update response and fix Lagrangian derivative

Author: harpolea

astronum_2019_MAESTROeX/astronum-maestroex.tex

@@ -101,7 +101,7 @@ \section{Low Mach number hydrodynamics} \label{sec:low_mach_hydro}
     \pd{\Ub}{t} &= - \Ub\cdot\nabla\Ub - \frac{\beta_0}{\rho}\nabla\left(\frac{\pi}{\beta_0}\right) - \frac{\rho - \rho_0}{\rho} g \bm{e}_r,\\
     \pd{\left(\rho h\right)}{t} &= -\nabla\cdot\left(\rho h \Ub\right) + \md{p_0}{t} + \rho H_{\mathrm{nuc}},
 \end{align}
-where $\rho$, $\Ub$ and $h$ are the mass density, fluid velocity and specific enthalpy, $X_k$ and $\dot{\omega}_k$ are the species mass fraction and production rate of species $k$, and $H_{\mathrm{nuc}}$ is the energy release per time per unit mass. The Lagrangian derivative is defined as $D/Dt = \partial/\partial t + \nabla\cdot$. \maestroex~defines the base state pressure $p_0$ to be consistent with the one-dimensional base state density, $\rho_0 = \rho_0(r, t)$, which represents the lateral average and is in hydrostatic equilibrium with $p_0$:
+where $\rho$, $\Ub$ and $h$ are the mass density, fluid velocity and specific enthalpy, $X_k$ and $\dot{\omega}_k$ are the species mass fraction and production rate of species $k$, and $H_{\mathrm{nuc}}$ is the energy release per time per unit mass. The Lagrangian derivative is defined as $D/Dt = \partial/\partial t + \Ub\cdot\nabla$. \maestroex~defines the base state pressure $p_0$ to be consistent with the one-dimensional base state density, $\rho_0 = \rho_0(r, t)$, which represents the lateral average and is in hydrostatic equilibrium with $p_0$:
 \begin{equation}
     \nabla p_0 = -\rho_0 g \bm{e}_r,
 \end{equation}

astronum_2019_MAESTROeX/referee_response.txt

@@ -1,3 +1,5 @@
+Dear Prof. Pogorelov,
+
 We thank the referee for their response and suggestions for modifications to the paper. We have outlined our changes below.
 
 1. "Modelling and modelled with two l's are the British spellings. Not sure if consistent US spelling is desired, but if so, they should be changed throughout."
@@ -14,11 +16,11 @@ We have added the definition of the Lagrangian derivative used in equation 3.
 
 4. "It might be worth defining \dot{omega_k} as the "production or destruction rate", since presumably the sum over k of the rates must be zero."
 
-We prefer using the term production rate as this indicates that positive values describe species creation, and negative values describe species destruction.
+We prefer using the term production rate as this indicates that positive values describe species creation, and negative values describe species destruction. This is also the term we have used in previous MAESTROeX and Castro papers, so we use it here to be consistent with the previous literature. 
 
 5. "In section 5, two alternative methods of defining the pressure in rotating stars are described.  Some conclusion should be drawn about whether both methods or only one (if either) will be pursued going forward."
 
-In section 5, we say that we are currently exploring all the methods described in the section. In the last paragraph, we describe how for the case of rotating stars we will most likely be using one of the simpler techniques, however for modelling X-ray bursts on neutron stars a more complex approach that properly captures the rotationally-induced deformation of thestar may be required. 
+In section 5, we say that we are currently exploring all the methods described in the section. In the last paragraph, we describe how for the case of rotating stars we will most likely be using one of the simpler techniques, however for modelling X-ray bursts on neutron stars a more complex approach that properly captures the rotationally-induced deformation of the star may be required. 
 
 
 In addition to these modifications, we have updated some references to reflect the fact that they have now been published (instead of citing the arXiv preprints).