-#LyX 1.6.0 created this file. For more info see http://www.lyx.org/
-\lyxformat 345
+#LyX 2.2 created this file. For more info see http://www.lyx.org/
+\lyxformat 508
\begin_document
\begin_header
+\save_transient_properties true
+\origin /systemlyxdir/examples/
\textclass aa
-\begin_preamble
-\usepackage{graphicx}
-%
-\end_preamble
-\options traditabstract
-\use_default_options false
+\use_default_options true
+\maintain_unincluded_children false
\language english
+\language_package default
\inputencoding auto
-\font_roman default
-\font_sans default
-\font_typewriter default
+\fontencoding global
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
\font_default_family default
+\use_non_tex_fonts false
\font_sc false
\font_osf false
-\font_sf_scale 100
-\font_tt_scale 100
+\font_sf_scale 100 100
+\font_tt_scale 100 100
\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command bibtex
+\index_command default
\paperfontsize default
\spacing single
\use_hyperref false
\papersize default
\use_geometry false
-\use_amsmath 0
-\use_esint 0
+\use_package amsmath 0
+\use_package amssymb 0
+\use_package cancel 0
+\use_package esint 0
+\use_package mathdots 1
+\use_package mathtools 0
+\use_package mhchem 1
+\use_package stackrel 0
+\use_package stmaryrd 0
+\use_package undertilde 0
\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
\use_bibtopic false
+\use_indices false
\paperorientation portrait
+\suppress_date false
+\justification true
+\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_layout Standard
+\begin_layout Title
\begin_inset Note Note
status open
\begin_layout Plain Layout
+
+\family roman
+\series medium
+\size normal
+This is an example \SpecialChar LyX
+ file for articles to be submitted to the Journal of
+ Astronomy & Astrophysics (A&A).
+ How to install the A&A \SpecialChar LaTeX
+ class to your \SpecialChar 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
+
+.
+\begin_inset Newline newline
+\end_inset
+
Depending on the submission state and the abstract layout, you need to use
- different document class options that are listed in the aa manual
-\family sans
-aadoc.pdf
+ different document class options that are listed in the aa manual.
\family default
-.
+
+\begin_inset Newline newline
+\end_inset
+
+
+\family roman
+\series default
+Note:
+\series medium
+ If you use accented characters in your document, you must use the predefined
+ document class option
+\series default
+latin9
+\series medium
+ in the document settings.
\end_layout
\end_inset
Received September 15, 1996; accepted March 16, 1997
\end_layout
-\begin_layout Abstract
-To investigate the physical nature of the `nuc\SpecialChar \-
+\begin_layout Abstract (unstructured)
+To investigate the physical nature of the `nuc\SpecialChar softhyphen
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.
\family sans
aa.lyx
\family default
- template file that comes with LyX.
+ template file that comes with \SpecialChar LyX
+.
\end_layout
\end_inset
\end_layout
\begin_layout Keywords
-giant planet formation --
+giant planet formation –
\begin_inset Formula $\kappa$
\end_inset
--mechanism -- stability of gas spheres
+-mechanism – stability of gas spheres
\end_layout
\begin_layout Section
Mizuno (
\begin_inset CommandInset citation
LatexCommand cite
-key "mizuno"
+key "Eisenstein2005"
\end_inset
) determined the critical mass of the core to be about
-\begin_inset Formula $12\, M_{\oplus}$
+\begin_inset Formula $12\,M_{\oplus}$
\end_inset
(
is investigated on the basis of Baker's (
\begin_inset CommandInset citation
LatexCommand cite
-key "baker"
+key "Abernethy2003"
\end_inset
protostellar cores explode (Tscharnuter
\begin_inset CommandInset citation
LatexCommand cite
-key "tscharnuter"
+key "Cotton1999"
\end_inset
, Balluch
\begin_inset CommandInset citation
LatexCommand cite
-key "balluch"
+key "Mena2000"
\end_inset
status open
\begin_layout Plain Layout
-\begin_inset Caption
+\begin_inset Caption Standard
\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
In this section the one-zone model of Baker (
\begin_inset CommandInset citation
LatexCommand cite
-key "baker"
+key "Abernethy2003"
\end_inset
Baker (
\begin_inset CommandInset citation
LatexCommand cite
-key "baker"
+key "Abernethy2003"
\end_inset
c) in Baker
\begin_inset CommandInset citation
LatexCommand cite
-key "baker"
+key "Abernethy2003"
\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
For a physical discussion of the stability criteria see Baker (
\begin_inset CommandInset citation
LatexCommand cite
-key "baker"
+key "Abernethy2003"
\end_inset
) or Cox (
\begin_inset CommandInset citation
LatexCommand cite
-key "cox"
+key "Parkin2005"
\end_inset
\begin_inset CommandInset ref
LatexCommand ref
-reference "KapSou"
+reference "tab:KapSou"
\end_inset
), are specified (in practice by specifying a chemical composition) the
one-zone stability can be inferred if the thermodynamic state is specified.
- The zone -- or in other words the layer -- will be stable or unstable in
+ The zone – or in other words the layer – will be stable or unstable in
whatever object it is imbedded as long as it satisfies the one-zone-model
assumptions.
