Thanks, Eve, for your detailed comments. We have responded to
all of them with corresponding changes that are marked in blue
in one of the two versions. Below our more detailed response:

> For abstract it is best to avoid terminology that is not generally known,
> as is the case for this phrase. This may be defined in main text but
> rewording here in a more explanatory fashion is needed

We have now replaced the former sentence "This is a manifestation of
catastrophic quenching, which is still an unsolved problem." by "This
could imply that the observed large-scale galactic magnetic fields might
not originate from a mean-field dynamo. Much of the current numerical
effort is focused on this unsolved problem."

> It is helpful to readers also to include references to other relatively
> recent reviews on magnetic fields in the ISM, including Hennebelle &
> Inutsuka (2019), and Crutcher (2012)

Thanks for the suggestion; we have done this now.

> It would be good to define magnetic helicity in the margin here. It does
> not seem to have been defined until p. 15, in the middle of a paragraph,
> but it would be helpful for readers to define it much earlier.

Right, we have done this now; see page 3.

> Delete "we can" in "then we can Faraday rotation ..."

Done: "then Faraday rotation ..."

> In the caption to Fig.1 is would be useful to indicate which is the
> projected major axis.

We have now added "The projection here is assumed along the line-of-sight
to the observer." in the caption to Fig.1 on page 5.

> It would be helpful to explain the winding in term of *differential*
> rotation, since it is not rotation itself but shear that is relevant
> for winding

We have now added "...due to the shear induced by the differential
rotation of the galaxy." at the end of the paragraph starting with
"However, a purely ..." on page 5.

> Regarding the vector u just after Eq.(3): here, lower case "u"
> is introduced for the velocity vector, whereas in eq.(4) uppercase
> "U" is used; it would be good to make these consistent. The adopted
> notation here should also be consistent with the notation that is used
> for mean and fluctuating parts of the flow. Since later, b = B - \bar B
> for fluctuating field b and mean field \bar B, to be consistent one
> would have u = U - \bar U, meaning that U is the total velocity and u
> is fluctuating velocity. However, here u seems to be the total rather
> than the fluctuating velocity.

Yes, this is right, and we have now corrected it to U.

> This choice for Omega may seem puzzling to readers since constant
> circular velocity at large radius (with Omega = V_c/\pomega) is a
> better approximation for realistic galaxies than velocity varying as
> 1/cylindrical radius (with Omega ~ \pomega^2).

Thanks for noticing this! The "2n" should have read "n", and it was
correct in the code (and in the quoted 1993 paper).

> see previous note about notation for u, U and \bar U

Now taken case of.

> Regarding the paragraph after Eq.(4): since this paragraph refers to
> microphysical conduction and electron collisions, it would be better to
> use the term "resistivity" here

Sometimes, resistivity refers to 1/sigma without the mu_0 factor. To
alleviate this problem, we have now written: "The magnetic resistivity,
or microphysical magnetic diffusivity, is then given by ..."

> The viscosity nu has not yet been introduced; please define nu within
> the text box. Also, for the convenience of readers it would be good
> to state within the text box that (1) eta is the resistivity, and (2)
> k_f is a characteristic flow wavenumber

Yes, we have done this now.

> Two paragraphs below Eq.(6): Since this paragraph is all about the
> eta=0 case, rather than the eta -> 0 limit, should this be revised?

We have now simply omitted the statement eta -> 0.

> Considering the central role of the alpha effect and the necessity for
> ARAA articles to be accessible to general readers, the article needs a
> brief section explaining what the alpha effect is, both mathematically
> and physically. The best place may be here, in between the current
> sections 2.3 and 2.4. Presently, the Roberts flows are introduced in
> the text box, and then eq. 9 states without explanation that the mean
> EMF contains a term linear in B. Novice/general readers will find
> themselves puzzled by this.

We have now added a new text box on that page (page 9).

> In the paragraph starting with "We summarize the essential features
> of flows~I--IV ...", the $\alpha$ effect was not yet been explained.

