From a0b5c8166375d72a192adfbdd378fb062ca358ec Mon Sep 17 00:00:00 2001 From: Hasan al Rasyid Date: Sun, 13 Mar 2022 00:43:44 +0900 Subject: [PATCH] clearer... tinggal table, numlist, dan formula --- Makefile | 3 +- manuscript.md | 123 ++++++++++++++++++++++++++++---------------------- pubsEngine | 1 - 3 files changed, 70 insertions(+), 57 deletions(-) mode change 120000 => 100644 Makefile delete mode 120000 pubsEngine diff --git a/Makefile b/Makefile deleted file mode 120000 index a0c57f2..0000000 --- a/Makefile +++ /dev/null @@ -1 +0,0 @@ -pubsEngine/Makefile.forDraft \ No newline at end of file diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..7980901 --- /dev/null +++ b/Makefile @@ -0,0 +1,2 @@ +article: + pubsEngine manuscript article diff --git a/manuscript.md b/manuscript.md index bb06142..cfe8b59 100644 --- a/manuscript.md +++ b/manuscript.md @@ -62,69 +62,75 @@ acknowledgements: # Introduction - In the \emph{nucleated instability\/} (also called core - instability) hypothesis of giant planet - formation, a critical mass for static core envelope - protoplanets has been found. \citet{langley00} determined - the critical mass of the core to be about $12 \,M_\oplus$ - ($M_\oplus=5.975 \times 10^{27}\,\mathrm{g}$ is the Earth mass), which - is independent of the outer boundary - conditions and therefore independent of the location in the - solar nebula. This critical value for the core mass corresponds - closely to the cores of today's giant planets. +In the \emph{nucleated instability\/} (also called core +instability) hypothesis of giant planet +formation, a critical mass for static core envelope +protoplanets has been found. \citet{langley00} determined +the critical mass of the core to be about $12 \,M_\oplus$ +($M_\oplus=5.975 \times 10^{27}\,\mathrm{g}$ is the Earth mass), which +is independent of the outer boundary +conditions and therefore independent of the location in the +solar nebula. This critical value for the core mass corresponds +closely to the cores of today's giant planets. - Although no hydrodynamical study has been available many workers - conjectured that a collapse or rapid contraction will ensue - after accumulating the critical mass. The main motivation for - this article - is to investigate the stability of the static envelope at the - critical mass. With this aim the local, linear stability of static - radiative gas spheres is investigated on the basis of Baker's - (\citeyear{mitchell80}) standard one-zone model. +Although no hydrodynamical study has been available many workers +conjectured that a collapse or rapid contraction will ensue +after accumulating the critical mass. The main motivation for +this article +is to investigate the stability of the static envelope at the +critical mass. With this aim the local, linear stability of static +radiative gas spheres is investigated on the basis of Baker's +(\citeyear{mitchell80}) standard one-zone model. - 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 \citeyear{kearns89}, Balluch \citeyear{MachineLearningI}), - whereas earlier studies found quasi-steady collapse flows. The - similarities in the (micro)physics, i.e., constitutive relations of - protostellar cores and protogiant planets serve as a further - motivation for this study. +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 \citeyear{kearns89}, Balluch \citeyear{MachineLearningI}), +whereas earlier studies found quasi-steady collapse flows. The +similarities in the (micro)physics, i.e., constitutive relations of +protostellar cores and protogiant planets serve as a further +motivation for this study. # Baker's standard one-zone model - \begin{figure*} - \centering - \caption{Adiabatic exponent $\Gamma_1$. - $\Gamma_1$ is plotted as a function of - $\lg$ internal energy $\mathrm{[erg\,g^{-1}]}$ and $\lg$ - density $\mathrm{[g\,cm^{-3}]}$.} - \label{FigGam}% - \end{figure*} - In this section the one-zone model of \citet{DudaHart2nd}, - originally used to study the Cephe{\"{\i}}d pulsation mechanism, will - be briefly reviewed. The resulting stability criteria will be - rewritten in terms of local state variables, local timescales and - constitutive relations. - \citet{DudaHart2nd} investigates the stability of thin layers in - self-gravitating, - spherical gas clouds with the following properties: - \begin{itemize} - \item hydrostatic equilibrium, - \item thermal equilibrium, - \item energy transport by grey radiation diffusion. - \end{itemize} - For the one-zone-model Baker obtains necessary conditions - for dynamical, secular and vibrational (or pulsational) - stability (Eqs.\ (34a,\,b,\,c) in Baker \citeyear{DudaHart2nd}). Using Baker's - notation: + + +\begin{figure*} +\centering +\includegraphics{Figure/icml_numpapers.eps} +\caption{Adiabatic exponent $\Gamma_1$. + $\Gamma_1$ is plotted as a function of + $\lg$ internal energy $\mathrm{[erg\,g^{-1}]}$ and $\lg$ + density $\mathrm{[g\,cm^{-3}]}$.} + \label{FigGam}% + \end{figure*} + +In this section the one-zone model of \citet{DudaHart2nd}, +originally used to study the Cephe\text{\"{\i}}d pulsation mechanism, will +be briefly reviewed. The resulting stability criteria will be +rewritten in terms of local state variables, local timescales and +constitutive relations. + +\citet{DudaHart2nd} investigates the stability of thin layers in +self-gravitating, +spherical gas clouds with the following properties: + +* hydrostatic equilibrium, +* thermal equilibrium, +* energy transport by grey radiation diffusion. + +For the one-zone-model Baker obtains necessary conditions +for dynamical, secular and vibrational (or pulsational) +stability (Eqs.\ (34a,\,b,\,c) in Baker \citeyear{DudaHart2nd}). Using Baker's +notation: \noindent and with the definitions of the \emph{local cooling time\/} - (see Fig.~\ref{FigGam}) + (see Fig. \ref{FigGam}) \begin{equation} \tau_{\mathrm{co}} = \frac{E_{\mathrm{th}}}{L_{r0}} \,, \end{equation} @@ -222,7 +228,7 @@ acknowledgements: from a simple equation of state, given for example, as a function of density and temperature. Once the microphysics, i.e.\ the thermodynamics - and opacities (see Table~\ref{KapSou}), are specified (in practice + and opacities (see Table \ref{KapSou}), 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 @@ -302,10 +308,16 @@ acknowledgements: thermodynamical state of the layer. Therefore the above relations define the one-zone-stability equations of state $S_{\mathrm{dyn}},\,S_{\mathrm{sec}}$ - and $S_{\mathrm{vib}}$. See Fig.~\ref{FigVibStab} for a picture of + and $S_{\mathrm{vib}}$. See Fig. \ref{FigVibStab} for a picture of $S_{\mathrm{vib}}$. Regions of secular instability are - listed in Table~1. + listed in Table 1. + + +![Vibrational stability equation of state $S_{\mathrm{vib}}(\lg e, \lg \rho)$. $>0$ means vibrational stability.](Figure/icml_numpapers.eps){#FigVibStab width=3.43in height=2.71in} + # Conclusions diff --git a/pubsEngine b/pubsEngine deleted file mode 120000 index 6e48984..0000000 --- a/pubsEngine +++ /dev/null @@ -1 +0,0 @@ -../../pubsEngine \ No newline at end of file