-#LyX 1.6.0svn 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
\usepackage{graphicx}
%
\end_preamble
+\options traditabstract
\use_default_options false
+\maintain_unincluded_children false
\language english
+\language_package default
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+\fontencoding global
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+\use_non_tex_fonts false
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+\default_output_format default
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\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
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-\author ""
-\author ""
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
\end_header
\begin_body
+\begin_layout Standard
+\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
+\family sans
+aadoc.pdf
+\family default
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
\begin_layout Title
Hydrodynamics of giant planet formation
\end_layout
\begin_layout Author
G.
- Wuchterl
+ Wuchterl
+\begin_inset Flex institutemark
+status open
+
+\begin_layout Plain Layout
+1
+\end_layout
+
+\end_inset
+
+
\begin_inset ERT
status collapsed
\backslash
-inst{1}
-\backslash
-and
+and
\end_layout
-\begin_layout Plain Layout
+\end_inset
-
+ C.
+ Ptolemy
+\begin_inset Flex institutemark
+status collapsed
+
+\begin_layout Plain Layout
+2
\end_layout
\end_inset
-C.
- Ptolemy
+
\begin_inset ERT
status collapsed
\backslash
-inst{2}
-\backslash
-fnmsep
+fnmsep
\end_layout
\end_inset
\end_inset
+\begin_inset Note Note
+status collapsed
+
+\begin_layout Plain Layout
+
+\backslash
+fnmsep is only needed for more than one consecutive notes/marks
+\end_layout
+
+\end_inset
+
+
\end_layout
\begin_layout Offprint
\end_inset
-\begin_inset ERT
-status collapsed
+\begin_inset Flex Email
+status open
\begin_layout Plain Layout
+wuchterl@amok.ast.univie.ac.at
+\end_layout
+\end_inset
-\backslash
-email{wuchterl@amok.ast.univie.ac.at}
-\backslash
-and
-\end_layout
+
+\begin_inset ERT
+status collapsed
\begin_layout Plain Layout
+
+\backslash
+and
\end_layout
\end_inset
\end_inset
-\begin_inset ERT
+\begin_inset Flex Email
status collapsed
\begin_layout Plain Layout
-
-
-\backslash
-email{c.ptolemy@hipparch.uheaven.space}
+c.ptolemy@hipparch.uheaven.space
\end_layout
\end_inset
-
+
\begin_inset Foot
status collapsed
\begin_layout Abstract
To investigate the physical nature of the `nuc\SpecialChar \-
leated instability' of proto
- giant planets (Mizuno
-\begin_inset CommandInset citation
-LatexCommand cite
-key "mizuno"
-
-\end_inset
-
-), the stability of layers in static, radiative gas spheres is analysed
- on the basis of Baker's
-\begin_inset CommandInset citation
-LatexCommand cite
-key "baker"
-
-\end_inset
-
- standard one-zone model.
+ 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
\end_inset
-mechanism is widespread under `cool' conditions.
-\begin_inset ERT
+\begin_inset Note Note
status open
\begin_layout Plain Layout
+Citations are not allowed in A&A abstracts.
+\end_layout
+\end_inset
-\backslash
-keywords{giant planet formation --
-\backslash
-(
-\backslash
-kappa
-\backslash
-)-mechanism -- stability of gas spheres }
+
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+This is the unstructured abstract type, an example for the structured abstract
+ is in the
+\family sans
+aa.lyx
+\family default
+ template file that comes with LyX.
\end_layout
\end_inset
-
+
+\end_layout
+
+\begin_layout Keywords
+giant planet formation --
+\begin_inset Formula $\kappa$
+\end_inset
+
+-mechanism -- stability of gas spheres
\end_layout
\begin_layout Section
\end_inset
), whereas earlier studies found quasi-steady collapse flows.
- The similarities in the (micro)physics, i.e.
+ The similarities in the (micro)physics, i.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
\begin_inset space \space{}
\end_inset
\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
.
The one-zone stability can therefore be determined from a simple equation
of state, given for example, as a function of density and temperature.
- Once the microphysics, i.e.
+ Once the microphysics, i.
+\begin_inset space \thinspace{}
+\end_inset
+
+g.
\begin_inset space \space{}
\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_inset
17/2--1.
-
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Note
+status open
+
+\begin_layout Plain Layout
+You can alternatively use BibTeX.
+ You must then use the BibTeX style
+\family sans
+aa.bst
+\family default
+ that is part of the A&A LaTeX-package.
+\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