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\begin{document}
\projeto{
%
%          TITULO DO PROJETO
%
An Empirical Test of the Crystallization theory
%
}
%
           {1.6}      % TELESCOPIO
%
%
           {~X~}    % PERIODO
           {~~~}
{
%
%          RESUMO DO PROJETO
%
For over 30 years we have assumed that crystallization takes place in
the core of the cool white dwarfs (WDs) without direct observational
evidence of it. With our discovery of a massive pulsating WD,
BPM~37093, at OPD/LNA we now have the opportunity to look for observational
evidence of crystallization.  Recent theoretical calculations show that
we can use the period spacing between successive radial overtone modes
of the star's oscillations to measure the crystallized mass fraction
(if any) in the core.  We propose to observe BPM37093 with 0.6m
telescope after the Whole Earth Telescope (WET) to extend the time
base of the data and monitor the amplitude modulation.
 To obtain an accurate measurement of the period spacing, we must find
as many pulsation modes as possible.  Although some pulsation modes of
BPM~37093 come and go, they are all normal modes and combining data
taken at different times will add the number of modes we can use to
measure the period spacing.  The constraints on the
theory of crystallization will have a profound impact on WD
cosmochronology as the  largest uncertainty associated with the age
estimate of the WDs has been the effect of crystallization. In
addition, we will be providing a basic test of a fundamental theory of
matter, heretofore untested.
}



%
%           RESPONSAVEL
%
\responsavel {S. O. Kepler}  % nome 
             {IF-UFRGS}                                % instituicao
             {kepler@if.ufrgs.br}                      % endereco eletronico


%
%           CO-AUTORES
%
\coautores {Ant\^onio Kanaan, D. E. Winget}     % nomes 
           {CCNE/UFSM, Univ. of Texas}   % instituicoes



%
%           ESTUDANTES
%
\estudantes {}                                    % ha' estudantes
            {}                                    % nao ha' estudantes
            {} % nome e nivel da tese







%
%          TEMPO DE TELESCOPIO
%
\tempotel  {10}                           % Numero de noites solicitadas
           {}                             % Duracao total do projeto
           {21 -- 30 abril}               % Periodo desejado
           {qq data fora deste per\'{\i}odo (por tratar-se de campanha)}  % Datas impossiveis
           {0 $\pm$ 5}                    % Lua necessaria (justificar em 14b.)



\instrumentos{
%
%         INSTRUMENTOS E MATERIAL A SEREM UTILIZADOS
%
      -- FOTEX \\
      -- Filtro U, B, V
%
%
}

%
%            FIM DA PRIMEIRA PAGINA
%
% ----------------------------------------------------------------------
\newpage
\parskip   2mm
\parindent 0mm 
{\bf 13. Justificativa cient\'{\i}fica: Discuta as bases cient\'{\i}ficas, os 
objetivos do seu programa de observa\c{c}\~{a}o e e as implica\c{c}\~oes dos 
resultados na \'area de pesquisa (m\'aximo de uma p\'agina de texto e uma 
p\'agina de figuras  -  o que exceder estes limites ser\'a desconsiderado).}
\vspace*{\begsec}
%
%
%
%
%          JUSTIFICATIVA CIENTIFICA DO PROJETO

SCIENTIFIC JUSTIFICATION

More than three decades have passed since Kirzhnitz (1960), Abrikosov
(1960) and Salpeter (1961) independently predicted that the cores of cool
white dwarfs should crystallize; and we still have no direct empirical
tests of this theory.

Understanding crystallization is very important for studies of white
dwarf cooling.  Winget et al. (1987) have shown how we can use white
dwarfs as chronometers to measure the age of stellar groups, and in
particular of our Galaxy, which in turn serves as a lower limit to the
age of the Universe.  Given the current disagreements between the age
of the Universe estimated from $H_0$ and stellar ages in the galaxy
(e.g. Jacoby 1994), white dwarf chronology has gained added
importance.  
Crystallization, if it occurs, adds roughly 1 Gyr to the
computed cooling times of white dwarfs.  There is a potentially larger
effect associated with possible phase separation of the elements
during crystallization which could add an extra 1--3 Gyr (Chabrier,
Segretain and M\'era 1996).  

