We thank the referee for useful remarks and suggestions that have
significantly improved the manuscript. We have responded to all of
the comments, as detailed below. The corresponding changes in the
paper are marked in blue.

> 1. In the introduction, the authors mention that the photosphere,
> chromosphere, etc, are ignored in their model. The authors should therefore
> make it clear how this assumption influences their results. How do the
> authors see this boundary being better approximated in future models? i.e.
> how can the effects of flux emergence be incorporated.

At the end of the introduction (page 2, bottom left column), we have now
mentioned that the implications of a cool photosphere are discussed at
the end of the paper. We refer here to a new Section 3.8, where we also
compare the plasma beta for our three models.

> 2. The authors rightly mention the work of Perri et al. (2018) in the
> introduction (another example of similar work is Pinto et al. 2011), but
> more recently this group have been working on a coupled code similar to
> that presented in this paper. It would be interesting to briefly compare
> these independent codes. Perri et al uses the PLUTO MHD code, in a similar
> way to the author’s model, see https://arxiv.org/pdf/1912.01271.pdf .

We have now added the Pinto+11 and Perri+18 references at the end of the
third paragraph of the introduction (page 1, bottom right and page 2,
to left). We have now also compared some of our parameters with theirs;
see the second half of Sect. 3.2 on page 5.

> 3. The figure captions are generally inadequate to describe the figure
> contents. Though the text describes the figures in a concise manner, often
> there are multiple lines in each panel which are not described and this
> causes confusion for the reader.

We have now expanded most of the figure captions and have also enhanced
the discussion of several important figure in the text.

> 4. Axis labels have been left off in Figures 2, 3, 5, 10, 11, and 12 which
> should be included to show the normalisation of the axes scale (either by
> the magnetic field strength, or length scale).

In Fig.2, we plot different quantities, which are labeled on the
corresponding lines. Therefore, no general y-title is really appropriate.
In Figs. 3 and 5, and 10-12, we have now added \varpi and z.

> 5. In Figure 5, a few panels show open magnetic field in the stellar wind to
> be disconnected from the surface (these appears as v-like structures in the
> stellar wind). Are these physically reasonable, or consequences of the
> numerical/chosen diffusivities in the model? In either case, these are
> significant features in the authors' model and should be discussed
> appropriately.

Yes, the V-type features are not textbook-like. This is a feature of
our time-dependent model. We have now added a corresponding discussion
of this in the second paragraph of Section 3.3 (pages 6 and 7).

> 6. Have the authors validated their model conserves other quantities like the
> open magnetic flux in the wind, and the angular momentum-loss rate, in the
> same way that they have evaluated the mass-loss rate, i.e. on concentric
> radial shells?

We have now added Figures 10 and 16 showing the angular momentum-loss
rate averaged over concentric radial shells; see pages 9 and 12,
respectively. For the two stationary models, the angular momentum-loss
rate is perfectly constant and outward, but for the slowly rotating
model there are regions at midlatitudes where the angular momentum
flux is negative. However, as was already discussed in the paper, those
rates would be too small to affect the angular momentum of the stellar
envelope significantly. We have now adapted the discussion in Section
3.5; see paragraphs 2 and 3 on pages 9 and 10. We also considered adding
a plot of the four invariants (flux ratio, angular velocity of magnetic
field lines, the angular momentum constant, and the Bernoulli constant),
similar to Fig.20 of von Rekowski et al. (2003), but because of the time
dependence, the significance of such lines is questionable.

> 7. In Section 3.4, the meaning of paragraph 4 (beginning "The kinetic..") is
> not very clear and should be clarified. Additionally, the authors may wish
> to consider reorganising this section since a number of the paragraphs are
> rather short. Perhaps the energy balance in the wind is better discussed
> after the kinetic and magnetic luminosities are introduced?

We have now moved the discussion about the energetics in the solar wind
to paragraphs 5 and 6 of Sect. 3.4 on page 8. We have significantly
enhanced the presentation and refer to the additional discussion at the
very end of the paper; see Sect. 3.8 one page 12 and 13.

> 8. In Figure 8, the y-labels are denoted L_K and L_M, whereas I think the
> quantities plotted are E_K and E_M. Though which is red/blue is also not

Yes, this is right and we have now corrected all labels.

> 9. What is the energy source for the increasing kinetic energy of the wind
> with radial distance, given the wind is isothermal, and the magnetic energy
> is ~20 times smaller than the kinetic energy? This should be clearly
> detailed within Section 3.4.

