feb2021_ref_response.txt

 >Reviewer's Comments: I read the new revised version with interest. Here are my
>main comments.

>1- I still object to the strategy adopted by the authors to NOT use a
>shock-divergence term in the vector potential equation. The authors explain
>that "the sixth-order Pencil code does require a small amount of mass
>divergence as well in order to ensure numerical stability when wall heating
>occurs from the interaction of strong shocks". I totally agree with this
>careful use of a stabilising mechanism in presence of strong shocks. I am
>however not convinced that removing this term in the vector potential equation
>is a wise choice, especially in the context of magnetic dynamos. Indeed, it is
>crucial to separate a true dynamo from a spurious one seeded by a numerical
>instability. I may be wrong, though. This is why I suggest that the authors try
>to repeat the same numerical experiment, keeping the divergence term in the
>vector potential equation. If the dynamo disappears completely then it is
>probably spurious. If the dynamo effect still occurs, then why not keeping the
>divergence term in the vector potential equation for sake of consistency and
>stability ?

Inclusion of the shock resistivity in Gent et al. (2013) was based on the
assumption that it would be required for numerical stability, but this 
conclusion was reached without systematic testing. In Gent et al. (2013) we did 
find that the inclusion of the shock resistivity was insufficient to suppress the
small-scale dynamo (SSD). In the context of setting up our current SSD 
experiments, however, we conducted tests with and without the shock resistivity. 
With shock resistivity, we find that magnetic fields at the shocks are 
substantially suppressed, while without shock resistivity the tests are passed 
without problems, and showed no signs of numerical instability. From these 
experiments we concluded that the shock resistivity was not necessary to 
prevent numerical instability, against our earlier expectations, and that 
more physical results are obtained without it. This motivates our choice 
in the SSD experiments reported in this Letter. We are planning to include 
these MHD tests into a more extensive manuscript on the SSD characteristics 
in the warm and hot phases.

As requested by the referee we have conducted an additional experiment with 1 pc
resolution and Pm = 10, but with shock resistivity included in the model. We
attach a plot for the editor and the referee, but not for inclusion in the
letter, that confirms that the SSD persists, but with drastically reduced 
growth rate and lower saturation level than the model without shock resistivity. 
We trust that this satisfies the referee that the SSD in our models is in fact 
physical, or at least not due to numerical instability due to shocks. The 
differences in the solutions can be explained by the rapid destruction of 
magnetic field due to unnecessary resistivity in the shock fronts.
We attach a slice of magnetic energy for both models at the same time and
location. Both models are clearly numerically resolved, and the largest 
difference occurs in the shell of the newly exploded SN, where magnetic energy
is reduced when shock resistivity is used. This also explains the lower
saturation level, where the equilibrium between dynamo growth and turbulent 
diffusion occurs at a lower energy. The stability of both solutions leads 
us to conclude that the divergence term in the induction equation should 
not be included because it is not necessary. In principle, any artificial 
numerical devices that would materially alter the turbulent properties of 
the magnetic field should be avoided, where possible, 

>2- The new figure 2 shows the kinetic energy in the box. It shows variations
>between a factor of 2 up to a factor of 10. This is far from being a true
>stationary state. I however agree with the authors that using the kinetic
>energy as a reference is better to illustrate the saturation level of the
>dynamo. I would therefore not fight them further on this point.

Noted.

>3- I am very surprised by the answer of the authors regarding the density
>fluctuations in their simulations. May be I misunderstood but I have the
>impression that there is a confusion between the mean density in the box, who
>should remain constant as mass is conserved, and the density variance or the
>r.m.s density in the box that should scale with the Mach number (at least for
>isothermal turbulence). For an adiabatic shock, one expect a compression of a
>factor of 4, and much more for a radiative shock with cooling. I would
>therefore expect in these simulations a wide range of densities.  In the
>context of ideal MHD, the frozen-in magnetic field evolution would result in a
>B \propto \rho^2/3 relation. I agree with the authors that it cannot explain
>many order of magnitude field amplification but it can certainly explain factor
>of 10, depending on the shock compression ratio. 

The mean density in all models remains 1 cm^-3. It is evident from our inspection
of the snapshots that magnetic field at some times and locations is stronger in
hot diffuse regions than in the warm, denser regions. The frozen-in assumption
therefore does not apply. Analysis and explanation of this behaviour is
complicated and requires extensive further investigation, which we will include
in our subsequent publication.

In addition to this written response, we have modified the y-axis labels in
Figure 5 to span two lines to improve comprehensibility, corrected names in a
few references, and made some minor edits for clarity (color font}, but
otherwise resubmit the Letter as it stands, trusting the evidence 
and arguments offered here satisfy the residual concerns expressed.