-#LyX 1.6.0svn created this file. For more info see http://www.lyx.org/
-\lyxformat 344
+#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
-\use_default_options false
+\use_default_options true
+\maintain_unincluded_children false
\language english
+\language_package default
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-\font_tt_scale 100
-
+\font_sf_scale 100 100
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\graphics default
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+\output_sync 0
+\bibtex_command bibtex
+\index_command default
\paperfontsize default
\spacing single
\use_hyperref false
\papersize default
\use_geometry false
-\use_amsmath 0
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+\use_package amsmath 0
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\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 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 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
+
+
+\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
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 (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 \SpecialChar 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
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
), 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
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
.
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
), 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 Bibliography
-\begin_inset CommandInset bibitem
-LatexCommand bibitem
-label "1966"
-key "baker"
-
-\end_inset
-
- Baker, N.
- 1966, in Stellar Evolution, ed.
-\begin_inset ERT
-status collapsed
-
-\begin_layout Plain Layout
-
-
-\backslash
-
-\end_layout
-
-\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"
+\begin_layout Standard
+\begin_inset CommandInset bibtex
+LatexCommand bibtex
+btprint "btPrintAll"
+bibfiles "biblioExample"
+options "aa"
\end_inset
- Tscharnuter W.
- M.
- 1987, A&A, 188, 55
-\end_layout
-\begin_layout Bibliography
-\begin_inset CommandInset bibitem
-LatexCommand bibitem
-label "1992"
-key "terlevich"
+\begin_inset Note Note
+status open
-\end_inset
+\begin_layout Plain Layout
- Terlevich, R.
- 1992, in ASP Conf.
- Ser.
- 31, Relationships between Active Galactic Nuclei and Starburst Galaxies,
- ed.
- A.
- V.
- Filippenko, 13
+\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 \SpecialChar LaTeX
+-package.
\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