-#LyX 1.6.0rc5 created this file. For more info see http://www.lyx.org/
-\lyxformat 344
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
\begin_document
\begin_header
\textclass aa
\end_preamble
\options traditabstract
\use_default_options false
+\maintain_unincluded_children false
\language english
+\language_package default
\inputencoding auto
+\fontencoding global
\font_roman default
\font_sans default
\font_typewriter default
\font_default_family default
+\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100
\font_tt_scale 100
\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
\paperfontsize default
\spacing single
\use_hyperref false
\use_geometry false
\use_amsmath 0
\use_esint 0
+\use_mhchem 1
+\use_mathdots 1
\cite_engine basic
\use_bibtopic false
+\use_indices false
\paperorientation portrait
+\suppress_date false
+\use_refstyle 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
-\defskip medskip
+\paragraph_indentation default
\quotes_language english
\papercolumns 2
\papersides 2
\paperpagestyle default
\tracking_changes false
\output_changes false
-\author ""
-\author ""
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
\end_header
\begin_body
\begin_inset Note Note
status open
+\begin_layout Plain Layout
+This is an example LyX file for articles to be submitted to the Journal
+ of Astronomy & Astrophysicssing (A&A).
+ How to install the A&A LaTeX class to your LaTeX system is explained in
+
+\begin_inset Flex URL
+status open
+
+\begin_layout Plain Layout
+
+http://wiki.lyx.org/Layouts/Astronomy-Astrophysics
+\end_layout
+
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
\begin_layout Plain Layout
Depending on the submission state and the abstract layout, you need to use
different document class options that are listed in the aa manual
\begin_inset Caption
\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:FigGam"
+
+\end_inset
+
Adiabatic exponent
\begin_inset Formula $\Gamma_{1}$
\end_inset
\end_inset
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset CommandInset label
-LatexCommand label
-name "FigGam"
-
-\end_inset
-
-
\end_layout
\end_inset
\begin_layout Standard
\align left
-\begin_inset Formula \begin{eqnarray*}
+\begin_inset Formula
+\begin{eqnarray*}
M_{r} & & \textrm{mass internal to the radius }r\\
m & & \textrm{mass of the zone}\\
r_{0} & & \textrm{unperturbed zone radius}\\
\rho_{0} & & \textrm{unperturbed density in the zone}\\
T_{0} & & \textrm{unperturbed temperature in the zone}\\
L_{r0} & & \textrm{unperturbed luminosity}\\
-E_{\textrm{th}} & & \textrm{thermal energy of the zone}\end{eqnarray*}
+E_{\textrm{th}} & & \textrm{thermal energy of the zone}
+\end{eqnarray*}
\end_inset
\begin_inset CommandInset ref
LatexCommand ref
-reference "FigGam"
+reference "fig:FigGam"
\end_inset
)
-\begin_inset Formula \begin{equation}
-\tau_{\mathrm{co}}=\frac{E_{\mathrm{th}}}{L_{r0}}\,,\end{equation}
+\begin_inset Formula
+\begin{equation}
+\tau_{\mathrm{co}}=\frac{E_{\mathrm{th}}}{L_{r0}}\,,
+\end{equation}
\end_inset
local free-fall time
\emph default
-\begin_inset Formula \begin{equation}
-\tau_{\mathrm{ff}}=\sqrt{\frac{3\pi}{32G}\frac{4\pi r_{0}^{3}}{3M_{\mathrm{r}}}}\,,\end{equation}
+\begin_inset Formula
+\begin{equation}
+\tau_{\mathrm{ff}}=\sqrt{\frac{3\pi}{32G}\frac{4\pi r_{0}^{3}}{3M_{\mathrm{r}}}}\,,
+\end{equation}
\end_inset
\end_inset
have the following form:
-\begin_inset Formula \begin{eqnarray}
+\begin_inset Formula
+\begin{eqnarray}
\sigma_{0} & = & \frac{\pi}{\sqrt{8}}\frac{1}{\tau_{\mathrm{ff}}}\\
-K & = & \frac{\sqrt{32}}{\pi}\frac{1}{\delta}\frac{\tau_{\mathrm{ff}}}{\tau_{\mathrm{co}}}\,;\end{eqnarray}
+K & = & \frac{\sqrt{32}}{\pi}\frac{1}{\delta}\frac{\tau_{\mathrm{ff}}}{\tau_{\mathrm{co}}}\,;
+\end{eqnarray}
\end_inset
\end_inset
has been used and
-\begin_inset Formula \begin{equation}
+\begin_inset Formula
+\begin{equation}
\begin{array}{l}
\delta=-\left(\frac{\partial\ln\rho}{\partial\ln T}\right)_{P}\\
-e=mc^{2}\end{array}\end{equation}
+e=mc^{2}
+\end{array}
+\end{equation}
\end_inset
is proportional to the ratio of the free-fall time and the cooling time.
