Thanks, Rainer, for your thorough reading of our paper. Below our responses.

> many thanks to you (Eva) for pointing me at your review. I read it yesterday
> in one of the heavily delayed DB trains on the way back from Berlin. You did
> a great job to summarize the history and recent developments of dynamo
> models. Pity that you disregarded comparing theory/models with observations.
> I assume that this was not your intention. Hopefully you (or someone else,
> but certainly not me) will write a follow-up review paper. The forthcoming
> SKA radio telescope will trigger progress in the field (see e.g.
> https://ui.adsabs.harvard.edu/#abs/2015aska.confE..94B/abstract).

Thanks for the tip to mention SKA, which we have now done on page 32. We
are already now clearly beyond our page and reference limit, so we'll
see where we can skip something. There have been many recent reviews on
practical issues, but not enough on the theoretical and numerical issues,
we felt.

> Here are my questions and comments:
> - I don't understand your statement in the Abstract and Conclusions that
> "the observed large-scale galactic magnetic fields might not entirely
> originate from a mean-field dynamo". As I showed in my reviews, observations
> are well consistent with mean-field dynamo models concerning e.g. the
> existence of galaxy-scale regular fields, spiral pitch angles, radial
> variation of pitch angles, the dominance of axisymmetric spiral field modes,
> the dominance of even-parity fields, etc.
> Which observations ARE in conflict with mean-field dynamo models? Or do you
> just want to say that, according to theory, there could be mechanisms other
> than the mean-field dynamo that may generate regular fields? What are the
> papers of these alternatives giving predictions that could be compared with
> observations? To my knowledge, alternative models did not yet present
> observational tests.

This statement upset also other readers. We have now shortened this part;
see http://norlx65.nordita.org/~brandenb/tmp/Galactic-Dynamos/paper.pdf
Remember, we were here talking about turbulence simulations, not
mean-field models with built-in alpha effect. So the problem is really
to understand how mean-field models can be right, if simulations don't
give the same result. (This applies to both the idealized ones and the
global ones you mention below.)

> Of course, we can never "know for sure whether galactic dynamos are of
> alpha-Omega type" (Section 2.6) because experimental science can never give
> us 100% evidence. However, the existing evidence from observations is rather
> high. Claiming "some other, possibly as yet unknown type of large-scale
> dynamo" seems just speculation.

Yes, so we have now written: "We do not know whether galactic dynamos
are of $\alpha\Omega$ type. Alternatives include the incoherent
$\alpha$--shear effect, but also the (magnetic) shear--current effect
has been discussed; see \Tab{TDynType} for a summary of the different
types of large-scale dynamos known so far."

> - Which of the dynamo types listed in Table 2 are not only of academic
> interest but are likely to occur in real astrophysical objects? How well are
> the physics behind these flows understood? Have observational tests been
> developed in order to investigate their importance?

In the modified sentence above, we now put the incoherent alpha-shear
effect in the foreground, but in the end, none of them are excluded. The
flows responsible for turbulent pumping are in principle well understood,
but the idea of them producing a dynamo is confirmed so far only for
laminar flows without boundaries.

> - As you argue in Section 7.2, numerical simulations based on "divergence
> cleaning" are unreliable. As a non-expert, I would like to learn whether
> such simulations are (a) mostly useful, (b) useful in some aspects, or (c)
> completely useless. In other words, do the "artifacts " disturb the results
> or do they generate mostly wrong results?

We don't know, but have now added the sentence "This suggests that
potential problems with divergence cleaning may not be severe."

> - I'm missing a critical discussion of the numerical simulations concerning
> the following issues:
> (a) The magnetic Reynolds and Prandtl numbers of the existing simulations
> are orders of magnitude off the real values of the ISM (Table 3). Hence, how
> realistic are the simulations? Could it be that they miss most of the
> important physics?

