-#LyX 1.4.0cvs created this file. For more info see http://www.lyx.org/
-\lyxformat 243
+#LyX 1.5.0svn created this file. For more info see http://www.lyx.org/
+\lyxformat 276
\begin_document
\begin_header
\textclass aa
\end_preamble
\language english
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+\use_esint 0
\cite_engine basic
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+\output_changes false
\end_header
\begin_body
\begin_layout Address
-Institute for Astronomy (IfA), University of Vienna, T\i \"{u}
+Institute for Astronomy (IfA), University of Vienna, Tü
rkenschanzstrasse
17, A-1180 Vienna
\newline
To investigate the physical nature of the `nuc\SpecialChar \-
leated instability' of proto
giant planets (Mizuno
-\begin_inset LatexCommand \cite{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{baker}
-
+\begin_inset LatexCommand cite
+key "baker"
\end_inset
standard one-zone model.
\begin_layout Standard
-In the
+In the
+\emph default
+
\emph on
nucleated instability
\begin_inset ERT
(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{mizuno}
-
+\begin_inset LatexCommand cite
+key "mizuno"
\end_inset
) determined the critical mass of the core to be about
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 (
-\begin_inset LatexCommand \cite{baker}
-
+\begin_inset LatexCommand cite
+key "baker"
\end_inset
) 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
-\begin_inset LatexCommand \cite{tscharnuter}
-
+\begin_inset LatexCommand cite
+key "tscharnuter"
\end_inset
, Balluch
-\begin_inset LatexCommand \cite{balluch}
-
+\begin_inset LatexCommand cite
+key "balluch"
\end_inset
), whereas earlier studies found quasi-steady collapse flows.
sideways false
status open
-\begin_layout Caption
+\begin_layout
+\begin_inset Caption
+
+\begin_layout
Adiabatic exponent
\begin_inset Formula \( \Gamma _{1} \)
\end_layout
-\begin_layout Standard
+\end_inset
+
+\end_layout
+
+\begin_layout Standard
-\begin_inset LatexCommand \label{FigGam}
+\begin_inset LatexCommand label
+name "FigGam"
\end_inset
\end_inset
In this section the one-zone model of Baker (
-\begin_inset LatexCommand \cite{baker}
-
+\begin_inset LatexCommand cite
+key "baker"
\end_inset
-), originally used to study the Cephe\i \"{\i}
+), originally used to study the Cepheı̈
d pulsation mechanism, will be briefly
reviewed.
The resulting stability criteria will be rewritten in terms of local state
\begin_layout Standard
Baker (
-\begin_inset LatexCommand \cite{baker}
-
+\begin_inset LatexCommand cite
+key "baker"
\end_inset
) investigates the stability of thin layers in self-gravitating, spherical
\end_inset
c) in Baker
-\begin_inset LatexCommand \cite{baker}
-
+\begin_inset LatexCommand cite
+key "baker"
\end_inset
).
\begin_layout Standard
\noindent
-and with the definitions of the
+and with the definitions of the
+\emph default
+
\emph on
local cooling time
\begin_inset ERT
\emph default
(see Fig.\InsetSpace ~
-\begin_inset LatexCommand \ref{FigGam}
-
+\begin_inset LatexCommand ref
+reference "FigGam"
\end_inset
)
\end_inset
- and the
+ and the
+\emph default
+
\emph on
local free-fall time
\emph default
\end_inset
- one obtains, after some pages of algebra, the conditions for
+ one obtains, after some pages of algebra, the conditions for
+\emph default
+
\emph on
stability
\begin_inset ERT
\end_inset
For a physical discussion of the stability criteria see Baker (
-\begin_inset LatexCommand \cite{baker}
-
+\begin_inset LatexCommand cite
+key "baker"
\end_inset
) or Cox (
-\begin_inset LatexCommand \cite{cox}
-
+\begin_inset LatexCommand cite
+key "cox"
\end_inset
).
