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\begin{document}
\title{Hydrodynamics of giant planet formation}
\subtitle{I. Overviewing the $\kappa$-mechanism}
\author{G. Wuchterl
\inst{1}
\and
C. Ptolemy\inst{2}\fnmsep\thanks{Just to show the usage
of the elements in the author field}
}
\institute{Institute for Astronomy (IfA), University of Vienna,
T\"urkenschanzstrasse 17, A-1180 Vienna\\
\email{wuchterl@amok.ast.univie.ac.at}
\and
University of Alexandria, Department of Geography, ...\\
\email{c.ptolemy@hipparch.uheaven.space}
\thanks{The university of heaven temporarily does not
accept e-mails}
}
\date{Received September 15, 1996; accepted March 16, 1997}
% \abstract{}{}{}{}{}
% 5 {} token are mandatory
\abstract
% context heading (optional)
% {} leave it empty if necessary
{To investigate the physical nature of the `nuc\-leated instability' of
proto giant planets, the stability of layers
in static, radiative gas spheres is analysed on the basis of Baker's
standard one-zone model.}
% aims heading (mandatory)
{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.}
% methods heading (mandatory)
{The stability equations of state are
calculated for solar composition and are displayed in the domain
$-14 \leq \lg \rho / \mathrm{[g\, cm^{-3}]} \leq 0 $,
$ 8.8 \leq \lg e / \mathrm{[erg\, g^{-1}]} \leq 17.7$. These displays
may be
used to determine the one-zone stability of layers 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 $\rho$, temperature $T$ or
specific internal energy $e$.
Regions of instability in the $(\rho,e)$-plane are described
and related to the underlying microphysical processes.}
% results heading (mandatory)
{Vibrational instability is found to be a common phenomenon
at temperatures lower than the second He ionisation
zone. The $\kappa$-mechanism is widespread under `cool'
conditions.}
% conclusions heading (optional), leave it empty if necessary
{}
\keywords{giant planet formation --
$\kappa$-mechanism --
stability of gas spheres
}
\maketitle
%
%-------------------------------------------------------------------
\section{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{mizuno} 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{baker}) 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{tscharnuter}, Balluch \citeyear{balluch}),
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.
%--------------------------------------------------------------------
\section{Baker's standard one-zone model}
%-------------------------------------- Two column figure (place early!)
\begin{figure*}
\centering
%%%\includegraphics{empty.eps}
%%%\includegraphics{empty.eps}
%%%\includegraphics{empty.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{baker},
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{baker} 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{baker}). Using Baker's
notation:
%%begin novalidate
\[
\begin{array}{lp{0.8\linewidth}}
M_{r} & mass internal to the radius $r$ \\
m & mass of the zone \\
r_0 & unperturbed zone radius \\
\rho_0 & unperturbed density in the zone \\
T_0 & unperturbed temperature in the zone \\
L_{r0} & unperturbed luminosity \\
E_{\mathrm{th}} & thermal energy of the zone
\end{array}
\]
%%end novalidate
\noindent
and with the definitions of the \emph{local cooling time\/}
(see Fig.~\ref{FigGam})
\begin{equation}
\tau_{\mathrm{co}} = \frac{E_{\mathrm{th}}}{L_{r0}} \,,
\end{equation}
and the \emph{local free-fall time}
\begin{equation}
\tau_{\mathrm{ff}} =
\sqrt{ \frac{3 \pi}{32 G} \frac{4\pi r_0^3}{3 M_{\mathrm{r}}}
}\,,
\end{equation}
Baker's $K$ and $\sigma_0$ have the following form:
\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}
where $ E_{\mathrm{th}} \approx m (P_0/{\rho_0})$ has been used and
\begin{equation}
\begin{array}{l}
\delta = - \left(
\frac{ \partial \ln \rho }{ \partial \ln T }
\right)_P \\
e=mc^2
\end{array}
\end{equation}
is a thermodynamical quantity which is of order $1$ and equal to $1$
for nonreacting mixtures of classical perfect gases. The physical
meaning of $ \sigma_0 $ and $K$ is clearly visible in the equations
above. $\sigma_0$ represents a frequency of the order one per
free-fall time. $K$ 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{displaymath}
\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{displaymath}
\begin{displaymath}
\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{displaymath}
one obtains, after some pages of algebra, the conditions for
\emph{stability\/} given
below:
\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}
%
For a physical discussion of the stability criteria see \citet{baker} or \citet{cox}.