Nature has provided us with a laboratory for investigating the theory
of crystallization in the star BPM~37093, a pulsating white dwarf with
a hydrogen atmosphere (DAV) discovered
to pulsate at OPD by Kanaan et al 1991.  Its mass ($1.09 M_{\odot}$) and
temperature (11,730~K) (Bergeron et al. 1995) suggest that a
significant fraction of its core should be crystallized.  Depending on
the relative mass fractions of C and O in its core, a minimum of 50\%
and possibly as much as 90\% should be crystallized.  In figure 1 we
show lines of constant crystallized core fraction as a function of
$T_{\rm eff}$ and mass; the position of BPM~37093 is indicated,
together with the associated uncertainties in its mass and
temperature.  We note that if the core contains substantial amounts of
elements heavier than O, it should be more than $ 90 \%$ crystallized.

According to theoretical models, a crystallized core would have a
strong effect on the observable pulsation modes of this star (Winget et
al.  1997).  The main effect we have identified is on the average
spacing between modes of successive overtone number.  We have used this
spacing in the past to determine white dwarf masses, and deviations
from uniform spacing to determine the mass of surface layers of white
dwarfs.  There is good agreement between spectroscopic and seismologic
total masses, while surface layer masses can only be determined by
seismology (for a discussion, see Kepler \& Bradley 1995 and references
therein).  For BPM~37093, if we assume the spectroscopically determined
mass is correct we can use the average period spacing to measure the
fraction of the core which is crystallized.

We have already been acquiring time series photometry on BPM~37093,
but we have found several difficulties to fully perform
asteroseismological analysis: the pulsations are very low amplitude (4
mmag for the highest amplitude mode) ; we were unable to resolve the
pulsation spectrum of this star from single-site observations; and the
pulsations show complex amplitude modulations (Kanaan 1996).  To
overcome the first two difficulties, we propose to observe BPM~37093
with the Whole Earth Telescope (WET, Nather et al.  1990).  In a
separate proposal in order to defy the third difficulty, we propose to
do time series CCD photometry of BPM~37093 using smaller telescopes
before and after the WET observation. Combined with the WET
observation, this will extend the time base of data and allow us to
monitor the complex amplitude modulation BPM~37093 exhibits.  

Our observations will, for the first time, test the predictions of a
fundamental theory in Astrophysics, the theory of crystallization in
the interior of cool white dwarfs.  When we reobserve this star in the
future we will also be able to measure rates of period change.  These
rates will be of extreme value in the calibration of cooling rates for
these objects, which in turn, are essential for the use of white dwarfs
as cosmic chronometers.

%From the work of Kleinman (1995a, 1995b), and Kleinman et al.
%(1997) on G29-38 which is a complex DAV with large amplitude
%modulation, we know that despite the fact that the modes come and go,
%they are all normal modes or the linear combinations of normal modes.
%Therefore we can obtain more normal modes, which is essential to measuring
%the crystallization fraction in the core of BPM~37093, by having an
%extensive data monitoring the amplitude modulation of the star. 

\clearpage

\vspace*{\fimsec}
\parskip   0.1mm
\parindent 0mm
{\bf Refer\^{e}ncias:}
\vspace*{\begsec}
%
%
%
%
%          REFERENCIAS BIBLIOGRAFICAS
%