Substituting into Baker's criteria, using thermodynamic identities and
definitions of thermodynamic quantities,
-\begin_inset Formula \[
-\Gamma_{1}=\left(\frac{\partial\ln P}{\partial\ln\rho}\right)_{S}\,,\;\chi_{\rho}^{}=\left(\frac{\partial\ln P}{\partial\ln\rho}\right)_{T}\,,\;\kappa_{P}^{}=\left(\frac{\partial\ln\kappa}{\partial\ln P}\right)_{T}\]
+\begin_inset Formula
+\[
+\Gamma_{1}=\left(\frac{\partial\ln P}{\partial\ln\rho}\right)_{S}\,,\;\chi_{\rho}^{}=\left(\frac{\partial\ln P}{\partial\ln\rho}\right)_{T}\,,\;\kappa_{P}^{}=\left(\frac{\partial\ln\kappa}{\partial\ln P}\right)_{T}
+\]
\end_inset
-\begin_inset Formula \[
-\nabla_{\mathrm{ad}}=\left(\frac{\partial\ln T}{\partial\ln P}\right)_{S}\,,\;\chi_{T}^{}=\left(\frac{\partial\ln P}{\partial\ln T}\right)_{\rho}\,,\;\kappa_{T}^{}=\left(\frac{\partial\ln\kappa}{\partial\ln T}\right)_{T}\]
+\begin_inset Formula
+\[
+\nabla_{\mathrm{ad}}=\left(\frac{\partial\ln T}{\partial\ln P}\right)_{S}\,,\;\chi_{T}^{}=\left(\frac{\partial\ln P}{\partial\ln T}\right)_{\rho}\,,\;\kappa_{T}^{}=\left(\frac{\partial\ln\kappa}{\partial\ln T}\right)_{T}
+\]
\end_inset
stability
\emph default
given below:
-\begin_inset Formula \begin{eqnarray}
+\begin_inset Formula
+\begin{eqnarray}
\frac{\pi^{2}}{8}\frac{1}{\tau_{\mathrm{ff}}^{2}}(3\Gamma_{1}-4) & > & 0\label{ZSDynSta}\\
\frac{\pi^{2}}{\tau_{\mathrm{co}}\tau_{\mathrm{ff}}^{2}}\Gamma_{1}\nabla_{\mathrm{ad}}\left[\frac{1-3/4\chi_{\rho}^{}}{\chi_{T}^{}}(\kappa_{T}^{}-4)+\kappa_{P}^{}+1\right] & > & 0\label{ZSSecSta}\\
-\frac{\pi^{2}}{4}\frac{3}{\tau_{\mathrm{co}}\tau_{\mathrm{ff}}^{2}}\Gamma_{1}^{2}\,\nabla_{\mathrm{ad}}\left[4\nabla_{\mathrm{ad}}-(\nabla_{\mathrm{ad}}\kappa_{T}^{}+\kappa_{P}^{})-\frac{4}{3\Gamma_{1}}\right] & > & 0\label{ZSVibSta}\end{eqnarray}
+\frac{\pi^{2}}{4}\frac{3}{\tau_{\mathrm{co}}\tau_{\mathrm{ff}}^{2}}\Gamma_{1}^{2}\,\nabla_{\mathrm{ad}}\left[4\nabla_{\mathrm{ad}}-(\nabla_{\mathrm{ad}}\kappa_{T}^{}+\kappa_{P}^{})-\frac{4}{3\Gamma_{1}}\right] & > & 0\label{ZSVibSta}
+\end{eqnarray}
\end_inset
\begin_inset CommandInset ref
LatexCommand ref
-reference "KapSou"
+reference "tab:KapSou"
\end_inset
\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
-name "KapSou"
+name "tab:KapSou"
\end_inset
\end_layout
\begin_layout Plain Layout
+\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
-<features>
+<features tabularvalignment="middle">
<column alignment="left" valignment="top" width="0pt">
<column alignment="left" valignment="top" width="0pt">
<row>
\end_inset
and it reduces to the criterion for dynamical stability
-\begin_inset Formula \begin{equation}
-\Gamma_{1}>\frac{4}{3}\,\cdot\end{equation}
+\begin_inset Formula
+\begin{equation}
+\Gamma_{1}>\frac{4}{3}\,\cdot
+\end{equation}
\end_inset
Stability of the thermodynamical equilibrium demands
-\begin_inset Formula \begin{equation}
-\chi_{\rho}^{}>0,\;\; c_{v}>0\,,\end{equation}
+\begin_inset Formula
+\begin{equation}
+\chi_{\rho}^{}>0,\;\; c_{v}>0\,,
+\end{equation}
\end_inset
and
-\begin_inset Formula \begin{equation}
-\chi_{T}^{}>0\end{equation}
+\begin_inset Formula
+\begin{equation}
+\chi_{T}^{}>0
+\end{equation}
\end_inset
holds for a wide range of physical situations.