The is now referred to in the new text box, where we write 
"... $\alpha$ effect; see the previous text box."

> At the end of the paragraph before Eq.(9): Elsewhere U is used for
> the total velocity, in which case \bar U rather than \bar u would be
> the notation for the mean flow. To avoid confusion for the readers,
> it's important to keep consistent notation.

This must have been a mistake on our part; we have now corrected this
to $\meanUU=0$.

> Regarding Eq.(10): Some words of explanation regarding *why* the mean
> EMF has this form for Flow I would be helpful.

In our new box about the alpha effect, we have now alluded to the
necessity of twist or swirl in the flow. To explain why Eq.(9), which
is now Eq.(10), has the form it has, we have now written "For flow I,
which is maximally helical, there is a systematic swirl and it is then not
surprising that there is also an $\alpha$ effect, and thus, we have..."

> Regarding Table 2 on page 13, what does the check mark for Roberts
> flow I indicate?

This did not make sense and we have now replaced it by "alpha^2 dynamo"

> Concerning the Galloway--Proctor flow in the footnote on page 12:
> you wrote Please add references as appropriate

We have now referred there to their Nature paper and write
"The Galloway--Proctor flow \blue{\citep{GP92}} is an example of..."

> On page 14: Is there a typo here? Should the gamma be a lambda?

Yes; we have now corrected it to "$k_\eta=\sqrt{\lambda/10\eta}$."

> In the second paragraph of Sect.3.1, B_eq has not been defined;
> please add explanation for what this represents. Is \Rm a typo?

Rm should be corrected here, but we have forgotten a "1/" in the
formula. This has now been corrected. To clarify this further, we have
now added below "Evidently, owing to the $\Rm$ factor in the expression
for $\alpha$, this dependence is ``catastrophic''." Also, we have now
added an explanation for Beq. "where $\Beq=\sqrt{\mu_0\rho_0}\urms$
is the equipartition field strength where kinetic and magnetic energy
densities are equal."

> In the expression 0=<(u x B_0).b>-2\eta\mu_0<j.b>, is the 2 a typo?

Yes, we have now removed it.

> Near the end of Sect.3.1, it is not clear how this relates to the
> numerical result on alpha from Cattaneo & Hughes mentioned above.
> More explanation is needed.

We have now inserted "This agrees with the heuristic quenching formula
$\alpha\propto1/(1+\Rm\meanBB^2/\Beq^2)$, which also predicts $\alpha\to0$
as $\Rm\to\infty$."

> Is there a typo in the first expression citing the Cattaneo & Hughes
> result? In this expression alpha is proportional to eta, whereas in the
> expression for alpha above cited from Cattaneo & Hughes, alpha would be
> inversely proportional to eta

This was related to our omission of "1/" in 1/(1+Rm B^2/Beq^2). We have
now added "$\alpha=-\eta\mu_0\bra{\jj\cdot\bb}/\BB_0^2$,
so $\alpha\to0$ as $\eta\to0$ or $\Rm\to\infty$."

> Regarding the box on the derivation of Eq.(11); since it is not done
> elsewhere, in this box the definition of E in terms of the other variables
> needs to be written (including a few words explaining this physically)

We have now defined E as the electric field in the second sentence of
the box, where we write dA/dt=-E-grad phi, where E=-UxB+eta*mu0*J is
the electric field and ..." We also recall that we allude to the analogy
with the Poynting flux, which should aid the physical understanding.

> Just before Eq.(12), I suggest writing as "the magnetic helicity
> A \dot B" to remind novice readers what this quantity is.

This is done now.

> Just after Eq.(13), which used to be Eq.(12): Eq. 12 instead of 15

We corrected this; the label was used twice.

> The wording here needs to be made more clear, as this is a very
> important point. EG, could say, "It has long been hypothesized that the
> action of magnetic helicity fluxes can overcome what would otherwise be
> an extremely slow approach to saturation (as described in Sections 3.1
> and 3.2)."

Changed accordingly.