We observe that these criteria for dynamical, secular and
vibrational stability, respectively, can be factorized into
\begin{enumerate}
\item a factor containing local timescales only,
\item a factor containing only constitutive relations and
their derivatives.
\end{enumerate}
The first factors, depending on only timescales, are positive
by definition. The signs of the left hand sides of the
inequalities~(\ref{ZSDynSta}), (\ref{ZSSecSta}) and (\ref{ZSVibSta})
therefore depend exclusively on the second factors containing
the constitutive relations. Since they depend only
on state variables, the stability criteria themselves are \emph{
functions of the thermodynamic state in the local zone}. 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.\ the thermodynamics
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
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 different for layers
in different objects.
%--------------------------------------------------- One column table
\begin{table}
\caption[]{Opacity sources.}
\label{KapSou}
$$
\begin{array}{p{0.5\linewidth}l}
\hline
\noalign{\smallskip}
Source & T / {[\mathrm{K}]} \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
Yorke 1979, Yorke 1980a & \leq 1700^{\mathrm{a}} \\
% Yorke 1979, Yorke 1980a & \leq 1700 \\
Kr\"ugel 1971 & 1700 \leq T \leq 5000 \\
Cox \& Stewart 1969 & 5000 \leq \\
\noalign{\smallskip}
\hline
\end{array}
$$
\end{table}
%
We will now write down the sign (and therefore stability)
determining parts of the left-hand sides of the inequalities
(\ref{ZSDynSta}), (\ref{ZSSecSta}) and (\ref{ZSVibSta}) and thereby
obtain \emph{stability equations of state}.
The sign determining part of inequality~(\ref{ZSDynSta}) is
$3\Gamma_1 - 4$ and it reduces to the
criterion for dynamical stability
\begin{equation}
\Gamma_1 > \frac{4}{3}\,\cdot
\end{equation}
Stability of the thermodynamical equilibrium demands
\begin{equation}
\chi^{}_\rho > 0, \;\; c_v > 0\, ,
\end{equation}
and
\begin{equation}
\chi^{}_T > 0
\end{equation}
holds for a wide range of physical situations.
With
\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}
we find the sign determining terms in inequalities~(\ref{ZSSecSta})
and (\ref{ZSVibSta}) respectively and obtain the following form
of the criteria for dynamical, secular and vibrational
\emph{stability}, respectively:
\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}
The constitutive relations are to be evaluated for the
unperturbed thermodynamic state (say $(\rho_0, T_0)$) of the zone.
We see that the one-zone stability of the layer depends only on
the constitutive relations $\Gamma_1$,
$\nabla_{\mathrm{ad}}$, $\chi_T^{},\,\chi_\rho^{}$,
$\kappa_P^{},\,\kappa_T^{}$.
These depend only on the unperturbed
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
$S_{\mathrm{vib}}$. Regions of secular instability are
listed in Table~1.
%
% One column figure
%-----------------------------------------------------------------
\begin{figure}
\centering
%%%\includegraphics[width=3cm]{empty.eps}
\caption{Vibrational stability equation of state
$S_{\mathrm{vib}}(\lg e, \lg \rho)$.
$>0$ means vibrational stability.
}
\label{FigVibStab}
\end{figure}
%-----------------------------------------------------------------
\section{Conclusions}
\begin{enumerate}
\item The conditions for the stability of static, radiative
layers in gas spheres, as described by Baker's (\citeyear{baker})
standard one-zone model, can be expressed as stability
equations of state. These stability equations of state depend
only on the local thermodynamic state of the layer.