%\vfill\eject

%\noindent Abrikosov, A. 1961, Soviet Phys. - JETP, 12, 1254

\noindent Abrikosov, A. 1960, JETP, 39, 1797

\noindent Bergeron, P. et al. 1995, ApJ, 449, 258

\noindent Chabrier, G., Segretain, L. and M\'era, D., 1996, ApJ, 468, L21

\noindent Jacoby, G.H. 1994, Nature, 371, 741

\noindent Kanaan, A., 1996, Ph.D. Thesis, University of Texas at Austin

\noindent Kepler, S.O. \& Bradley, P.A. 1995, Baltic Astronomy, 4, 166

\noindent Kirzhnitz, D.A. 1960, JETP, 38, 503

%\noindent Kirzhnitz, D.A. 1960, Soviet Phys. - JETP, 11, 365

\noindent Kleinman, S. J., 1995a, Ph.D. Thesis, University of Texas at Austin

\noindent Kleinman, S. J., 1995b, Balt. Astronomy, vol. 4, 270

\noindent Kleinman, S.J., 1997, ApJ, in press

\noindent Nather, R.E. et al. 1990, ApJ, 361, 309

\noindent Salpeter, E. 1961, ApJ, 134, 669

\noindent Winget et al. 1987, ApJ, 315, L77

\noindent Winget et al. 1997, ApJ, 487, L191


%\refer {Pogge, R.W., 1989.}{Astrophys. J. Suppl. Ser.}{71}{433}
%\refer {Unger, S.W., Pedlar, A., Axon, D.J., Whittle, M., Meurs, E.J.A.,
%       \& Ward, M.J.,1987.}{Mon. Not. R. astr. Soc.\ }{228}{671}
%\refer {van Groningen, E. \& de Bruyn, A.G., 1989.}{Astr. Astrophys.}{211}{293}
%\book  {Wilson, A.S. \& Heckman, T.M., 1985. 
%       In:  Astrophysics of Active galaxies and Quasi-stellar Objects, 
%       p. 39, ed. Miller, J.S., D. Reidel.}
%\refer {Wilson, A.S. \& Nath, B., 1990.}{Astrophys. J. Suppl. Ser.}{74}{731}
%\refer {Whittle, M., 1985.}{Mon. Not. R. astr. Soc.}{216}{817}
%

\begin{figure}%[hbt]
%\epsscale{0.65}
\epsfig{file=figure1.eps,width=5.0truein,height=5.0truein}
\caption{Theoretical crystallization curves based on models by
Wood (1990) plotted with the best-fit point for BPM37093 from
Bergeron et al. (1995) and error bars from Bragaglia et al. (1995).
The darker set of lines is for carbon core models and the lighter
set is for oxygen core models. The different styles of lines denote
different percentages of crystallization.}
\end{figure}



\vspace*{\fimsec}
\newpage
\parskip   2mm
\parindent 0mm
%
{\bf 14. Detalhes do programa. Descreva sumariamente os procedimentos de 
observa\c{c}\~ao e redu\c{c}\~ao. Indique as propriedades medidas nos dados 
e discuta os m\'etodos de an\'alise utilizados na obten\c{c}\~ao dos 
resultados. Se existirem problemas t\'ecnicos particulares associados com esta 
proposta, forne\c{c}a informa\c{c}\~oes suficientes para que a CP possa avaliar 
sua factibilidade.}
\vspace*{\begsec}\\
%
%         DETALHES DO PROGRAMA
Usaremos o FOTEX para analisar as varia\c c\~oes temporais do brilho
de uma an\~a branca.  As ferramentas para aquisi\c c\~ao e an\'alise
dos dados vem sendo usadas com sucesso no LNA h\'a mais de uma
d\'ecada.
%
%
\vspace*{\fimsec}\\
{\bf 15. Justificativa da solicita\c{c}\~{a}o do tipo de telesc\'{o}pio, 
n\'{u}mero de noites, datas e lua necess\'aria, incluindo os c\'alculos para se chegar 
ao tempo de exposi\c{c}\~ao. Forne\c{c}a a rela\c{c}\~ao sinal/ruido 
necess\'aria e outras informa\c{c}\~oes \'uteis para a CP. Quantifique os 
resultados de sua estimativa de exposi\c{c}\~ao. Indique se as observa\c{c}\~oes est\~ao sendo dimensionadas em fun\c{c}\~ao da cobertura temporal de fen\^omenos vari\'aveis.}
\vspace*{\begsec}\\
%
%
%
%          JUSTIFICATIVA DO TELESCOPIO E NUMERO DE NOITES