> Just after Eq.(15): it would be good to remind the reader (right after
> \Eq{dAmBmdt2}) that \bar \cal E \equiv \bar{u \cross b}

Done now: "where we recall that $\meanEMF\equiv\overline{\uu\times\bb}$
is the mean electromotive force."

> Regarding Eqs.(16) and (17), F_m and F_f have not been defined.

We have now defined them by adding after the respective equations
"where F_m is the magnetic helicity flux for the mean field" and
"where F_f is the magnetic helicity flux for the fluctuating field".

> In Eq.(17), looks like an overbar is missing on a.b

Yes; this has now been corrected; replaced () by \overline{}

> It would help readers to provide more of a physical understanding
> of the role of magnetic helicity flux. Mathematically, it has been
> demonstrated that if the fluxes integrate to zero, saturation is
> very slow. But it would be helpful to provide some intuition about
> why removal of magnetic helicity might hasten the approach to
> saturation.

We have now addressed this concern by discussing in the beginning
of Sect. 3.3 what is called the vacuum cleaner experiment.

> I have recommended adding a short section on the alpha effect between
> the current sections 2.3 and 2.4. Presumably there the simpler form
> of \Eq{EMFi} (multiplication only) will be given, explaining where this
> comes from. Then, when the representation in \Eq{EMFi} is introduced
> here, it can be motivated as a generalization.

We have now commented on this at the end of the next text box on
the alpha effect.

> In the second sentence of Sect 4.5, was the intention to refer to the
> box "Evolution equation for nonlocality in space and time"?

Yes, we have now corrected this and moved the former reference to the
memory effect to a later place in the same section.

> Please add an explanation that Eq.(19) is a model equation that assumes
> a certain form of alpha_ij and eta_ij, as motivated by the numerical
> simulations mentioned in section 4.5 (for the spatial nonlocality)

Yes, so we now write "simplest empirical approximations", but instead of
talking about "model equation", "as obtained with the test-field method"

> In Eq.(21): is this sign correct?

No, it should have been a minus sign.

> Near the end of Sect. 5.1.4, was this intended to be "massive galaxies"?
> The first stars presumably formed within galaxies, but very small ones.

We didn't really mean massive galaxies, so we have now rephased this
sentence and write "After that, galaxies start growing through continuous
gas accretion and mergers."

> Regarding Figure 8, a higher quality version of this figure is needed
> if it is going to appear in the article

We have made an attempt at adapting the figure from the published paper.

> Regarding the penultimate paragraph of Sect. 5.1.5, should refer to
> Fig 3 here with the discussion of Martin-Alvarez et al

Yes, we have done this now further below.

> Regarding Fig.9, a higher quality version of this figure is needed

Done.

> In the beginning of Sect. 6.2, better to use "galaxy" as this is the
> standard terminology

Done.

> In the beginning of Sect. 6.3, it would be helpful to explain this in
> more detail. What is the advective helicity flux?

We have added here now "similarly to what was discussed in Sect. 3.3."
to refer to advective helicity flux as discussed in that section which
has now been mentioned there in response to this comment.

> In numerical MHD simulations that employ finite volume methods, it is
> frequently the case that no explicit resistivity or viscosity is included.
> However, there is inevitably effective numerical resistivity and
> viscosity, and only moderate Re and Re_M are achievable. In discussing
> the simulations, it would be valuable to comment on this, in light of (1)
> the argument (section 3.1 and 3.2) that the rate at which saturation is
> reached is reduced at higher Re_M, corresponding to higher resolution,
> and (2) the hypothesis (section 3.3) that magnetic helicity flux --
> which is present in both the shearing-box and global simulations --
> enhances mean field growth. In particular, are there resolution studies
> from the simulations discussed in Section 7.3 and 7.4 that either show
> slower saturation at higher resolution (indicating a dominance of #1
> at the achievable resolution) or convergence in saturation at higher
> resolution (possibly in combination with measurements of large magnetic
> helicity flux), supporting #2?

We have now added an extra paragraph on this right at the end of Sect. 7.4.

> Regarding Fig.16, need higher quality figure

Done.