The increase in kinetic energy is a consequence of the radial increase
of the radial wind, which makes the dominant contribution to the kinetic
energy. We have now discussed this in the aforementioned revised and
enhanced paragraph 5 of Sect. 3.4 on page 8, where we discuss the
energetics of the solar wind.

> 10. In Section 3.5, the angular momentum flux in the kinetic term is said to
> dominate over the magnetic term, with Figure 9 showing this to be true for
> almost all radial distances. However, for a Weber & Davis (1967) stellar
> wind, with which this model should be in accord, the angular momentum in
> the kinetic and magnetic term varies with radial distance as stresses in
> the magnetic field transfer angular momentum into the kinetic term. Why is
> this not the case in the authors' model? Perhaps the magnetic field is so
> weak that it lies in an extreme part of the parameter space, and so this
> effect is difficult to distinguish? Plotting the angular momentum-loss rate
> versus radial distance (i.e. on concentric radial shell) for the kinetic,
> magnetic, turbulent terms and their total, may shed light on this.

We have now done this in the new Figure 10, where we show the three
contributions to the time- and latitude-averaged angular momentum flux;
see page 9. We see that the magnetic and kinetic contributions can be of
comparable magnitude at around the Alfven radius. We now mention Weber &
Davis (1967) in that connection; see the text in the second paragraph
of Sect.3.5 on the lower left and right of page 9. We have now also
emphasized that Figure 9 applies to large radii beyond the sonic point.

> 11. The authors note that the kinetic angular momentum flux varies from
> positive to negative, which can be seen in Figure 9. This is highly unusual
> for this kind of Parker wind model, implying that the wind is rotating
> opposite to the direction of stellar rotation in these open field regions.
> Could the authors please explain how this is possible, perhaps there is a
> need to investigate the azimuthal flow of the wind at the surface boundary
> (R).

This is correct and of course, at first sight, surprising. We now argue
that this is mostly caused by our primitive modeling of the hydrodynamics
inside the star. The latitudinal angular velocity variations are further
exaggerated by the fact that the plasma beta in our models in not small
enough. This is now discussed in Sect.3.8 on page 13. On page 10, left
column, we also make reference to recent Parker Solar Probe observations
of negative angular momentum flux in the fast wind at certain longitudes.

> 12. I would encourage the authors to consider adding some material which
> relates to the dynamo-wind coupling, and how it changes with increasing
> rotation etc. This could be included at the end of Section 3. The abstract
> and conclusion should also reflect this as it is an exciting and new aspect
> to this kind of research.

In our new Fig. 17, we compare with the more rapidly rotating models.
However, the plasma betas are larger in those more rapidly rotating
models. Therefore, to make more astrophysically relevant statements
about dynamo-wind coupling, we would need to await the development of
more realistic models.

> Minor Comments:
> 13. In the conclusion of the abstract, the authors' remarks are quite generic
> i.e. commenting on results which are, in general, expected based on
> previous steady-state and uncoupled wind models. For example, variable
> angular momentum flux is shown in Perri et al. (2018), and the collimating
> effect of rapid rotation on the wind outflow in Washimi & Shibata (1993).
> In my opinion, the abstract would be enhanced if the authors considered
> what features of their work are novel and modify their conclusions
> accordingly.

We have now mentioned the latter paper when we introduce our more rapidly
rotating models at the end of paragraph 4 of Sect. 3.7 on page 11. We
have changed the last sentence of the conclusions in the abstract to
reflect the caveats resulting from not being able to reach small enough
plasma betas.

> 14. The use of r_* and R throughout the paper is a little confusing, the
> authors could consider changing r_* (which is the sonic/critical point in
> the wind) to r_c, or something similar.

We have now replaced r_* by r_c throughout.

> 15. The authors set r_*=1 (the sonic/critical point) though in Figure 3 the
> transonic surface is actually smaller than 0.5 (shown with a solid line).
> What causes this change in parameter space? This should be made clear in
> the text.

The surface at r=0.5 (or 0.4) is actually the Alfv\'en surface. The
transmagnetosonic surface is indeed near r=1. We have now corrected
the labeling.

> 16. In equation (26), omega bar has not been defined in J_* (it doesn't seem
> to be defined anywhere in the paper, despite being used further in Section
> 3.5). Additionally, the authors' method for calculating M dot, and J dot,
> are not shown in Section 2.5, yet values are quoted for both quantities. I
> suggest referencing the later Sections that discuss them.