\item 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.
\item For solar composition gas the $\kappa$-mechanism is
working in the regions of the ice and dust features
in the opacities, the $\mathrm{H}_2$ 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
instability than the second He ionization zone
that drives the Cephe{\"\i}d pulsations.
\end{enumerate}
\begin{acknowledgements}
Part of this work was supported by the German
\emph{Deut\-sche For\-schungs\-ge\-mein\-schaft, DFG\/} project
number Ts~17/2--1.
\end{acknowledgements}
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\begin{thebibliography}{}
\bibitem[Baker(1966)]{baker} Baker, N. 1966,
in Stellar Evolution,
ed.\ R. F. Stein,\& A. G. W. Cameron
(Plenum, New York) 333
\bibitem[Balluch(1988)]{balluch} Balluch, M. 1988,
A\&A, 200, 58
\bibitem[Cox(1980)]{cox} Cox, J. P. 1980,
Theory of Stellar Pulsation
(Princeton University Press, Princeton) 165
\bibitem[Cox(1969)]{cox69} Cox, A. N.,\& Stewart, J. N. 1969,
Academia Nauk, Scientific Information 15, 1
\bibitem[Mizuno(1980)]{mizuno} Mizuno H. 1980,
Prog. Theor. Phys., 64, 544
\bibitem[Tscharnuter(1987)]{tscharnuter} Tscharnuter W. M. 1987,
A\&A, 188, 55
\bibitem[Terlevich(1992)]{terlevich} Terlevich, R. 1992, in ASP Conf. Ser. 31,
Relationships between Active Galactic Nuclei and Starburst Galaxies,
ed. A. V. Filippenko, 13
\bibitem[Yorke(1980a)]{yorke80a} Yorke, H. W. 1980a,
A\&A, 86, 286
\bibitem[Zheng(1997)]{zheng} Zheng, W., Davidsen, A. F., Tytler, D. \& Kriss, G. A.
1997, preprint
\end{thebibliography}
\end{document}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Example below of non-structurated natbib references
To use the v8.3 macros with this form of composition of bibliography,
the option "bibyear" should be added to the command line
"\documentclass[bibyear]{aa}".
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{thebibliography}{}
\bibitem[1966]{baker} Baker, N. 1966,
in Stellar Evolution,
ed.\ R. F. Stein,\& A. G. W. Cameron
(Plenum, New York) 333
\bibitem[1988]{balluch} Balluch, M. 1988,
A\&A, 200, 58
\bibitem[1980]{cox} Cox, J. P. 1980,
Theory of Stellar Pulsation
(Princeton University Press, Princeton) 165
\bibitem[1969]{cox69} Cox, A. N.,\& Stewart, J. N. 1969,
Academia Nauk, Scientific Information 15, 1
\bibitem[1980]{mizuno} Mizuno H. 1980,
Prog. Theor. Phys., 64, 544
\bibitem[1987]{tscharnuter} Tscharnuter W. M. 1987,
A\&A, 188, 55
\bibitem[1992]{terlevich} Terlevich, R. 1992, in ASP Conf. Ser. 31,
Relationships between Active Galactic Nuclei and Starburst Galaxies,
ed. A. V. Filippenko, 13
\bibitem[1980a]{yorke80a} Yorke, H. W. 1980a,
A\&A, 86, 286
\bibitem[1997]{zheng} Zheng, W., Davidsen, A. F., Tytler, D. \& Kriss, G. A.
1997, preprint
\end{thebibliography}
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Examples for figures using graphicx
A guide "Using Imported Graphics in LaTeX2e" (Keith Reckdahl)
is available on a lot of LaTeX public servers or ctan mirrors.
