We thank the referee for making very useful and constructive comments.
We have now revised the paper accordingly. All relevant changes are in
blue characters.

> 1. The idea to analyse the azimuthal averages for quantities that exhibit
> clear periodic variations with azimuth and are not sign-constant does not
> seem good to me. (What I mean is that, if you average sin x over 0 ≤
> x ≤ 2π, you’ll get zero but this is not the only – and not the
> most important – feature of sin x.) I am sure the authors are aware
> of that. I would suggest that the authors try to carefully consider the
> azimuthal variation of Q, U , E and B at various latitudes and try to
> fit them with a simple periodic function like sin(aφ + δ). The desired
> symmetry may be clearly visible in the dependence of δ on θ. Otherwise,
> a window averaging in azimuth with the window width of about 45◦
> might help to suppress the noise without removing the φ-dependence. The
> desired parity might, again, manifest itself in the phase shift between
> the Galactic hemispheres. If the authors decide to leave their analysis
> as it is, they should address this question and justify their approach.

We understand this concern and have addressed it as follows: Instead of 
using the sine function we use the
appropriate decomposition of our \tilde{R}_lm, or, more conveniently
\tilde{E}_lm and \tilde{B}_lm. There is a dominant m=2 variation, which
is quantified by the expansion coefficients of Eq.(1), of which the
first few are now listed in Table 1, and more are given in the online
material; see the new text on page 3 with a reference to the link. The
m=0 variation is independent of the others, and all these parts may be
interesting in their own right. Just think of how much was lost when the
Maunders constructed their butterfly diagram by longitudinal averages.
Our online version with DOI numbers enable the readers to inspect the
data reduction for themselves and to compare with new ones.

> 2. The magnetic field distribution around the observer is not
> cylindrically symmetric, and one might expect a weaker signal from the
> anticentre direction (l 180◦) and stronger, from the Galactic centre,
> l 0◦ . And yet, such an asymmetry is rather weak in Fig. 1 and is
> not present in Fig. 3. Why? It seems that most of the observed signal
> is accumulated in the near vicinity of the Sun. Note that the lines
> of sight with the Galactic latitude |b| > 10◦ leave the disc within
> a few kiloparsec of the Sun. This should be discussed and, if this
> explanation is acceptable, this can simplify the data interpretation
> significantly since the form of the large-scale magnetic field near
> the Sun is known relatively well. This would also explain why the very
> crude dynamo model with so many unrealistic parameters leads to such a
> good agreement with the observations: only the local field structure
> matters, i.e., the quadrupolar field symmetry, whereas the details of
> the field distribution along the galactocentric radius matter little.

If one looks at the B polarization, is shows a cloverleaf-shaped pattern
at the Galactic center. At the anticenter, there is no similar pattern.
We now mention this at the end of the first paragraph of Sect. 4.1:

  Around the Galactic center, the B polarization has a characteristic
  cloverleaf-shaped pattern, which is best seen in the recentered lower
  panels of Fig.1; see the white box. This is similar to what was reported
  in the appendix of BF20. This pattern is a result of the B-decomposition
  of a purely vertical magnetic field near the Galactic center.

> 3. §4.2.1: Mention in the text that the rotation curve in the model is
> very different from that of the Milky Way – this undoubtedly affects
> details of the polarization distribution. You may wish to note that,
> despite a distortion of the details, the overall pattern and symmetry
> are not affected. Perhaps you may wish to promise the reader to repeat
> the analysis with a better model of the Milky Way. 1

This is now mentioned in the blue text in the second sentence of the
first paragraph of Sect.4.2.3.

> 4. op. cit.: The scale height for the α-effect, 1.5 kpc, seems to be too
> large (0.5 kpc looks more realistic). Explain your choice and comment on
> the effect it has on the results. Also, apart from the central magnitude
> of α, specify the value of α at the distance of order 10 kpc from the
> centre (the expected magnitude is of order 0.5–1 km/s).