\varpi is the cylindrical radius and is now defined directly after
Eq.(26); see page 4. J_* is the angular momentum of the stellar envelope,
as is now also said directly after Eq.(26). We now refer to Sect. 3.5,
where Jdot is calculated. We decided not to refer to Sect. 3.1 for the
calculation of Mdot, because here we just talk about the time scale,
and Mdot=1 was already given as our initial condition.

> 17. In Figure 4, the colorbar is difficult to read and obscures some of the
> data.

We have now made the color bars smaller and shifted them further to
the right. Since the pattern is periodic, the occulted parts are not
critical. The numbers are still legible.

> 18. Figures 6, 7, and 8 are very busy. Each panel within a figure showing a
> different time step, and then either many different radial or latitudinal
> profiles. Again the lack of accompanying detail in the figure captions
> makes these hard to understand. Additionally, the figures are not discussed
> within the text to justify their complexity. Therefore, the figures should
> either be better discussed in the figure caption or main body text, or the
> content of each panel should be made simpler. For example, why not show the
> average profile for each time step along with the maximum and minimum
> variances, or just show fewer radial/latitudinal profiles in each panel.
> Small text should be avoided, and the line colors and styles should be
> described adequately in the figure captions.

The difficulty with fewer panels is simply the resulting temporal
discontinuity by not being able to understand how they belong together.
To address the suggestion of the referee, we have now enhanced the figure
captions and the discussion around theses figures.

> 19. Equation (34) is very similar to the poloidal vorticity-current stream
> function (\Lambda) which is often used in stellar wind studies (Keppens and
> Goedbloed 1999, Reville et al 2015, Pantolmos et al. 2017) and has recently
> been used in studies of the solar wind (Finley et al. 2019). It might be
> worth connecting this to previous works, in order to increase the impact of
> this paper.

We thank the referee for alerting us to these important references and
have added them now just below Eq.(34) on page 10.

> 20. In Section 3.6, "breaking" is used instead of braking.

We have now corrected this in all 4 occurrences; see pages 1 and 10.

> 21. In Figure 10, the angular velocity contours are easily confused with
> field lines as they are the same color etc as Figures 3 and 5. Perhaps
> change the color or linestyle of these (to make it clear that they
> are different between figures)? It would also be interesting to see
> the field lines and Alfven surface for the rapidly rotating cases,
> to compare these with the solar case.

We have now changed the white lines to black ones and have added the
Alfven and transonic surfaces; see Figs 11 and 12 on pages 10 and 11.

> 22. When introducing the contours of rotation in Section 3.7, it would be
> useful to compare the contours for the solar case to the rapidly rotating
> cases. Perhaps all the 3 models could be shown in Figure 10?

We have now done this by introducing a new Figure 11, which shows contours
of angular and radial velocity at different times. This is now discussed
in paragraph 3 of Section 3.5 on page 10, at the end of paragraph 4
of Section 3.7 on page 11, and also again in the conclusions, where we
speculate that the occurrence of inward angular momentum transport in our
slowly rotating model could be a consequence of our primitive modeling of
differential rotation in the star; see page 13, right column. Again, there
is an interesting connection with the fast solar wind in some longitudes.

> 23. In Figures 11 and 12, it looks like there is no B_phi in the grey
> part of the domain, is this a choice in colorbar or actuality? Why are
> field lines not shown for the rest of the domain?

The magnetic field is never vanishing, but it is indeed very small
in the exterior. This is now explicitly discussed in paragraph 5 of
Section 3.7; see page 11, right column.  Poloidal field lines must
always be uniformly spaced, so it is difficult to show the weak parts
in the exterior. The toroidal field could be represented nonuniformly,
but the resulting plots look very unnatural, so we have refrained from
showing such representations, given that the main point was just to show
how the field looks like in the dynamo region, and then to discuss why
it is still not oscillatory (Calpha still needs to be rather large for
the dynamo to be excited).

> 24. The x axis of figure 12 has been incorrectly labelled as B_phi.

This is now corrected; this is now Fig.14 on page 12.

> 25. The authors might consider moving Figure 14 to the appendix as it is not
> discussed enough within the text and is only shown for completeness. The
> current material within the appendix could be removed as it is not new and
> does not serve a purpose in the paper.

In view of the many other newly added figures, this one is now redundant
and we have removed it. We have now also removed the old appendix.