. 

I would not dare saying that "the mathematical and numerical analysis of the smoothed signal GW150914 can hardly be reproduced, since [1] does not contain details on the methods used. " On the contrary, on the web page "https://www.ligo.org" and "https://www.gw-openscience.org/" there are repositories of the data concerning GW150914 and other detected signals together with numerical scripts for the analysis of these signals. 

In conclusion, I regret to say that the paper is not suitable for publication.      

Author Response

See the enclosed file.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper has a novelty idea where the redshift of the binary black hole mergers is studied, they propose a specific term (z+1) which was found in another work. I would like to see a comparative study of the observational results with the ones they can calculate with their new proposal.

Author Response

See the enclosed file.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The revised manuscript has been improved in many aspects. However, I sustain my opinion that the main reasoning about crucial role of gravitational redshift near the BH horizon is seriously flawed. The chirp signal comes from the system as a whole (from accelerating orbital motion) and has nothing to do with gravitational redshift of BHs. It is similar to the claim that people neglect gravitational redshift of post merger object (possibly a BH) in studying gamma ray bursts. The effect the authors discuss could be relevant to the merger and post merger GW signals, but not for the chirp from the inspiral phase. Masses and distance are estimated from the inspiral phase and will not be so severely affected by neglecting the gravitational redshift as the authors claim.

Therefore, I regret to say that in my opinion the paper is flawed in its core claims.

Author Response

Please see the attachement.

Author Response File: Author Response.doc