diff --git a/development/Win32/packaging/AltInstaller/Updated.nsh b/development/Win32/packaging/AltInstaller/Updated.nsh index 96f5c1934b..940dc6be1f 100644 --- a/development/Win32/packaging/AltInstaller/Updated.nsh +++ b/development/Win32/packaging/AltInstaller/Updated.nsh @@ -42,6 +42,7 @@ Function UpdateModifiedFiles SetOutPath "$INSTDIR\Resources\doc\uk" File "${PRODUCT_SOURCEDIR}\Resources\doc\uk\Intro.lyx" SetOutPath "$INSTDIR\Resources\examples" + File "${PRODUCT_SOURCEDIR}\Resources\examples\aa_sample.lyx" File "${PRODUCT_SOURCEDIR}\Resources\examples\docbook_article.lyx" File "${PRODUCT_SOURCEDIR}\Resources\examples\modernCV.lyx" SetOutPath "$INSTDIR\Resources\examples\ca" diff --git a/lib/examples/aa_sample.lyx b/lib/examples/aa_sample.lyx index 0c841c1472..1cde71b8fc 100644 --- a/lib/examples/aa_sample.lyx +++ b/lib/examples/aa_sample.lyx @@ -1,4 +1,4 @@ -#LyX 1.5.0svn created this file. For more info see http://www.lyx.org/ +#LyX 1.5.7svn created this file. For more info see http://www.lyx.org/ \lyxformat 276 \begin_document \begin_header @@ -7,6 +7,7 @@ \usepackage{graphicx} % \end_preamble +\options traditabstract \language english \inputencoding auto \font_roman default @@ -37,27 +38,26 @@ \paperpagestyle default \tracking_changes false \output_changes false +\author "" +\author "" \end_header \begin_body \begin_layout Title - Hydrodynamics of giant planet formation \end_layout \begin_layout Subtitle - I. Overviewing the -\begin_inset Formula \( \kappa \) +\begin_inset Formula $\kappa$ \end_inset -mechanism \end_layout \begin_layout Author - G. Wuchterl \begin_inset ERT @@ -65,6 +65,7 @@ status collapsed \begin_layout Standard + \backslash inst{1} \backslash @@ -72,6 +73,7 @@ and \end_layout \begin_layout Standard + \end_layout @@ -84,6 +86,7 @@ status collapsed \begin_layout Standard + \backslash inst{2} \backslash @@ -97,26 +100,21 @@ fnmsep status collapsed \begin_layout Standard - Just to show the usage of the elements in the author field \end_layout \end_inset - \end_layout \begin_layout Offprint - G. Wuchterl \end_layout \begin_layout Address - -Institute for Astronomy (IfA), University of Vienna, Tü -rkenschanzstrasse +Institute for Astronomy (IfA), University of Vienna, Türkenschanzstrasse 17, A-1180 Vienna \newline @@ -125,6 +123,7 @@ status collapsed \begin_layout Standard + \backslash email{wuchterl@amok.ast.univie.ac.at} \backslash @@ -145,6 +144,7 @@ status collapsed \begin_layout Standard + \backslash email{c.ptolemy@hipparch.uheaven.space} \end_layout @@ -156,48 +156,34 @@ email{c.ptolemy@hipparch.uheaven.space} status collapsed \begin_layout Standard - The university of heaven temporarily does not accept e-mails \end_layout \end_inset - \end_layout \begin_layout Date - Received September 15, 1996; accepted March 16, 1997 \end_layout \begin_layout Abstract - To investigate the physical nature of the `nuc\SpecialChar \- leated instability' of proto - giant planets (Mizuno -\begin_inset 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 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 equations of state which are universal for a given composition. The stability equations of state are calculated for solar composition and are displayed in the domain -\begin_inset Formula \( -14\leq \lg \rho /[\mathrm{g}\, \mathrm{cm}^{-3}]\leq 0 \) +\begin_inset Formula $-14\leq\lg\rho/[\mathrm{g}\,\mathrm{cm}^{-3}]\leq0$ \end_inset , -\begin_inset Formula \( 8.8\leq \lg e/[\mathrm{erg}\, \mathrm{g}^{-1}]\leq 17.7 \) +\begin_inset Formula $8.8\leq\lg e/[\mathrm{erg}\,\mathrm{g}^{-1}]\leq17.7$ \end_inset . @@ -205,92 +191,84 @@ key "baker" in stellar or planetary structure models by directly reading off the value of the stability equations for the thermodynamic state of these layers, specified by state quantities as density -\begin_inset Formula \( \rho \) +\begin_inset Formula $\rho$ \end_inset , temperature -\begin_inset Formula \( T \) +\begin_inset Formula $T$ \end_inset or specific internal energy -\begin_inset Formula \( e \) +\begin_inset Formula $e$ \end_inset . Regions of instability in the -\begin_inset Formula \( (\rho ,e) \) +\begin_inset Formula $(\rho,e)$ \end_inset -plane are described and related to the underlying microphysical processes. Vibrational instability is found to be a common phenomenon at temperatures lower than the second He ionisation zone. The -\begin_inset Formula \( \kappa \) +\begin_inset Formula $\kappa$ \end_inset -mechanism is widespread under `cool' conditions. -\begin_inset ERT -status collapsed +\begin_inset Note Note +status open \begin_layout Standard - -\end_layout - -\begin_layout Standard - -\backslash -keywords{giant planet formation -- -\backslash -( -\backslash -kappa -\backslash -)-mechanism -- stability of gas spheres } +Citations are not allowed in A&A abstracts. \end_layout \end_inset - + +\begin_inset Note Note +status open + +\begin_layout Standard +This is the unstructured abstract type, an example for the structured abstract + is in the aa.lyx 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 - Introduction \end_layout \begin_layout Standard - -In the -\emph default - +In the \emph on nucleated instability -\begin_inset ERT -status collapsed - -\begin_layout Standard - -\backslash -/{} -\end_layout - -\end_inset - - \emph default (also called core instability) hypothesis of giant planet formation, a critical mass for static core envelope protoplanets has been found. Mizuno ( \begin_inset LatexCommand cite key "mizuno" + \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 ( -\begin_inset Formula \( M_{\oplus }=5.975\, 10^{27}\, \mathrm{g} \) +\begin_inset Formula $M_{\oplus}=5.975\,10^{27}\,\mathrm{g}$ \end_inset is the Earth mass), which is independent of the outer boundary conditions @@ -300,7 +278,6 @@ key "mizuno" \end_layout \begin_layout Standard - Although no hydrodynamical study has been available many workers conjectured that a collapse or rapid contraction will ensue after accumulating the critical mass. @@ -310,23 +287,25 @@ Although no hydrodynamical study has been available many workers conjectured is investigated on the basis of Baker's ( \begin_inset LatexCommand cite key "baker" + \end_inset ) standard one-zone model. \end_layout \begin_layout Standard - Phenomena similar to the ones described above for giant planet formation have been found in hydrodynamical models concerning star formation where protostellar cores explode (Tscharnuter \begin_inset LatexCommand cite key "tscharnuter" + \end_inset , Balluch \begin_inset LatexCommand cite key "balluch" + \end_inset ), whereas earlier studies found quasi-steady collapse flows. @@ -336,45 +315,42 @@ lar cores and protogiant planets serve as a further motivation for this \end_layout \begin_layout Section - Baker's standard one-zone model \end_layout \begin_layout Standard - \begin_inset Float figure wide true sideways false status open -\begin_layout +\begin_layout Standard \begin_inset Caption -\begin_layout - +\begin_layout Standard Adiabatic exponent -\begin_inset Formula \( \Gamma _{1} \) +\begin_inset Formula $\Gamma_{1}$ \end_inset . -\begin_inset Formula \( \Gamma _{1} \) +\begin_inset Formula $\Gamma_{1}$ \end_inset is plotted as a function of -\begin_inset Formula \( \lg \) +\begin_inset Formula $\lg$ \end_inset internal energy -\begin_inset Formula \( [\mathrm{erg}\, \mathrm{g}^{-1}] \) +\begin_inset Formula $[\mathrm{erg}\,\mathrm{g}^{-1}]$ \end_inset and -\begin_inset Formula \( \lg \) +\begin_inset Formula $\lg$ \end_inset density -\begin_inset Formula \( [\mathrm{g}\, \mathrm{cm}^{-3}] \) +\begin_inset Formula $[\mathrm{g}\,\mathrm{cm}^{-3}]$ \end_inset @@ -386,10 +362,9 @@ Adiabatic exponent \end_layout \begin_layout Standard - - \begin_inset LatexCommand label name "FigGam" + \end_inset @@ -400,20 +375,20 @@ name "FigGam" In this section the one-zone model of Baker ( \begin_inset LatexCommand cite key "baker" + \end_inset -), originally used to study the Cepheı̈ -d pulsation mechanism, will be briefly +), originally used to study the Cepheı̈d pulsation mechanism, will be briefly reviewed. The resulting stability criteria will be rewritten in terms of local state variables, local timescales and constitutive relations. \end_layout \begin_layout Standard - Baker ( \begin_inset LatexCommand cite key "baker" + \end_inset ) investigates the stability of thin layers in self-gravitating, spherical @@ -421,17 +396,14 @@ key "baker" \end_layout \begin_layout Itemize - hydrostatic equilibrium, \end_layout \begin_layout Itemize - thermal equilibrium, \end_layout \begin_layout Itemize - energy transport by grey radiation diffusion. \end_layout @@ -445,6 +417,7 @@ status collapsed \begin_layout Standard + \backslash \end_layout @@ -457,6 +430,7 @@ status collapsed \begin_layout Standard + \backslash , \end_layout @@ -469,6 +443,7 @@ status collapsed \begin_layout Standard + \backslash , \end_layout @@ -478,6 +453,7 @@ status collapsed c) in Baker \begin_inset LatexCommand cite key "baker" + \end_inset ). @@ -486,16 +462,14 @@ key "baker" \begin_layout Standard \align left - \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}\\ +\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 @@ -504,124 +478,102 @@ E_{\textrm{th}} & & \textrm{thermal energy of the zone} \begin_layout Standard \noindent -and with the definitions of the -\emph default - +and with the definitions of the \emph on local cooling time -\begin_inset ERT -status collapsed - -\begin_layout Standard - -\backslash -/{} -\end_layout - -\end_inset - - \emph default (see Fig.\InsetSpace ~ \begin_inset LatexCommand ref reference "FigGam" + \end_inset ) \begin_inset Formula \begin{equation} -\tau _{\mathrm{co}}=\frac{E_{\mathrm{th}}}{L_{r0}}\, , -\end{equation} +\tau_{\mathrm{co}}=\frac{E_{\mathrm{th}}}{L_{r0}}\,,\end{equation} \end_inset - and the -\emph default - + and the \emph on 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} +\tau_{\mathrm{ff}}=\sqrt{\frac{3\pi}{32G}\frac{4\pi r_{0}^{3}}{3M_{\mathrm{r}}}}\,,\end{equation} \end_inset Baker's -\begin_inset Formula \( K \) +\begin_inset Formula $K$ \end_inset and -\begin_inset Formula \( \sigma _{0} \) +\begin_inset Formula $\sigma_{0}$ \end_inset have the following form: \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} +\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} \end_inset where -\begin_inset Formula \( E_{\mathrm{th}}\approx m(P_{0}/{\rho _{0}}) \) +\begin_inset Formula $E_{\mathrm{th}}\approx m(P_{0}/{\rho_{0}})$ \end_inset has been used and \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} +\delta=-\left(\frac{\partial\ln\rho}{\partial\ln T}\right)_{P}\\ +e=mc^{2}\end{array}\end{equation} \end_inset is a thermodynamical