Hasan al Rasyid 3 years ago
parent c8f9322f80
commit f1e35b8389
  1. 60
      manuscript.md

@ -74,11 +74,8 @@ similarities in the (micro)physics, i.e., constitutive relations of
protostellar cores and protogiant planets serve as a further
motivation for this study.
# Baker's standard one-zone model
<!-- we need figure* for make it full screen, so it must be in latex code as follows
-->
@ -102,6 +99,14 @@ constitutive relations.
self-gravitating,
spherical gas clouds with the following properties:
~~~
* hydrostatic equilibrium,
* thermal equilibrium,
* energy transport by grey radiation diffusion.
~~~
non-numbered list can be written as above, and shown as:
* hydrostatic equilibrium,
* thermal equilibrium,
* energy transport by grey radiation diffusion.
@ -109,12 +114,11 @@ spherical gas clouds with the following properties:
For equations, we can use several environment:
~~~
\begin{equation}
$$ $$ is equal with \begin{equation}
\begin{eqnarray}
\begin{array}
\begin{displaymath}
\begin{align}
~~~
This is an example:
@ -133,6 +137,16 @@ This is an example:
\nabla \times \vec{E} &= -\frac{\vec{B}}{t}
\end{align}
And this is another example for inline equation, such as: $$y = 5\cdot x^2$$
You can see that inline equation have automatically numbered.
Independent paragraph equation is not numbered, as below.
$$
\nabla \cdot \vec{W} = \sigma W \nonumber
$$
The block should be as an independent paragraph (blank line above and under the block).
For the one-zone-model Baker obtains necessary conditions
for dynamical, secular and vibrational (or pulsational)
stability (Eqs. (34a,b,c) in Baker \citeyear{DudaHart2nd}). Using Baker's
@ -412,25 +426,23 @@ create label for \ref{FigVibStab} using #FigVibStab
# Conclusions
\begin{enumerate}
\item The conditions for the stability of static, radiative
layers in gas spheres, as described by Baker's (\citeyear{DudaHart2nd})
standard one-zone model, can be expressed as stability
equations of state. These stability equations of state depend
only on the local thermodynamic state of the layer.
\item If the constitutive relations -- equations of state and
Rosseland mean opacities -- are specified, the stability
equations of state can be evaluated without specifying
properties of the layer.
\item For solar composition gas the $\kappa$-mechanism is
working in the regions of the ice and dust features
in the opacities, the $\mathrm{H}_2$ dissociation and the
combined H, first He ionization zone, as
indicated by vibrational instability. These regions
of instability are much larger in extent and degree of
instability than the second He ionization zone
that drives the Cephe\text{\"\i}d pulsations.
\end{enumerate}
1. The conditions for the stability of static, radiative
layers in gas spheres, as described by Baker's (\citeyear{DudaHart2nd})
standard one-zone model, can be expressed as stability
equations of state. These stability equations of state depend
only on the local thermodynamic state of the layer.
2. If the constitutive relations -- equations of state and
Rosseland mean opacities -- are specified, the stability
equations of state can be evaluated without specifying
properties of the layer.
3. For solar composition gas the $\kappa$-mechanism is
working in the regions of the ice and dust features
in the opacities, the $\mathrm{H}_2$ dissociation and the
combined H, first He ionization zone, as
indicated by vibrational instability. These regions
of instability are much larger in extent and degree of
instability than the second He ionization zone
that drives the Cephe\text{\"\i}d pulsations.

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