We have now added a sentence where we refer to the earlier paper of
Brandenburg et al. (1993), who motivated their choice by the possible
importance of the thick disk (Reynolds layer). Better models should
of course be considered in future. We have now added one more model
with a galactic wind for NGC891 in the Brandenburg & Furuya paper,
but those more complex models add new features to the result that make
it hard to identify the important features. We have now mentioned thick
disk and Reynolds layer in the second sentence of the last paragraph of
Sect. 4.2.1.

> 5. §4.2.2 and further throughout the text: nCR |b⊥ |σ is the
> synchrotron emissivity – please avoid inventing a new and not quite
> correct term “intrinsic intensity of synchrotron emission”. Likewise,
> intrinsic complex polarization → emissivity in the complex polarization.

Done; see the blue parts just before Eq. (5).

> 6. Plots in Fig. 2 (a,c) should be presented with error bars: if you know
> an average, you also know: (1) the statistical error of the mean and
> (2) the sample standard deviation, right? Both should be presented. I
> won’t be surprised if most of the variation in Q/E (but perhaps not
> in U/B), apart from the signal near θ = 90◦, is comparable to the
> sample standard deviation although the error of the mean might be smaller.

We now show both as light and dark gray shades. This is now also explained
in the text in the second sentence of the second paragraph of Section 4.1.

> 7. §4.2.3, last para: I think it would be useful to discuss, in this
> context, the ratio br/bφ (the pitch angle of magnetic lines). It is
> known from observations (at least in the Solar vicinity) and allows one
> to estimate the expected current helicity of the large-scale magnetic
> field [see the beginning of Section 7.4.3 in Shukurov A., Introduction to
> galactic dynamos. In: Mathematical Aspects of Natural Dynamos, E. Dormy
> and A. M. Soward (Editors), The Fluid Mechanics of Astrophysics and
> Geophysics, Vol. 13, Chapman and Hall/CRC, London, 2007, pp. 313–359
> (astro-ph/0411739)].

The pitch angle is 8-9 degrees, which is small, but perhaps not too bad.
However, we have now omitted the corresponding discussion on current
helicity in favor of a more explicitly analysis of the Galactic spiral.

> Minor points and typos (I can’t be sure if I found all of them:
> 1. Please explain early in the introduction what is the ‘handedness’,
> how it might be defined and how it is related to the helicities of the
> magnetic field.

This has now been done; see the second part of the last paragraph of
Section 1.

> 2. §1, line 12: tracing cosmic rays to their origins. → tracing
> high-energy cosmic rays to their origin.

Corrected; see the left column of page 1.

> 3. §1, para. 2: A suitable recent review of the models for the Milky Way
> magnetic field can be found in Boulanger et al., IMAGINE: a comprehensive
> view of the interstellar medium, Galactic magnetic fields and cosmic
> rays, Journal of Cosmology and Astroparticle Physics, Issue 08, article
> id. 049 (2018).

We have added this now; see the last sentence of the second paragraph of
Sect. 1 on page 1.

> 4. §1, lines 5–4 from right bottom: the polarization segments only
> give “arrow-less” magnetic field vectors → the polarization data
> are only sensitive to the magnetic field orientation in the sky plane
> but not to its direction.

Corrected; see the bottom right of page 1.

> 5. §2, last para: parity-even and parity-odd constituents. →
> parity-even and parity-odd parts.

Corrected; see the first sentence of the last paragraph of Sect. 1.

> 6. Eq.(4): remove comma after m in the exponent of (−1).

No, the comma is correct; see Eq.(25) of Vasil+18. It means the larger one
of the two numbers m and -s, so for m=-1 and s=2, we have max(m,-s)=-1.

> 7. §2, last para: Note that we have here included an additional
> 2π factor: 2π does not appear in Eq. (4), so please reword [e.g.,
> The normalization constant in Eq. (4) differs from that in Eq. (25)
> of ... by the factor 2π to ensure the correct normalization].

We have now rephrased this as suggested; see the text just below Eq. (4).

> 8. §4.1, line 4: φ = 0 and 135◦ → l = 0 and 135◦

Corrected, but we chose to quote values of phi; see the first few
sentences of Sect. 4.1.

> 9. §4.1, line 7: φ = 45◦ and 225◦ → l = 45◦ and 225◦.

Corrected, similarly to item 8.

> 10. §4.1, end of para 1: “The B polarization is positive (negative)
> near the Galactic North (South) pole.” The B polarization varies in sign
> with azimuth near the poles. I guess the authors mean one thing but write
> something different. (By the way, I believe that B here, and likewise E
> for the other polarization mode, should be typed in Roman rather italics.)

We have now corrected this and similar things in the same paragraph.
Regarding Roman characters for E and B, we know that soome people do this,
but they are just standard dimensional mathematical variables, and not
names, so we continue using italics characters.

> 11. §4.1, para 2, line 4: Q··· → 2π 0 Q · · ·.

Done; see the second sentence of the second paragraph of Sect. 4.1.

> 12. 5 lines further down: but both are antisymmetric → but both are
> roughly antisymmetric.

Done; see further down.

> 13. The colour bars in Fig. 1 are hardly visible. I suggest that they
> are shown next to the images. To save space, the tick mark labels on the
> inner four sides of the frames could be removed (so that the labels are
> only shown along the perimeter of the figure) and the tick marks are
> shown on the outer side of the images to make them clearly visible.

For the color bars it is important to see the colors and some numbers.
We agree that the numbers have been too thin, so we made them thicker now.
We felt the arrangements with the tick marks was acceptable in the present
form, so we left them unchanged.

> 14. Caption to Fig. 1: (button) → (bottom).

Corrected.

> 15. §4.1, last para: breaks the independence of the rotational →
> breaks the rotational

Corrected; see the third paragraph of Sect. 4.1.

> 16. 2–3 lines further down: 2× depends solely → correlates solely

Since m=0, the dependence of E solely on Q and that of B solely on U
is exact, so the usage of correlates would not reflect this. We have
therefore left this unchanged.

> 17. §4.2.1, end of the 2nd para: use \citep rather than \citet when
> referring to Brandenburg & Dobler 2010.

Corrected; see the end of the penultimate paragraph of Sect. 4.2.1.

> 18. §4.2.1, penultimate para, line 3 from the end: and a characteristic
> transition → and the turnover

Done; but "penultimate para, line 3 from the end" doesn't seem correct,
at least now it is line 6 of the last paragraph.

> 19. §4.2.1, last para, line 2: declining → declines

Done and slightly modified (line 7 from the bottom).

> 20. Two lines further down: delete “formalism”.

Done (line 4-5 from the bottom).

> 21. Caption to Fig. 2: Bottom: . . .: U φ → B φ.

Done.

> 22. Page 5, left column, 4th line: polarization has to do with the
> electric field, which is rotated by 90◦ relative to the magnetic
> field → the polarization plane represents the electric vector of the
> radiation which is orthogonal to the magnetic field in the sky plane.

Done; see the text between Eqs. (5) and (6).

> 23. §4.2.2: The vertical distributions and scale heights of the cosmic
> ray and thermal electrons are different in the Milky Way (the reference
> to Jasson & Farrar cannot change this fact). I understand that there is
> no need to have a very realistic model of the Milky Way in this paper,
> but it would be better to admit the lack of (unnecessary) realism and just
> to say something like “For the sake of illustration, we adopt ...”.

Done; see 4 lines below Eq. (6).

> 24. §4.2.3, right column, lines 4–5: dependence is found → pattern
> emerges.

Changed; see lines 11-12 of Sect. 4.2.3.

> 25. op. cit.: 4 lines further down: what is meant by “flipped
> latitudinal profile”? Please use a precise language (not necessarily
> English: American would do as long as it is appropriate). Do you mean
> ‘the sign of ... changes” or anything like that?

Yes, we have now changed it to "the sign of B(theta) changes, and the
profile becomes similar to that shown in ..."; see line 16 of Sect. 4.2.3.

> 26. §5, para 2, line 4: zero—even → zero even

Done; see line 4 of paragraph 4.

> 27. §5, right column, line 3: positive (negative) → negative (positive)

We have corrected this now by changing 135 -> 45 and 315 -> 225; see
the end of the last paragraph.

> 28. nest line: delete “detailed”

That part is now rewritten.

> 29. next line: flipped → changed

That part is now rewritten.

$Id: response1.txt,v 1.14 2020/05/23 09:22:30 cvs Exp $