The file is : epslatex.pdf
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%-------------------------------------------------------------
% A figure as large as the width of the column
%-------------------------------------------------------------
\begin{figure}
\centering
\includegraphics[width=\hsize]{empty.eps}
\caption{Vibrational stability equation of state
$S_{\mathrm{vib}}(\lg e, \lg \rho)$.
$>0$ means vibrational stability.
}
\label{FigVibStab}
\end{figure}
%
%-------------------------------------------------------------
% One column rotated figure
%-------------------------------------------------------------
\begin{figure}
\centering
\includegraphics[angle=-90,width=3cm]{empty.eps}
\caption{Vibrational stability equation of state
$S_{\mathrm{vib}}(\lg e, \lg \rho)$.
$>0$ means vibrational stability.
}
\label{FigVibStab}
\end{figure}
%
%-------------------------------------------------------------
% Figure with caption on the right side
%-------------------------------------------------------------
\begin{figure}
\sidecaption
\includegraphics[width=3cm]{empty.eps}
\caption{Vibrational stability equation of state
$S_{\mathrm{vib}}(\lg e, \lg \rho)$.
$>0$ means vibrational stability.
}
\label{FigVibStab}
\end{figure}
%
%-------------------------------------------------------------
% Figure with a new BoundingBox
%-------------------------------------------------------------
\begin{figure}
\centering
\includegraphics[bb=10 20 100 300,width=3cm,clip]{empty.eps}
\caption{Vibrational stability equation of state
$S_{\mathrm{vib}}(\lg e, \lg \rho)$.
$>0$ means vibrational stability.
}
\label{FigVibStab}
\end{figure}
%
%-------------------------------------------------------------
% The "resizebox" command
%-------------------------------------------------------------
\begin{figure}
\resizebox{\hsize}{!}
{\includegraphics[bb=10 20 100 300,clip]{empty.eps}
\caption{Vibrational stability equation of state
$S_{\mathrm{vib}}(\lg e, \lg \rho)$.
$>0$ means vibrational stability.
}
\label{FigVibStab}
\end{figure}
%
%-------------------------------------------------------------
% Two column Figure
%-------------------------------------------------------------
\begin{figure*}
\resizebox{\hsize}{!}
{\includegraphics[bb=10 20 100 300,clip]{empty.eps}
\caption{Vibrational stability equation of state
$S_{\mathrm{vib}}(\lg e, \lg \rho)$.
$>0$ means vibrational stability.
}
\label{FigVibStab}
\end{figure*}
%
%-------------------------------------------------------------
% Simple A&A Table
%-------------------------------------------------------------
%
\begin{table}
\caption{Nonlinear Model Results} % title of Table
\label{table:1} % is used to refer this table in the text
\centering % used for centering table
\begin{tabular}{c c c c} % centered columns (4 columns)
\hline\hline % inserts double horizontal lines
HJD & $E$ & Method\#2 & Method\#3 \\ % table heading
\hline % inserts single horizontal line
1 & 50 & $-837$ & 970 \\ % inserting body of the table
2 & 47 & 877 & 230 \\
3 & 31 & 25 & 415 \\
4 & 35 & 144 & 2356 \\
5 & 45 & 300 & 556 \\
\hline %inserts single line
\end{tabular}
\end{table}
%
%-------------------------------------------------------------
% Two column Table
%-------------------------------------------------------------
%
\begin{table*}
\caption{Nonlinear Model Results}
\label{table:1}
\centering