Only the specific growth rates (depending upon the time scales) will be
status open
\begin_layout Plain Layout
-\begin_inset Caption
+\begin_inset Caption Standard
\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
These depend only on the unperturbed thermodynamical state of the layer.
Therefore the above relations define the one-zone-stability equations of
state
-\begin_inset Formula $S_{\mathrm{dyn}},\, S_{\mathrm{sec}}$
+\begin_inset Formula $S_{\mathrm{dyn}},\,S_{\mathrm{sec}}$
\end_inset
and
\begin_inset CommandInset ref
LatexCommand ref
-reference "FigVibStab"
+reference "fig:VibStabEquation"
\end_inset
status open
\begin_layout Plain Layout
-\begin_inset Caption
+\begin_inset Caption Standard
\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
as described by Baker's (
\begin_inset CommandInset citation
LatexCommand cite
-key "baker"
+key "Abernethy2003"
\end_inset
\end_layout
\begin_layout Enumerate
-If the constitutive relations -- equations of state and Rosseland mean opacities
- -- are specified, the stability equations of state can be evaluated without
+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.
\end_layout
\begin_layout Acknowledgement
Part of this work was supported by the German
\emph on
-Deut\SpecialChar \-
-sche For\SpecialChar \-
-schungs\SpecialChar \-
-ge\SpecialChar \-
-mein\SpecialChar \-
+Deut\SpecialChar softhyphen
+sche For\SpecialChar softhyphen
+schungs\SpecialChar softhyphen
+ge\SpecialChar softhyphen
+mein\SpecialChar softhyphen
schaft, DFG
\emph default
project number Ts
\begin_inset space ~
\end_inset
-17/2--1.
+17/2–1.
\end_layout
\begin_layout Standard
+\begin_inset CommandInset bibtex
+LatexCommand bibtex
+btprint "btPrintAll"
+bibfiles "biblioExample"
+options "aa"
+
+\end_inset
+
+
\begin_inset Note Note
status open
\begin_layout Plain Layout
-You can alternatively use BibTeX.
- You must then use the BibTeX style
+
+\series bold
+Note:
+\series default
+ If you cannot see the bibliography in the output, assure that you have
+ gievn the full path to the Bib\SpecialChar TeX
+ style file
\family sans
aa.bst
\family default
- that is part of the A&A LaTeX-package.
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Bibliography
-\begin_inset CommandInset bibitem
-LatexCommand bibitem
-label "1966"
-key "baker"
-
-\end_inset
-
- Baker, N.
- 1966, in Stellar Evolution, ed.
-\begin_inset space \space{}
-\end_inset
-
-R.
- F.
- Stein,& A.
- G.
- W.
- Cameron (Plenum, New York) 333
-\end_layout
-
-\begin_layout Bibliography
-\begin_inset CommandInset bibitem
-LatexCommand bibitem
-label "1988"
-key "balluch"
-
-\end_inset
-
- Balluch, M.
- 1988, A&A, 200, 58
-\end_layout
-
-\begin_layout Bibliography
-\begin_inset CommandInset bibitem
-LatexCommand bibitem
-label "1980"
-key "cox"
-
-\end_inset
-
- Cox, J.
- P.
- 1980, Theory of Stellar Pulsation (Princeton University Press, Princeton)
- 165
-\end_layout
-
-\begin_layout Bibliography
-\begin_inset CommandInset bibitem
-LatexCommand bibitem
-label "1969"
-key "cox69"
-
-\end_inset
-
- Cox, A.
- N.,& Stewart, J.
- N.
- 1969, Academia Nauk, Scientific Information 15, 1
-\end_layout
-
-\begin_layout Bibliography
-\begin_inset CommandInset bibitem
-LatexCommand bibitem
-label "1980"
-key "mizuno"
-
-\end_inset
-
- Mizuno H.
- 1980, Prog.
- Theor.
- Phys., 64, 544
-\end_layout
-
-\begin_layout Bibliography
-\begin_inset CommandInset bibitem
-LatexCommand bibitem
-label "1987"
-key "tscharnuter"
-
-\end_inset
-
- Tscharnuter W.
- M.
- 1987, A&A, 188, 55
+ that is part of the A&A \SpecialChar LaTeX
+-package.
\end_layout
-\begin_layout Bibliography
-\begin_inset CommandInset bibitem
-LatexCommand bibitem
-label "1992"
-key "terlevich"
-
\end_inset
- Terlevich, R.
- 1992, in ASP Conf.
- Ser.
- 31, Relationships between Active Galactic Nuclei and Starburst Galaxies,
- ed.
- A.
- V.
- Filippenko, 13
-\end_layout
-
-\begin_layout Bibliography
-\begin_inset CommandInset bibitem
-LatexCommand bibitem
-label "1980a"
-key "yorke80a"
-
-\end_inset
-
- Yorke, H.
- W.
- 1980a, A&A, 86, 286
-\end_layout
-
-\begin_layout Bibliography
-\begin_inset CommandInset bibitem
-LatexCommand bibitem
-label "1997"
-key "zheng"
-
-\end_inset
-Zheng, W., Davidsen, A.
- F., Tytler, D.
- & Kriss, G.
- A.
- 1997, preprint
\end_layout
\end_body
projects / lyx.git / blobdiff