We thank the reviewer for detailed remarks and constructive
suggestions. We were happy to respond to all of them:

> 1. In the text of Section 1 and in the relations (1) or (2) the quantity
> $\rho$, simply declared as ``gas density", has obviously to be interpreted
> as a mean quantity. The same applies to $\rho$ in relations like
> $\bV = \rho^\sigma \bu$, $\bmH = \bmB / \rho^\sigma$ and
> $\blambda = - \nabla \ln \rho$ in Section 2.2.
> In expressions like $\overline{\rho \bu^2}$ or $\overline{\rho \bu^3}$
> at the beginning of Section 2, in relation (3) or in the equation
> $p = c^2_s \rho$ in Section 2.1, however, $\rho$ can hardly be interpreted
> in this way.  Clear statements on the meaning of $\rho$ at the different
> places (perhaps the replacement of $\rho$ by $\overline{\rho}$ at some
> of them) would be very desirable.

In the revised paper we decompose the total density \rho into the mean
and fluctuating parts. Corresponding changes have been made in all paper.

> 2. It would be helpful for the reader to say at the beginning of
> Section 2 that vanishing mean motion is assumed.

This is now done at the beginning of Section 2 (before 2.1, in the
4th sentence) of the revised paper.

> 3. The sentence ``The fluid velocity satisfies the continuity equation"
> at the end of Section 2.1 sounds like a consequence of equations given
> before. It should be clearly said that it is an additional requirement
> on the level of equations (3) and (4).

In the revised paper we added the continuity equation (5) for fluctuations
of \rho' of fluid density.

> 4. What means $\rho'$ in equation (22), what means $\Lambda$ ?

$\rho'$ is now defined in Sect. 1 after Eq. (1), and
${\bm \Lambda}={\bm k} - i \sigma {\bm \lambda}$ is now defined at the
end of Sect. 2.4. In addition, the cooling function $\tilde \Lambda(T)$,
defined in Sect. 3.4, is now written with a tilde.

> 5. Why $\alpha_\perp$, introduced with (26), corresponds to
> $\alpha$ given by (2), and why not $\alpha_\parallel$?

In the text we explain:

  Eq.(2) is expected to apply to $\alpha_\perp$, while $\alpha_\parallel$
  is known to behave differently and can have opposite sign
  \citep{BNPST90,Fer92,RK93}. This is why we associate in the following
  $\alpha$ in this equation with the $\alpha_\perp$ defined in Eq.(27).

According to Eq.(27), the notation $\perp$ in $\alpha_\perp$ implies
a direction that is perpendicular to the direction $\hat{\bm e}$ (i.e.,
to the direction of gravity), rather than to the direction of the mean
magnetic field.

> 6. The sentence ``In our units, $c_s = k_1 = \rho_0 = \mu_0 =1$"
> in Section 3.3 is not understandable.
> Can it not simply be canceled?

Yes, we have now omitted this.

> 7. $\tilde{\alpha}_\parallel$, shown in Fig.~4, is not defined.

The tilde was explained before saying

  We denote the corresponding non-dimensional quantities by a tilde
  and quote in the following their average values over an interval
  $z_1\leq z\leq z_2$, in which these ratios are approximately constant.

and {\alpha}_\parallel was explained as a coefficient in the equation.
We have now repeated the explicit definition in this case.

> 8. Numbers for $z_1$ and $z_2$ in Section 3.3?

We have now added those values in the paragraph after Eq.(28)

> 9. Definition of $l_0$ in Section 3.4?

The definition of $l_0$ is now added in Sect. 3.4, at the end of the
second paragraph.

> 10. Unit of $\tau_{corr}$ in Fig. 6?

The unit of $\tau_{corr}$ is Myr (see revised Fig. 6)

> 11. The remarks made in Sections 3.5 and 4 on the possibility of
> vanishing $\alpha$ in the case of $z$-independent $\overline{\rho u^3}$
> seem to rest on interpreting this quantity as $(\overline{\rho}^{1/3}
> u_{\rm{rms}})^3$.  There is however hardly any reason for an equality of
> these two quantities. Note that $\overline{\rho u^3} = \overline{\rho}
> \overline{u^3} + \overline{\rho' u^3}$ and $\overline{u^3} = 0$, that
> is $\overline{\rho u^3} = \overline{\rho' u^3}$, where $\overline{\rho}$
> and $\rho'$ denote the mean and fluctuating parts of $\rho$.

We have now clarified this by writing:

  In stellar mixing length theory \citep{Vit53}, one assumes that the
  temperature fluctuation, $T'$, is proportional to $\urms^2$, so
  the convective flux $\overline{(\rho\uu)'c_p T'}$ is well approximated by
  $\meanrho\urms^3$, which is also confirmed by simulations \citep{BCNS05}.

We hope that with these modifications our paper is now ready for publication
in the mail issue of the Astrophysical Journal.