The Effect of a Spiral Density Wave on the Galaxy’s Rotation Curve, as Applied to the Andromeda Galaxy (M31)
Round 1
Reviewer 1 Report
The paper investigates the rotational velocities in a spiral galaxy within a model using a soliton solution of the nonlinear Schrödinger equation specifying a surface mass density wave inside the galactic disk. It is shown that the proposed nonlinear spiral solution is capable of maintaining the observed flat rotation rate curve at large distances in the absence of mass deficit. By choosing the parameters, it was possible to achieve a satisfactory correspondence of the obtained results to the observed data. This circumstance adds interest to the calculations presented in the manuscript.
At the same time, it is necessary to make the following observation.
The present work is purely computational in nature, while the theoretical substantiation of the model is presented in another paper by the author. Therefore, the initial formulas should be more clearly formulated. So, for example, the formula (6) is not used (as indicated in the text) when specifying the potential, but an approximate formula is used. It is necessary to specify exactly this approximate formula. Also it is necessary not only to assume, but also to justify the physical meaning of parameters a, b, c .
I believe that after elimination of the noted drawbacks the article can be published in "Universe".
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The novelty of this paper is not particularly high.
Hence, for now I focus on three main points, waiting for the real final version of the manuscript, but I really intend to see the numerical results otherwise it's impossible to me to take a final decision.
So, below my preliminary points of evaluations:
1) the paper fails to explain why this approach would be better than previous literature. In dark matter scenarios we don't include particular effects as simulations would indicate a clustering that could not match well real observations. Here N-body simulations are forgotten at all. There's no mention about plausible dark matter equation of state and pressure (if any). So, I need the author explains better the physics of this model in view of current standard model of dark matter.
2) Connecting to the first point, the CDM hypothesis works in the field of cosmology. Which consequences are expected in that field assuming the underlying hypothesis reported in this work?
3) Why general relativity effects seem not to be relevant in this landscape? the author made a particular choice of what? Explanations are needful. it is well-known that pressure is a GR effect, not a Newtonian one. So, why including those "corrections" but ignoring the GR effects?
After these changes, I can revise better the manuscript, since in its present version it does not fit the standards of this journal.
Additional points：
1) In eq. 9, the functional evolution of V is linear at very high radii. However, rotational curves are not flat at all! Several curves don't exhibit a flatness but fuzzy behaviors! The author might explain carefully this limitation of the model, declaring that it does not fit properly the curves as he, instead, declares.
2) The fact I was saying above is also certified by the fact that figures are reported only for M31 galaxy and no more galaxies. Why?
3) Eq. 8 must be the sum of all contributions, e.g., dust, gas, stars, halo, etc. It seems to me that is not at all.
This makes the "analysis", performed by the author and plotted in the figures, just extremely approximate and likely non-physical. Which explanations can be written by the author to justify this fact?
Besides these points, I need to see the answers to the previous queries I raised to take my final decision.
p.s. the changes might be reported in bold in the text, please. Thanks.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Honestly I don't see the physical soundess of this model. But, it's not an impression that has to stop a research. So, even if the model in my opinion is not well justified, the paper can be accepted.
