From d04e5efb691717a1cb82d4158fac6803c785490c Mon Sep 17 00:00:00 2001
From: Hasan al Rasyid <hasanalrasyid@home>
Date: Sun, 13 Mar 2022 08:21:00 +0900
Subject: [PATCH] light edit

---
 manuscript.md | 42 ++++++++++--------------------------------
 1 file changed, 10 insertions(+), 32 deletions(-)

diff --git a/manuscript.md b/manuscript.md
index db24b61..35c7504 100644
--- a/manuscript.md
+++ b/manuscript.md
@@ -26,40 +26,18 @@ appendix:
   - appendix/2
 abstractTex:
   \abstract{To investigate the physical nature of the `nuc\-leated instability' of
-  proto giant planets, the stability of layers
-  in static, radiative gas spheres is analysed on the basis of Baker's
-  standard one-zone model.}
+  proto giant planets, the stability of layers in static, radiative gas spheres is analysed on the basis of Baker's standard one-zone model.}
   {To investigate the physical nature of the `nuc\-leated instability' of
-  proto giant planets, the stability of layers
-  in static, radiative gas spheres is analysed on the basis of Baker's
-  standard one-zone model.}
-  {It is shown that stability depends only upon the equations of state, the opacities and the local
-  thermodynamic state in the layer. Stability and instability can
-  therefore be expressed in the form of stability equations of state
-  which are universal for a given composition.}
-  {The stability equations of state are
-  calculated for solar composition and are displayed in the domain
-  $-14 \leq \lg \rho / \mathrm{[g\, cm^{-3}]} \leq 0 $,
-  $ 8.8 \leq \lg e / \mathrm{[erg\, g^{-1}]} \leq 17.7$. These displays
-  may be
-  used to determine the one-zone stability of layers in stellar
-  or planetary structure models by directly reading off the value of
-  the stability equations for the thermodynamic state of these layers,
-  specified
-  by state quantities as density $\rho$, temperature $T$ or
-  specific internal energy $e$.
-  Regions of instability in the $(\rho,e)$-plane are described
-  and related to the underlying microphysical processes.}
-  {Vibrational instability is found to be a common phenomenon
-  at temperatures lower than the second He ionisation
-  zone. The $\kappa$-mechanism is widespread under `cool'
-  conditions.}
+  proto giant planets, the stability of layers in static, radiative gas spheres is analysed on the basis of Baker's standard one-zone model.}
+  {It is shown that stability depends only upon the equations of state, the opacities and the local thermodynamic state in the layer. Stability and instability can therefore be expressed in the form of stability equations of state which are universal for a given composition.}
+  {The stability equations of state are calculated for solar composition and are displayed in the domain $-14 \leq \lg \rho / \mathrm{[g\, cm^{-3}]} \leq 0 $, $ 8.8 \leq \lg e / \mathrm{[erg\, g^{-1}]} \leq 17.7$. These displays may be used to determine the one-zone stability of layers in stellar or planetary structure models by directly reading off the value of the stability equations for the thermodynamic state of these layers, specified  by state quantities as density $\rho$, temperature $T$ or specific internal energy $e$. Regions of instability in the $(\rho,e)$-plane are described and related to the underlying microphysical processes.}
+  {Vibrational instability is found to be a common phenomenon at temperatures lower than the second He ionisation zone. The $\kappa$-mechanism is widespread under `cool' conditions.}
   {}
 keywords: giant planet formation -- $\kappa$-mechanism -- stability of gas spheres
 acknowledgements:
       Part of this work was supported by the German
-      \emph{Deut\-sche For\-schungs\-ge\-mein\-schaft, DFG\/} project
-      number Ts~17/2--1.
+      *Deutsche Forschungsgemeinschaft, DFG* project
+      number Ts 17/2--1.
 
 ---
 
@@ -222,7 +200,7 @@ notation:
    \end{enumerate}
    The first factors, depending on only timescales, are positive
    by definition. The signs of the left hand sides of the
-   inequalities~(\ref{ZSDynSta}), (\ref{ZSSecSta}) and (\ref{ZSVibSta})
+   inequalities (\ref{ZSDynSta}), (\ref{ZSSecSta}) and (\ref{ZSVibSta})
    therefore depend exclusively on the second factors containing
    the constitutive relations. Since they depend only
    on state variables, the stability criteria themselves are \emph{
@@ -267,7 +245,7 @@ notation:
    (\ref{ZSDynSta}), (\ref{ZSSecSta}) and (\ref{ZSVibSta}) and thereby
    obtain \emph{stability equations of state}.
 
-   The sign determining part of inequality~(\ref{ZSDynSta}) is
+   The sign determining part of inequality (\ref{ZSDynSta}) is
    $3\Gamma_1 - 4$ and it reduces to the
    criterion for dynamical stability
    \begin{equation}
@@ -288,7 +266,7 @@ notation:
       \Gamma_1     = \chi_\rho^{} + \chi_T^{} (\Gamma_3 -1)&>&0\\
       \nabla_{\mathrm{ad}}  = \frac{\Gamma_3 - 1}{\Gamma_1}         &>&0
    \end{eqnarray}
-   we find the sign determining terms in inequalities~(\ref{ZSSecSta})
+   we find the sign determining terms in inequalities (\ref{ZSSecSta})
    and (\ref{ZSVibSta}) respectively and obtain the following form
    of the criteria for dynamical, secular and vibrational
    \emph{stability}, respectively: