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\begin{document}


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\Title{VLBI OBSERVATIONS OF THE TINT\'IN AND MIL\'U NEBULAE}

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% AUTHORS GO HERE. PLEASE, ADD THE NECESSARY 
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% THAN TWO INSTITUTIONS


%  M. Ortadelo comes from one institution:

M.~Ortadelo\\

{\small{\it T\'ecnicos de Investigaci\'on Aeroterrestre,
Ministerio de Asuntos Intermedios, Rue del Percebe 13,
E-08001, Madrid, SPAIN}} \\


% F. Ilemon and B. Acterio come from another institution:

\medskip

F.~Ilem\'on, B.~Acterio\\

{\small{\it Dpto. Astrolog\'ia Medieval,
Universidad de Alfarras\'i, C/ San Jer\'onimo 13,
E-46001, Valencia, SPAIN}} \\

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% address of the corresponding author(s).




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\runninghead {M.~Ortadelo, F.~Ilem\'on \& B.~Acterio}
{VLBI Observations of Tint\'in and Mil\'u Nebulae}


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%% HERE COMES THE ABSTRACT:

{\small 
{\bf Abstract:} And here you write whatever you think is appropriate.

}


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% HERE BEGINS YOUR CONTRIBUTION. ADD AS MANY SECTIONS AS YOU NEED:

\section{Introduction}

Thompson et al. \cite{thompson} begin like that:
``The techniques of radio interferometry as applied to astronomy
and astrometry have developed enormously in the past four decades,
and the attainable angular resolution has advanced from degrees to
milliarcseconds, a range of over six orders of magnitude.  As
arrays for synthesis mapping have developed, techniques in the radio 
domain have overtaken those in optics in pfoviding the finest angular 
detail in astronomical images.  The same general developments have
introduced new capabilities in astrometry and in the measurement
of the earth's polar and crustal motions.  The theories and techniques
that underlie these advances continue to evolve, but have reached by now
a sufficient state of maturity that is appropriate to offer a detailed
exposition." Some of the advances mentioned there may be reported 
in the Proceedings of PERE 2006.

In the next lines, you will find a sample text to answer your questions 
about the style and format of these proceedings. 

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\begin{figure}[!htb]
\begin{center}
\epsfig{file=sample_fig1.eps, height=1.75in}
\caption{This is a really big radiotelescope.}
\label{fig:radiotel}
\end{center}
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   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. Mizuno \cite{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
   \cite{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 \cite{tscharnuter}, Balluch \cite{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.


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\begin{table}[!hb]
\begin{center}
\begin{tabular}{l|c|l}  
 Telescope   & Diam. (m)    & Country     \\ \hline
 Arecibo     &    305       & Puerto Rico \\
 Green Bank  &    110       & USA         \\
 Effelsberg  &    100       & Germany     \\
 Lovell      &     76       & England     \\
 Robledo     &     70       & Spain       \\
 Goldstone   &     70       & USA         \\ 
 Medicina    &     32       & Italy       \\ \hline
\end{tabular}
\caption{A few examples of big radiotelescopes.}
\label{tab:someradiotels}
\end{center}
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\section{Baker's standard one-zone model}

   In this section the one-zone model of Baker \cite{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.
   Baker \cite{baker} investigates the stability of thin layers in
   self-gravitating,
   spherical gas clouds with the following properties:\\
      $\bullet$ hydrostatic equilibrium,\\
      $\bullet$ thermal equilibrium,\\
      $\bullet$ 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 \cite{baker}). Using Baker's
   notation:
   \[
      \begin{array}{lp{0.8\linewidth}}
         M_{r}  & mass internal to the radius $r$     \\
         m               & mass of the zone                    \\
         r_0             & unperturbed zone radius             \\
         \rho_0          & unperturbed density in the zone     \\
         T_0             & unperturbed temperature in the zone \\
         L_{r0}          & unperturbed luminosity              \\
         E_{\mathrm{th}} & thermal energy of the zone
      \end{array}
   \]
\noindent
   and with the definitions of the \emph{local cooling time\/}
   
   \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 Baker
   \cite{baker} or Cox \cite{cox}.

   We observe that these criteria for dynamical, secular and
   vibrational stability, respectively, can be factorized into\\
      1. a factor containing local timescales only,\\
      2. a factor containing only constitutive relations and
         their derivatives.\\
   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. 

\section{Conclusions}

Everything has a beginning and an end.  That is the end of this sample
paper.  Have fun by writing your one!



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\bigskip


{\it Acknowledgements:} Here come, as it is obvious, the acknowledgements. 


\begin{small}
\begin{thebibliography}{99}

  \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[1515]{ptolemy15} Ptolemy, C. 1515, 
      Almagestum (Venice)
   
   \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[1730]{thomas30} Thomas, C. 1730, Mercurii philosophici 
      firmamentum firmianum descriptionem et vum globi artificialis
      coelistis (Frankfurt, Leipzig)

   \bibitem[1985]{thompson} Thompson, A. R., Moran, J. M. \& Swenson, G. W.
      1985,
      Interferometry and Synthesis in Radio Astronomy
      (John Wiley \& Sons, New York) 

   \bibitem[1997]{zheng} Zheng, W., Davidsen, A. F., Tytler, D. \& Kriss, G. A.
      1997, preprint


\end{thebibliography}
\end{small}
 
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