quantity which is of order -\begin_inset Formula \( 1 \) +\begin_inset Formula $1$ \end_inset and equal to -\begin_inset Formula \( 1 \) +\begin_inset Formula $1$ \end_inset for nonreacting mixtures of classical perfect gases. The physical meaning of -\begin_inset Formula \( \sigma _{0} \) +\begin_inset Formula $\sigma_{0}$ \end_inset and -\begin_inset Formula \( K \) +\begin_inset Formula $K$ \end_inset is clearly visible in the equations above. -\begin_inset Formula \( \sigma _{0} \) +\begin_inset Formula $\sigma_{0}$ \end_inset represents a frequency of the order one per free-fall time. -\begin_inset Formula \( K \) +\begin_inset Formula $K$ \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 \[ -\Gamma _{1}=\left( \frac{\partial \ln P}{\partial \ln \rho }\right) _{S}\, ,\; \chi ^{}_{\rho }=\left( \frac{\partial \ln P}{\partial \ln \rho }\right) _{T}\, ,\; \kappa ^{}_{P}=\left( \frac{\partial \ln \kappa }{\partial \ln P}\right) _{T}\] +\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 \[ -\nabla _{\mathrm{ad}}=\left( \frac{\partial \ln T}{\partial \ln P}\right) _{S}\, ,\; \chi ^{}_{T}=\left( \frac{\partial \ln P}{\partial \ln T}\right) _{\rho }\, ,\; \kappa ^{}_{T}=\left( \frac{\partial \ln \kappa }{\partial \ln T}\right) _{T}\] +\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 - one obtains, after some pages of algebra, the conditions for -\emph default - + one obtains, after some pages of algebra, the conditions for \emph on stability \begin_inset ERT @@ -629,6 +581,7 @@ status collapsed \begin_layout Standard + \backslash /{} \end_layout @@ -639,68 +592,66 @@ status collapsed \emph default given below: \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}}{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} \end_inset For a physical discussion of the stability criteria see Baker ( \begin_inset LatexCommand cite key "baker" + \end_inset ) or Cox ( \begin_inset LatexCommand cite key "cox" + \end_inset ). \end_layout \begin_layout Standard - We observe that these criteria for dynamical, secular and vibrational stability, respectively, can be factorized into \end_layout \begin_layout Enumerate - a factor containing local timescales only, \end_layout \begin_layout Enumerate - a factor containing only constitutive relations and their derivatives. \end_layout \begin_layout Standard - The first factors, depending on only timescales, are positive by definition. The signs of the left hand sides of the inequalities\InsetSpace ~ ( \begin_inset LatexCommand ref reference "ZSDynSta" + \end_inset ), ( \begin_inset LatexCommand ref reference "ZSSecSta" + \end_inset ) and ( \begin_inset LatexCommand ref reference "ZSVibSta" + \end_inset ) therefore depend exclusively on the second factors containing the constitutive relations. Since they depend only on state variables, the stability criteria themselves - are -\emph default - + are \emph on functions of the thermodynamic state in the local zone \emph default @@ -713,6 +664,7 @@ status collapsed \begin_layout Standard + \backslash \end_layout @@ -723,6 +675,7 @@ the thermodynamics and opacities (see Table\InsetSpace ~ \begin_inset LatexCommand ref reference "KapSou" + \end_inset ), are specified (in practice by specifying a chemical composition) the @@ -735,20 +688,18 @@ reference "KapSou" \end_layout \begin_layout Standard - \begin_inset Float table wide false sideways false status open -\begin_layout +\begin_layout Standard \begin_inset Caption -\begin_layout - - +\begin_layout Standard \begin_inset LatexCommand label name "KapSou" + \end_inset