\begin{tabular}{c c c c l l l } % 7 columns
\hline\hline
% To combine 4 columns into a single one
HJD & $E$ & Method\#2 & \multicolumn{4}{c}{Method\#3}\\
\hline
1 & 50 & $-837$ & 970 & 65 & 67 & 78\\
2 & 47 & 877 & 230 & 567& 55 & 78\\
3 & 31 & 25 & 415 & 567& 55 & 78\\
4 & 35 & 144 & 2356& 567& 55 & 78 \\
5 & 45 & 300 & 556 & 567& 55 & 78\\
\hline
\end{tabular}
\end{table*}
%
%-------------------------------------------------------------
% Table with notes
%-------------------------------------------------------------
%
% A single note
\begin{table}
\caption{\label{t7}Spectral types and photometry for stars in the
region.}
\centering
\begin{tabular}{lccc}
\hline\hline
Star&Spectral type&RA(J2000)&Dec(J2000)\\
\hline
69 &B1\,V &09 15 54.046 & $-$50 00 26.67\\
49 &B0.7\,V &*09 15 54.570& $-$50 00 03.90\\
LS~1267~(86) &O8\,V &09 15 52.787&11.07\\
24.6 &7.58 &1.37 &0.20\\
\hline
LS~1262 &B0\,V &09 15 05.17&11.17\\
MO 2-119 &B0.5\,V &09 15 33.7 &11.74\\
LS~1269 &O8.5\,V &09 15 56.60&10.85\\
\hline
\end{tabular}
\tablefoot{The top panel shows likely members of Pismis~11. The second
panel contains likely members of Alicante~5. The bottom panel
displays stars outside the clusters.}
\end{table}
%
% More notes
%
\begin{table}
\caption{\label{t7}Spectral types and photometry for stars in the
region.}
\centering
\begin{tabular}{lccc}
\hline\hline
Star&Spectral type&RA(J2000)&Dec(J2000)\\
\hline
69 &B1\,V &09 15 54.046 & $-$50 00 26.67\\
49 &B0.7\,V &*09 15 54.570& $-$50 00 03.90\\
LS~1267~(86) &O8\,V &09 15 52.787&11.07\tablefootmark{a}\\
24.6 &7.58\tablefootmark{1}&1.37\tablefootmark{a} &0.20\tablefootmark{a}\\
\hline
LS~1262 &B0\,V &09 15 05.17&11.17\tablefootmark{b}\\
MO 2-119 &B0.5\,V &09 15 33.7 &11.74\tablefootmark{c}\\
LS~1269 &O8.5\,V &09 15 56.60&10.85\tablefootmark{d}\\
\hline
\end{tabular}
\tablefoot{The top panel shows likely members of Pismis~11. The second
panel contains likely members of Alicante~5. The bottom panel
displays stars outside the clusters.\\
\tablefoottext{a}{Photometry for MF13, LS~1267 and HD~80077 from
Dupont et al.}
\tablefoottext{b}{Photometry for LS~1262, LS~1269 from
Durand et al.}
\tablefoottext{c}{Photometry for MO2-119 from
Mathieu et al.}
}
\end{table}
%
%-------------------------------------------------------------
% Table with references
%-------------------------------------------------------------
%
\begin{table*}[h]
\caption[]{\label{nearbylistaa2}List of nearby SNe used in this work.}
\begin{tabular}{lccc}
\hline \hline
SN name &
Epoch &
Bands &
References \\
&
(with respect to $B$ maximum) &
&
\\ \hline
1981B & 0 & {\it UBV} & 1\\
1986G & $-$3, $-$1, 0, 1, 2 & {\it BV} & 2\\
1989B & $-$5, $-$1, 0, 3, 5 & {\it UBVRI} & 3, 4\\
1990N & 2, 7 & {\it UBVRI} & 5\\
1991M & 3 & {\it VRI} & 6\\
\hline
\noalign{\smallskip}
\multicolumn{4}{c}{ SNe 91bg-like} \\
\noalign{\smallskip}
\hline
1991bg & 1, 2 & {\it BVRI} & 7\\
1999by & $-$5, $-$4, $-$3, 3, 4, 5 & {\it UBVRI} & 8\\
\hline
\noalign{\smallskip}
\multicolumn{4}{c}{ SNe 91T-like} \\
\noalign{\smallskip}
\hline
1991T & $-$3, 0 & {\it UBVRI} & 9, 10\\
2000cx & $-$3, $-$2, 0, 1, 5 & {\it UBVRI} & 11\\ %
\hline
\end{tabular}
\tablebib{(1)~\citet{branch83};
(2) \citet{phillips87}; (3) \citet{barbon90}; (4) \citet{wells94};
(5) \citet{mazzali93}; (6) \citet{gomez98}; (7) \citet{kirshner93};
(8) \citet{patat96}; (9) \citet{salvo01}; (10) \citet{branch03};
(11) \citet{jha99}.