Conforme colocamos na justificativa cient\'{\i}fica o uso a campanha
com o WET tem dois objetivos principais: 1) detectar novos modos de
pulsa\c c\~ao, com amplitude mais baixa; 2) resolver completamente o
espectro de frequ\^encias.  A nossa experi\^encia em campanhas
pr\'evias com estrelas semelhantes prova que para atingir o objetivo
2) precisamos de aproximadamente duas semanas de observa\c c\~oes
espalhadas pelo globo terrestre com uma parte central de cerca de uma
semana com uma cobertura muito pr\'oxima aos 100\%.  No \'{\i}tem 1),
tamb\'em de experi\^encias anteriores, sabemos que podemos atingir
n\'{\i}veis de detec\c c\~ao pr\'oximos a 0.1~mmag com o mesmo
per\'{\i}odo de observa\c c\~oes, desde que os telesc\'opios envolvidos
tenham di\^ametro de cerca de dois metros.  O modo de pulsa\c c\~ao
com maior amplitude na estrela BPM37093 \'e de 4~mmag.  Para alcan\c
carmos nosso objetivo de descobrir mais modos precisaremos que o
limite de detec\c c\~ao seja realmente de 0.1~mmag.  Talvez possamos
desta vez atingir n\'{\i}veis ainda mais baixos devido ao fato de que
a maioria dos telesc\'opios participantes deste turno ser\~ao maiores
que 1.5m.


\vspace*{\fimsec}
\newpage
{\bf 16. Lista dos objetos a serem observados:}

\begin{center}
\begin{tabular}{cccc}
\hline
&    RA (2000.0)  &     Dec (2000.0)       &       \\
Object Name  & (hh:mm:ss) &  (dd:mm:ss)  & Mag.  \\
\hline
BPM37093       & 12 36 062  &   $-$49 33.    & 13.73 \\
\hline
\end{tabular}
\end{center}


%\vspace*{\begsec}
%\large
%
%
%
%
%          LISTA DE OBJETOS
%
% \objetos  {V }    % Magnitude na tabela e' V
%
%
%
% OBJETO          A.R.             DEC.           MAG.  TIPO     COMENT. 
%
%NGC 5506   &   14:10:39    &   -02:58:27    &    14.0   & G2 &  mag. integrada\\
%NGC 1068   &   02:40:07    &   -00:13:31    &    10.8   &    & \\
%NGC 5506   &   14:10:39    &   -02:58:27    &    14.0   &    & \\
%NGC 1068   &   02:40:07    &   -00:13:31    &    10.8   &    & \\ 
%NGC 5506   &   14:10:39    &   -02:58:27    &    14.0   &    & \\
%NGC 1068   &   02:40:07    &   -00:13:31    &    10.8   &    & \\ 
%NGC 5506   &   14:10:39    &   -02:58:27    &    14.0   &    & \\
%NGC 1068   &   02:40:07    &   -00:13:31    &    10.8   &    & \\ 
%NGC 5506   &   14:10:39    &   -02:58:27    &    14.0   &    & \\
%NGC 1068   &   02:40:07    &   -00:13:31    &    10.8   &    & \\ \hline
%
%
%
%\end{tabular}\end{center}\normalsize\vspace*{\fimsec}
\parskip   2mm
\parindent 0mm
{\bf 17. Relat\'orio das miss\~oes anteriores que produziram resultado cient\'{\i}fico n\~ao publicado (este \'{\i}tem \'e particularmente importante para projetos de longa dura\c{c}\~ao). Publica\c{c}\~oes devem ser comunicadas \`a secretaria do LNA (secret@lna.br) para divulga\c{c}\~ao via WWW (http://www.lna.br), sendo utilizadas na avalia\c{c}\~ao. N\~ao \'e necess\'ario 
incluir as publica\c{c}\~oes neste relat\'orio.
\vspace*{\begsec}

- Miss\~ao em Mar\c co/1996: ``BPM37093: uma an\~a branca pulsante cristalizada?'' (Autor)

- trabalho apresentado em ``The Fourth WET Workshop'' em Koninki--Pol\^onia.
T\'{\i}tulo: ``BPM37093: our way to the interior of crystallized pulsators''

- trabalho aceito para publica\c c\~ao em Baltic Astronomy

- Miss\~ao em Mar\c co/1996: ``Espectroscopia de An\~as Brancas''.
Dados em an\'alise.

-Miss\~oes anteriores a 1996:

O. Giovannini, S. O. Kepler, A. Kanaan, A. F. M. Costa \& D. Koester
BPM~24754: A New Southern ZZ Ceti Star
(Based on observations
obtained at the Laborat\'orio Nacional de Astrof\'{\i}sica/CNPq, Brazil, 
and at the Cerro Tololo Inter-American Observatory, CTIO is operated by 
AURA, Inc. under contract to the National Science Foundation.)
(1997) Astrophysical Journal, in press.
    