We don't think it affects (or should affect) the large-scale dynamo. We
have therefore now added "At large $\Pm$, the small-scale magnetic energy
tends to dominate and the dynamo returns much of the magnetic energy
back into kinetic \citep{BR19}.  However, no effect on the large-scale
dynamo has been reported as yet." at the end of paragraph 2 of Sec.7.1.

> (b) All existing simulations predict an energy density of the saturated
> magnetic field that is much below the energy density of turbulence. Hence,
> the predicted field strengths are far below the observed ones. This problem
> may be related to issue (a). For example, Federrath et al. (2014) showed
> that the magnetic energy density of the small-scale dynamo increases with
> the magnetic Prandtl number, but simulations are still far away from
> reality.

The increase found in Federrath et al. (2014) is small, and there is
no increase in Brandenburg (2014, ApJ 791, 12; see Fig.2). Federrath
et al. (2014) emphasized mostly that the dynamo still works for Pm<1,
but this was already shown by Iskakov+07 and Brandenburg11, and is not
relevant for Galactic dynamos. So the problem of strong magnetic fields
is still unsolved. We have now added some more text in paragraph 2 of
Sect.7.1.

> (c) None of the existing simulations was able to generate a galaxy-wide
> regular field, as e.g. observed in M31, so that no large-scale dynamo
> appears (except for Eva's 2020 paper that has other issues). Is this
> discrepancy also related to problem (a)?

The lack of a regular field is perhaps (and hopefully) related to
insufficient magnetic helicity fluxes. How to make them larger is still
unclear. Artificially constructed small-scale magnetic field removal
helps, but we don't quite know how a galaxy can do this; see our reference
to vacuum cleaner experiment in paragraph 1 of Sect.3.3.

> (d) Simulations do not include anisotropic turbulence (to my knowledge),
> although there is observational evidence that most of the "ordered" fields
> seen in radio and FIR polarisation are in fact anisotropic turbulent (or
> tangled regular) ones.

Do you mean a striated field? But this is something that should come out
and is not something to put in. But we aren't sure whether this aspect is
really in disagreement with observations. Some simulations start with a
strong field, so those are then initially more anisotropic perhaps.

> - In the Summary Points of your review you say that "Simulations suggest
> that the efficiency of large-scale dynamos decreases with increasing
> resolution". However, I cannot find this statement in the main text. Only
> Eva's 2020 paper has a working large-scale dynamo; do you refer to this
> paper? Eva's simulation lacks a small-scale dynamo. The operation of a
> large-scale without a small-scale dynamo is not realistic, and so is the
> statement about efficiency.

This problem is discussed at the end of Sec.3.3.

> - Section 6.2: As I wrote in my various reviews, the result of a
> predominantly nonaxisymmetric field in M81 from 1989 is most probably
> incorrect. That result was based on RMs between 6cm and 20cm, where the 20cm
> data are strongly affected by Faraday depolarisation. New data have been
> obtained, but results are not yet available.

So what do you suggest we do? We have now again referred to Beck+19, but
there you just write that M81 and M83 have perhaps BSS.

> - In the last para of Section 6.2, the most recent paper on NGC4631 is
> missing (https://ui.adsabs.harvard.edu/#abs/2019A%26A...632A..11M/abstract),
> presenting high-resolution RM data for the first time. The halo of this
> galaxy has clearly no quadrupolar symmetry as stated in Section 6.5, but
> shows several field reversals on scales of a few kpc.

OK, so we have have now changed this sentence to "The resulting magnetic
fields were thought to have quadrupolar symmetry also in the halo,
but this now seems to be ruled out by new observations \citep{NGC4631}."

> - The statement in Section 6.5 that "the equipartition assumption may have
> overestimate the actual field strength by a factor of about 1.5" is
> incorrect. This overestimation factor refers to the case of strong magnetic
> fluctuations and has nothing to do with the equipartition assumption itself.

We have now rephrased the relevant text as: "They argue that ignoring
the nonlinear dependence of the synchrotron emission on the plane-of-the
sky magnetic field component can lead to an overestimation of the actual
magnetic field by up to a factor of 1.5."
Cheers, Eva & Axel