}
\end{table}
%-------------------------------------------------------------
% A rotated Two column Table in landscape
%-------------------------------------------------------------
\begin{sidewaystable*}
\caption{Summary for ISOCAM sources with mid-IR excess
(YSO candidates).}\label{YSOtable}
\centering
\begin{tabular}{crrlcl}
\hline\hline
ISO-L1551 & $F_{6.7}$~[mJy] & $\alpha_{6.7-14.3}$
& YSO type$^{d}$ & Status & Comments\\
\hline
\multicolumn{6}{c}{\it New YSO candidates}\\ % To combine 6 columns into a single one
\hline
1 & 1.56 $\pm$ 0.47 & -- & Class II$^{c}$ & New & Mid\\
2 & 0.79: & 0.97: & Class II ? & New & \\
3 & 4.95 $\pm$ 0.68 & 3.18 & Class II / III & New & \\
5 & 1.44 $\pm$ 0.33 & 1.88 & Class II & New & \\
\hline
\multicolumn{6}{c}{\it Previously known YSOs} \\
\hline
61 & 0.89 $\pm$ 0.58 & 1.77 & Class I & \object{HH 30} & Circumstellar disk\\
96 & 38.34 $\pm$ 0.71 & 37.5& Class II& MHO 5 & Spectral type\\
\hline
\end{tabular}
\end{sidewaystable*}
%-------------------------------------------------------------
% A rotated One column Table in landscape
%-------------------------------------------------------------
\begin{sidewaystable}
\caption{Summary for ISOCAM sources with mid-IR excess
(YSO candidates).}\label{YSOtable}
\centering
\begin{tabular}{crrlcl}
\hline\hline
ISO-L1551 & $F_{6.7}$~[mJy] & $\alpha_{6.7-14.3}$
& YSO type$^{d}$ & Status & Comments\\
\hline
\multicolumn{6}{c}{\it New YSO candidates}\\ % To combine 6 columns into a single one
\hline
1 & 1.56 $\pm$ 0.47 & -- & Class II$^{c}$ & New & Mid\\
2 & 0.79: & 0.97: & Class II ? & New & \\
3 & 4.95 $\pm$ 0.68 & 3.18 & Class II / III & New & \\
5 & 1.44 $\pm$ 0.33 & 1.88 & Class II & New & \\
\hline
\multicolumn{6}{c}{\it Previously known YSOs} \\
\hline
61 & 0.89 $\pm$ 0.58 & 1.77 & Class I & \object{HH 30} & Circumstellar disk\\
96 & 38.34 $\pm$ 0.71 & 37.5& Class II& MHO 5 & Spectral type\\
\hline
\end{tabular}
\end{sidewaystable}
%
%-------------------------------------------------------------
% Table longer than a single page
%-------------------------------------------------------------
% All long tables will be placed automatically at the end of the document
%
\longtab{
\begin{longtable}{lllrrr}
\caption{\label{kstars} Sample stars with absolute magnitude}\\
\hline\hline
Catalogue& $M_{V}$ & Spectral & Distance & Mode & Count Rate \\
\hline
\endfirsthead
\caption{continued.}\\
\hline\hline
Catalogue& $M_{V}$ & Spectral & Distance & Mode & Count Rate \\
\hline
\endhead
\hline
\endfoot
%%
Gl 33 & 6.37 & K2 V & 7.46 & S & 0.043170\\
Gl 66AB & 6.26 & K2 V & 8.15 & S & 0.260478\\
Gl 68 & 5.87 & K1 V & 7.47 & P & 0.026610\\
& & & & H & 0.008686\\
Gl 86
\footnote{Source not included in the HRI catalog. See Sect.~5.4.2 for details.}
& 5.92 & K0 V & 10.91& S & 0.058230\\
\end{longtable}
}
%
%-------------------------------------------------------------
% Table longer than a single page
% and in landscape,
% in the preamble, use: \usepackage{lscape}
%-------------------------------------------------------------