With
-\begin_inset Formula \begin{eqnarray}
+\begin_inset Formula
+\begin{eqnarray}
\Gamma_{3}-1=\frac{P}{\rho T}\frac{\chi_{T}^{}}{c_{v}} & > & 0\\
\Gamma_{1}=\chi_{\rho}^{}+\chi_{T}^{}(\Gamma_{3}-1) & > & 0\\
-\nabla_{\mathrm{ad}}=\frac{\Gamma_{3}-1}{\Gamma_{1}} & > & 0\end{eqnarray}
+\nabla_{\mathrm{ad}}=\frac{\Gamma_{3}-1}{\Gamma_{1}} & > & 0
+\end{eqnarray}
\end_inset
stability
\emph default
, respectively:
-\begin_inset Formula \begin{eqnarray}
+\begin_inset Formula
+\begin{eqnarray}
3\Gamma_{1}-4=:S_{\mathrm{dyn}}> & 0\label{DynSta}\\
\frac{1-3/4\chi_{\rho}^{}}{\chi_{T}^{}}(\kappa_{T}^{}-4)+\kappa_{P}^{}+1=:S_{\mathrm{sec}}> & 0\label{SecSta}\\
-4\nabla_{\mathrm{ad}}-(\nabla_{\mathrm{ad}}\kappa_{T}^{}+\kappa_{P}^{})-\frac{4}{3\Gamma_{1}}=:S_{\mathrm{vib}}> & 0\,.\label{VibSta}\end{eqnarray}
+4\nabla_{\mathrm{ad}}-(\nabla_{\mathrm{ad}}\kappa_{T}^{}+\kappa_{P}^{})-\frac{4}{3\Gamma_{1}}=:S_{\mathrm{vib}}> & 0\,.\label{VibSta}
+\end{eqnarray}
\end_inset
\begin_inset CommandInset ref
LatexCommand ref
-reference "FigVibStab"
+reference "fig:VibStabEquation"
\end_inset
\begin_inset Caption
\begin_layout Plain Layout
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:VibStabEquation"
+
+\end_inset
+
Vibrational stability equation of state
\begin_inset Formula $S_{\mathrm{vib}}(\lg e,\lg\rho)$
\end_inset
\end_inset
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset CommandInset label
-LatexCommand label
-name "FigVibStab"
-
-\end_inset
-
-
\end_layout
\end_inset
\end_layout
\begin_layout Bibliography
+\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "1966"
\end_layout
\begin_layout Bibliography
+\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "1988"
\end_layout
\begin_layout Bibliography
+\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "1980"
\end_layout
\begin_layout Bibliography
+\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "1969"
\end_layout
\begin_layout Bibliography
+\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "1980"
\end_layout
\begin_layout Bibliography
+\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "1987"
\end_layout
\begin_layout Bibliography
+\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "1992"
\end_layout
\begin_layout Bibliography
+\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "1980a"
\end_layout
\begin_layout Bibliography
+\labelwidthstring References
\begin_inset CommandInset bibitem
LatexCommand bibitem
label "1997"
projects / lyx.git / blobdiff