J. E. S. Costa \& S. O. Kepler 
Direct Measurement of the Secular Pulsational Variation of the DOV Star 
 PG~1159-035 (1997), Baltic Astronomy, vol. 8, in press

O. Giovannini, S. O. Kepler, A. Kanaan, M. A. Wood, C. F. Claver, and D.Koester
Blue Edge versus Mass. (1997), Baltic Astronomy, vol. 8, in press


\newpage
%*********************************************************************
%
%    Escolha aqui a configuracao do equipamento a ser utilizado na 
%    missao. Preencha os campos de sua opcao como no exemplo abaixo:
%
%    \coudedetector
%    {~x~}       %CCD#48 (770x1152) pixel size 22.5microns coating UV
%    {~~~}       %CCD#09 (384x576) pixel size 22microns coating UV
%    {~~~}       %CCD#38 (384x576) pixel size 22microns sem coating
%
%*********************************************************************    
\equipamento{~~~}


\telescopio
{~X~}     % 1,6m B&C   (f/10; 12,9"/mm)
{~~~}     % 0,6m Zeiss (f/12,5; 27,5"/mm)
{~~~}     % 0,6m B&C   (f/13,5; 25,4"mm)
%******************* Espectrografo coude *****************************
\coude{~~~}
\lcentral 
{~~~}        % Comprimentos de onda centrais
{~~~}        
{~~~}        
\couderedes
{~~~}        %600 linhas/mm - 800nm
{~~~}        %1800 linhas/mm -
{~~~}
%****************** Espectrografo Cassegrain **************************
\Cassegrain {~~~}
\llcentral 
{~~~}        % Comprimentos de onda centrais
{~~~}        
{~~~}
\Cassfiltros
{~~~}        
{~~~}
{~~~}     
\Cassredes
{~~~}        %300 linhas/mm  -  19nm/mm  -  300nm
{~~~}        %300 linhas/mm  -  19nm/mm  -  500nm
{~~~}        %300 linhas/mm  -  19nm/mm  -  640nm
{~~~}        %300 linhas/mm  -  18nm/mm  -  1000nm
{~~~}        %600 linhas/mm  - 9,3nm/mm  -  500nm
{~~~}        %830 linhas/mm -  5,9nm/mm  -  820nm
{~~~}        %900 linhas/mm  - 5,7nm/mm  -  550nm
{~~~}        %1200 linhas/mm -   4nm/mm  -  400nm
{~~~}        %1200 linhas/mm -   4nm/mm   - 550nm
\CCassredes
{~~~}        %1200 linhas/mm -   4nm/mm  -  600nm
{~~~}        %1200 linhas/mm -   4nm/mm  -  750nm
%************************ Camera CCD direto ***************************
\camera {~~~}
\camfiltros 
{~~~}        %Default ( U, B, V, R, I )
{~~~}        %Outros
\camredutor 
{~~~}        %Sim
{~~~}        %Nao
%************************ Fotmetro Texas - FOTEX ***********************
\fotex {~X~}
\fotexfotomultiplicadora 
\fotexfiltros 
{~~~}        %Clear, B, V, R   
{~X~}        %Clear, U, B, V
{~~~}        %Strongen (u, v, b, y)
{~~~}        %Outros
\fotexdiafragmas 
{~~~}        %D2: 2,52 2,39 1,23 1,19 1,09
{~X~}        %D3: 2,47 1,91 1,13 0,95 0,70 0,44
{~~~}        %D4: 0,39 0,95 1,53 3,45 4,00 4,73 7,15 9,5 
{~~~}        %D5: 0,73 0,80 1,00 1,12 1,32 1,84 2,71
%        2 Canal: 0,50 0,70 0,77 1,00 1,08 1,16 2,48
CCD para guiagem !!!


%*********************Fotometro rapido - FOTRAP **********************
\fotrap {~~~}
\fotrapfotomultiplicadora 
\fotrapfiltros 

\end{document}