% All long tables will be placed automatically at the end of the document
%
\longtab{
\begin{landscape}
\begin{longtable}{lllrrr}
\caption{\label{kstars} Sample stars with absolute magnitude}\\
\hline\hline
Catalogue& $M_{V}$ & Spectral & Distance & Mode & Count Rate \\
\hline
\endfirsthead
\caption{continued.}\\
\hline\hline
Catalogue& $M_{V}$ & Spectral & Distance & Mode & Count Rate \\
\hline
\endhead
\hline
\endfoot
%%
Gl 33 & 6.37 & K2 V & 7.46 & S & 0.043170\\
Gl 66AB & 6.26 & K2 V & 8.15 & S & 0.260478\\
Gl 68 & 5.87 & K1 V & 7.47 & P & 0.026610\\
& & & & H & 0.008686\\
Gl 86
\footnote{Source not included in the HRI catalog. See Sect.~5.4.2 for details.}
& 5.92 & K0 V & 10.91& S & 0.058230\\
\end{longtable}
\end{landscape}
}
%
%-------------------------------------------------------------
% Appendices have to be placed at the end, after
% \end{thebibliography}
%-------------------------------------------------------------
\end{thebibliography}
\begin{appendix} %First appendix
\section{Background galaxy number counts and shear noise-levels}
Because the optical images used in this analysis...
\begin{figure*}%f1
\includegraphics[width=10.9cm]{1787f23.eps}
\caption{Shown in greyscale is a...}
\label{cl12301}
\end{figure*}
In this case....
\begin{figure*}
\centering
\includegraphics[width=16.4cm,clip]{1787f24.ps}
\caption{Plotted above...}
\label{appfig}
\end{figure*}
Because the optical images...
\section{Title of Second appendix.....} %Second appendix
These studies, however, have faced...
\begin{table}
\caption{Complexes characterisation.}\label{starbursts}
\centering
\begin{tabular}{lccc}
\hline \hline
Complex & $F_{60}$ & 8.6 & No. of \\
...
\hline
\end{tabular}
\end{table}
The second method produces...
\end{appendix}
%
%
\end{document}
%
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% Table will be print automatically at the end of the document,
% after the whole appendices
\begin{appendix} %First appendix
\section{Background galaxy number counts and shear noise-levels}
% In the appendices do not forget to put the counter of the table
% as an option
\longtab[1]{
\begin{longtable}{lrcrrrrrrrrl}
\caption{Line data and abundances ...}\\
\hline
\hline
Def & mol & Ion & $\lambda$ & $\chi$ & $\log gf$ & N & e & rad & $\delta$ & $\delta$
red & References \\
\hline
\endfirsthead
\caption{Continued.} \\
\hline
Def & mol & Ion & $\lambda$ & $\chi$ & $\log gf$ & B & C & rad & $\delta$ & $\delta$
red & References \\
\hline
\endhead
\hline
\endfoot
\hline
\endlastfoot
A & CH & 1 &3638 & 0.002 & $-$2.551 & & & & $-$150 & 150 & Jorgensen et al. (1996) \\
\end{longtable}
}% End longtab
\end{appendix}
%-------------------------------------------------------------
% For appendices and landscape, large table:
% in the preamble, use: \usepackage{lscape}
%-------------------------------------------------------------
\begin{appendix} %First appendix
%
\longtab[1]{
\begin{landscape}
\begin{longtable}{lrcrrrrrrrrl}
...
\end{longtable}
\end{landscape}
}% End longtab
\end{appendix}
%%%% End of aa.dem