Opacity sources @@ -760,9 +711,7 @@ Opacity sources \end_layout \begin_layout Standard - - -\begin_inset Tabular +\begin_inset Tabular @@ -772,7 +721,6 @@ Opacity sources \begin_inset Text \begin_layout Standard - Source \end_layout @@ -782,9 +730,7 @@ Source \begin_inset Text \begin_layout Standard - - -\begin_inset Formula \( T/[\textrm{K}] \) +\begin_inset Formula $T/[\textrm{K}]$ \end_inset @@ -798,7 +744,6 @@ Source \begin_inset Text \begin_layout Standard - Yorke 1979, Yorke 1980a \end_layout @@ -808,9 +753,7 @@ Yorke 1979, Yorke 1980a \begin_inset Text \begin_layout Standard - - -\begin_inset Formula \( \leq 1700^{\textrm{a}} \) +\begin_inset Formula $\leq1700^{\textrm{a}}$ \end_inset @@ -824,7 +767,6 @@ Yorke 1979, Yorke 1980a \begin_inset Text \begin_layout Standard - Krügel 1971 \end_layout @@ -834,9 +776,7 @@ Krügel 1971 \begin_inset Text \begin_layout Standard - - -\begin_inset Formula \( 1700\leq T\leq 5000 \) +\begin_inset Formula $1700\leq T\leq5000$ \end_inset @@ -850,7 +790,6 @@ Krügel 1971 \begin_inset Text \begin_layout Standard - Cox & Stewart 1969 \end_layout @@ -860,9 +799,7 @@ Cox & Stewart 1969 \begin_inset Text \begin_layout Standard - - -\begin_inset Formula \( 5000\leq \) +\begin_inset Formula $5000\leq$ \end_inset @@ -879,9 +816,7 @@ Cox & Stewart 1969 \end_layout \begin_layout Standard - - -\begin_inset Formula \( ^{\textrm{a}} \) +\begin_inset Formula $^{\textrm{a}}$ \end_inset This is footnote a @@ -893,21 +828,22 @@ This is footnote a of the left-hand sides of the inequalities ( \begin_inset LatexCommand ref reference "ZSDynSta" + \end_inset ), ( \begin_inset LatexCommand ref reference "ZSSecSta" + \end_inset ) and ( \begin_inset LatexCommand ref reference "ZSVibSta" + \end_inset -) and thereby obtain -\emph default - +) and thereby obtain \emph on stability equations of state \emph default @@ -915,45 +851,41 @@ stability equations of state \end_layout \begin_layout Standard - The sign determining part of inequality\InsetSpace ~ ( \begin_inset LatexCommand ref reference "ZSDynSta" + \end_inset ) is -\begin_inset Formula \( 3\Gamma _{1}-4 \) +\begin_inset Formula $3\Gamma_{1}-4$ \end_inset and it reduces to the criterion for dynamical stability \begin_inset Formula \begin{equation} -\Gamma _{1}>\frac{4}{3}\, \cdot -\end{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} +\chi_{\rho}^{}>0,\;\; c_{v}>0\,,\end{equation} \end_inset and \begin_inset Formula \begin{equation} -\chi ^{}_{T}>0 -\end{equation} +\chi_{T}^{}>0\end{equation} \end_inset holds for a wide range of physical situations. With \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} +\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} \end_inset @@ -961,61 +893,60 @@ reference "ZSDynSta" ( \begin_inset LatexCommand ref reference "ZSSecSta" + \end_inset ) and ( \begin_inset LatexCommand ref reference "ZSVibSta" + \end_inset ) respectively and obtain the following form of the criteria for dynamical, - secular and vibrational -\emph default - + secular and vibrational \emph on stability \emph default , respectively: \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} +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} \end_inset The constitutive relations are to be evaluated for the unperturbed thermodynami c state (say -\begin_inset Formula \( (\rho _{0},T_{0}) \) +\begin_inset Formula $(\rho_{0},T_{0})$ \end_inset ) of the zone. We see that the one-zone stability of the layer depends only on the constitutiv e relations -\begin_inset Formula \( \Gamma _{1} \) +\begin_inset Formula $\Gamma_{1}$ \end_inset , -\begin_inset Formula \( \nabla _{\mathrm{ad}} \) +\begin_inset Formula $\nabla_{\mathrm{ad}}$ \end_inset , -\begin_inset Formula \( \chi _{T}^{},\, \chi _{\rho }^{} \) +\begin_inset Formula $\chi_{T}^{},\,\chi_{\rho}^{}$ \end_inset , -\begin_inset Formula \( \kappa _{P}^{},\, \kappa _{T}^{} \) +\begin_inset Formula $\kappa_{P}^{},\,\kappa_{T}^{}$ \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 Formula \( S_{\mathrm{vib}} \) +\begin_inset Formula $S_{\mathrm{vib}}$ \end_inset . @@ -1023,10 +954,11 @@ e relations \begin_inset LatexCommand ref reference "FigVibStab" + \end_inset for a picture of -\begin_inset Formula \( S_{\mathrm{vib}} \) +\begin_inset Formula $S_{\mathrm{vib}}$ \end_inset . @@ -1035,24 +967,22 @@ reference "FigVibStab" \end_layout \begin_layout Standard - \begin_inset Float figure wide false sideways false status open -\begin_layout +\begin_layout Standard \begin_inset Caption -\begin_layout - +\begin_layout Standard Vibrational stability equation of state -\begin_inset Formula \( S_{\mathrm{vib}}(\lg e,\lg \rho ) \) +\begin_inset Formula $S_{\mathrm{vib}}(\lg e,\lg\rho)$ \end_inset . -\begin_inset Formula \( >0 \) +\begin_inset Formula $>0$ \end_inset means vibrational stability @@ -1064,10 +994,9 @@ Vibrational stability equation of state \end_layout \begin_layout Standard - - \begin_inset LatexCommand label name "FigVibStab" + \end_inset @@ -1075,19 +1004,19 @@ name "FigVibStab" \end_inset + \end_layout \begin_layout Section - Conclusions \end_layout \begin_layout Enumerate - The conditions for the stability of static, radiative layers in gas spheres, as described by Baker's ( \begin_inset LatexCommand cite key "baker" + \end_inset ) standard one-zone model, can be expressed as stability equations of state. @@ -1097,7 +1026,6 @@ key "baker" \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 specifying properties of the layer. @@ -1105,29 +1033,24 @@ If the constitutive relations -- equations of state and Rosseland mean opacities \end_layout \begin_layout Enumerate - For solar composition gas the -\begin_inset Formula \( \kappa \) +\begin_inset Formula $\kappa$ \end_inset -mechanism is working in the regions of the ice and dust features in the opacities, the -\begin_inset Formula \( \mathrm{H}_{2} \) +\begin_inset Formula $\mathrm{H}_{2}$ \end_inset 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 instabilit -y than the second He ionization zone that drives the Cepheı̈ -d pulsations. +y than the second He ionization zone that drives the Cepheı̈d pulsations. \end_layout \begin_layout Acknowledgement - -Part of this work was supported by the German -\emph default - +Part of this work was supported by the German \emph on Deut\SpecialChar \- sche For\SpecialChar \- @@ -1135,18 +1058,6 @@ schungs\SpecialChar \- ge\SpecialChar \- mein\SpecialChar \- schaft, DFG -\begin_inset ERT -status collapsed - -\begin_layout Standard - -\backslash -/{} -\end_layout - -\end_inset - - \emph default project number Ts\InsetSpace ~ 17/2--1. @@ -1161,18 +1072,7 @@ key "baker" \end_inset Baker, N. - 1966, in Stellar Evolution, ed. -\begin_inset ERT -status collapsed - -\begin_layout Standard - -\backslash - -\end_layout - -\end_inset - + 1966, in Stellar Evolution, ed.\InsetSpace \space{} R. F. Stein,& A. diff --git a/status.15x b/status.15x index 824faade08..476efe2b24 100644 --- a/status.15x +++ b/status.15x @@ -183,6 +183,8 @@ What's new - Fix wrong image paths in the example file "docbook_article.lyx". +- Fix example file "aa_sample.lyx" so that it is compilable. + * BUILD/INSTALLATION