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{ZSDynSta}
-
+\begin_inset LatexCommand ref
+reference "ZSDynSta"
\end_inset
), (
-\begin_inset LatexCommand \ref{ZSSecSta}
-
+\begin_inset LatexCommand ref
+reference "ZSSecSta"
\end_inset
) and (
-\begin_inset LatexCommand \ref{ZSVibSta}
-
+\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
+ are
+\emph default
+
\emph on
functions of the thermodynamic state in the local zone
\emph default
the thermodynamics and opacities (see Table\InsetSpace ~
-\begin_inset LatexCommand \ref{KapSou}
-
+\begin_inset LatexCommand ref
+reference "KapSou"
\end_inset
), are specified (in practice by specifying a chemical composition) the
sideways false
status open
-\begin_layout Caption
+\begin_layout
+\begin_inset Caption
+\begin_layout
-\begin_inset LatexCommand \label{KapSou}
+\begin_inset LatexCommand label
+name "KapSou"
\end_inset
Opacity sources
\end_layout
+\end_inset
+
+
+\end_layout
+
\begin_layout Standard
\begin_layout Standard
-Krügel 1971
+Krügel 1971
\end_layout
\end_inset
We will now write down the sign (and therefore stability) determining parts
of the left-hand sides of the inequalities (
-\begin_inset LatexCommand \ref{ZSDynSta}
-
+\begin_inset LatexCommand ref
+reference "ZSDynSta"
\end_inset
), (
-\begin_inset LatexCommand \ref{ZSSecSta}
-
+\begin_inset LatexCommand ref
+reference "ZSSecSta"
\end_inset
) and (
-\begin_inset LatexCommand \ref{ZSVibSta}
-
+\begin_inset LatexCommand ref
+reference "ZSVibSta"
\end_inset
-) and thereby obtain
+) and thereby obtain
+\emph default
+
\emph on
stability equations of state
\emph default
The sign determining part of inequality\InsetSpace ~
(
-\begin_inset LatexCommand \ref{ZSDynSta}
-
+\begin_inset LatexCommand ref
+reference "ZSDynSta"
\end_inset
) is
we find the sign determining terms in inequalities\InsetSpace ~
(
-\begin_inset LatexCommand \ref{ZSSecSta}
-
+\begin_inset LatexCommand ref
+reference "ZSSecSta"
\end_inset
) and (
-\begin_inset LatexCommand \ref{ZSVibSta}
-
+\begin_inset LatexCommand ref
+reference "ZSVibSta"
\end_inset
) respectively and obtain the following form of the criteria for dynamical,
- secular and vibrational
+ secular and vibrational
+\emph default
+
\emph on
stability
\emph default
.
See Fig.\InsetSpace ~
-\begin_inset LatexCommand \ref{FigVibStab}
-
+\begin_inset LatexCommand ref
+reference "FigVibStab"
\end_inset
for a picture of
sideways false
status open
-\begin_layout Caption
+\begin_layout
+\begin_inset Caption
+
+\begin_layout
Vibrational stability equation of state
\begin_inset Formula \( S_{\mathrm{vib}}(\lg e,\lg \rho ) \)
means vibrational stability
\end_layout
-\begin_layout Standard
+\end_inset
-\begin_inset LatexCommand \label{FigVibStab}
+\end_layout
+\begin_layout Standard
+
+
+\begin_inset LatexCommand label
+name "FigVibStab"
\end_inset
The conditions for the stability of static, radiative layers in gas spheres,
as described by Baker's (
-\begin_inset LatexCommand \cite{baker}
-
+\begin_inset LatexCommand cite
+key "baker"
\end_inset
) standard one-zone model, can be expressed as stability equations of state.
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 Cephe\i \"{\i}
+y than the second He ionization zone that drives the Cepheı̈
d pulsations.
\end_layout
\begin_layout Acknowledgement
-Part of this work was supported by the German
+Part of this work was supported by the German
+\emph default
+
\emph on
Deut\SpecialChar \-
sche For\SpecialChar \-
\end_layout
\begin_layout Bibliography
-\bibitem [1966]{baker}
+\begin_inset LatexCommand bibitem
+label "1966"
+key "baker"
+
+\end_inset
Baker, N.
1966, in Stellar Evolution, ed.
\end_layout
\begin_layout Bibliography
-\bibitem [1988]{balluch}
+\begin_inset LatexCommand bibitem
+label "1988"
+key "balluch"
+
+\end_inset
Balluch, M.
1988, A&A, 200, 58
\end_layout
\begin_layout Bibliography
-\bibitem [1980]{cox}
+\begin_inset LatexCommand bibitem
+label "1980"
+key "cox"
+
+\end_inset
Cox, J.
P.
\end_layout
\begin_layout Bibliography
-\bibitem [1969]{cox69}
+\begin_inset LatexCommand bibitem
+label "1969"
+key "cox69"
+
+\end_inset
Cox, A.
N.,& Stewart, J.
\end_layout
\begin_layout Bibliography
-\bibitem [1980]{mizuno}
+\begin_inset LatexCommand bibitem
+label "1980"
+key "mizuno"
+
+\end_inset
Mizuno H.
1980, Prog.
\end_layout
\begin_layout Bibliography
-\bibitem [1987]{tscharnuter}
+\begin_inset LatexCommand bibitem
+label "1987"
+key "tscharnuter"
+
+\end_inset
Tscharnuter W.
M.
\end_layout
\begin_layout Bibliography
-\bibitem [1992]{terlevich}
+\begin_inset LatexCommand bibitem
+label "1992"
+key "terlevich"
+
+\end_inset
Terlevich, R.
1992, in ASP Conf.
\end_layout
\begin_layout Bibliography
-\bibitem [1980a]{yorke80a}
+\begin_inset LatexCommand bibitem
+label "1980a"
+key "yorke80a"
+
+\end_inset
Yorke, H.
W.
\end_layout
\begin_layout Bibliography
-\bibitem [1997]{zheng}
+\begin_inset LatexCommand bibitem
+label "1997"
+key "zheng"
+
+\end_inset
Zheng, W., Davidsen, A.
F., Tytler, D.
projects / lyx.git / blobdiff