CMB Multipole Expansion in a Frame Dragging-Sustained Milky Way

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I have reviewed the manuscript “CMB multipole expansion in a frame dragging-sustained MilkyWay” by Federico Re, Marco Galoppo, and Massimo Dotti. The authors discuss the impact of some peculiar rotational motion on galactic scales can have on the CMB map via their general relativistic effects. In particular, they investigate the effects of a frame-dragging vortex on the CMB anisotropy. Through their analysis, they show that the impacts show up only on large multipole moments, and hence they don’t impact the standard CMB analysis, and don’t explain the claimed anomalies in the CMB.

The work is clearly motivated and presented, and I commend the authors on a well-structured manuscript. I would be happy to reconsider the manuscript for publication in Galaxies once some questions and comments I have are addressed; I list these below:

1. Lines 43-48: The discussion on why stationary observers have non-zero angular momentum could be expanded a little bit, possibly by talking briefly about the reason why, and by including some references.
2. Lines 89-92: The authors explain their assumption of a simple disk shape of the galaxy, and their neglect of bars, spirals etc. Could they give a qualitative assessment of how these structures would impact their analysis? Also, is the presence  of a central bulge important to their analysis, and is it neglected?
3. Eqn. (1): I am confused as to what spacetime the metric represents — is it the spacetime element just outside the galaxies considered, or inside?
4. Eqn. (3): There is a normalization factor H(r,z) in the definition of the four-velocity; what is the corresponding normalization condition? Is the form of H shown in Eq. (7), and the condition used for that, universal?
5. Lines 136-137: What is the justification for choosing the forms of W and A leading to the LEL approximation?
6. Lines 142-144: It is a bit unclear what it means for “a relevant fraction of the rotation curve of a MW-like galaxy” to not exceed 1.
7. Eq. (16) and Lines 250-255: If the magnitude of the dipole term is of the order of 10^{-7}, is it correct to say it emerges from a “strong” dragging?
8. Line 257: I would advise the authors to replace “the above GR formulas” to “the above results”, or something similar.
9. Line 266: Why is the interest restricted to the quadrupole level since in principle, the kinematic effects would also show up on octupole and higher moments? Would the effects be too negligible to see?
10. Lines 393-396: One or a few references about the debate between the SO and ZAMO points of view regarding the speed of galactic matter would be helpful.
11. Since the mentioned CMB anisotropy tensions fall within the cosmic variance limits, I would urge the authors to discuss how the latter is relevant to their analysis.

I look forward to reviewing the manuscript once more when the above concerns are addressed.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In this paper, the impact of galaxy rotation on the CMB multipole expansion is studied. The authors use General Relativity to compute the effects of spacetime dragging and to derive the corrections to the multipoles, albeit with a few reasonable approximations.

I find the paper to be of significant interest to the community. It is well written and well motivated, and the results are presented clearly. For this reason, I have no objections to its publication.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I have reviewed the revised version of “CMB multipole expansion in a frame dragging-sustained MilkyWay” by Federico Re, Marco Galoppo, and Massimo Dotti. The authors have satisfactorily addressed almost all of my questions and comments, and I recommend the manuscript for publication in Galaxies once the few minor points below are clarified.

1. In response to my comment #2 in my previous report, the authors clarified how structures in galaxies affect their analysis. However, I could not locate in the manuscript the footnote they referred to in the reply.
2. My comment #7 in the previous report dealt with “strong” dragging, which the authors clarified. However, a definition or categorization of what qualifies as a strong coupling may be helpful (preferably as a footnote); however, I leave this to the authors’ judgement.

Apart from these, I once again commend the authors for a well-written manuscript.

Author Response

The reply letter is attached

Author Response File: Author Response.pdf