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\title{Scientific Justification for PG1336-018}
\author{PI: Mike Reed}
\author{Co-Is: Steve Kawaler and Dave Kilkenny}

\begin{abstract}

Studies of pulsating subdwarf B (sdBV or EC14026) stars have blossomed since
their discovery just a few years ago. Yet despite the incredible member discovery
rate, we know very little about the pulsations themselves. Only a few EC14026 stars
have had the advantage of multi-site data, and only one of these has yielded
reasonably secure mode identifications (Kawaler, 1999); a necessary step to combine theory and observations.
PG~1336-018 is an EC14026 star in an eclipsing binary system. This allows us
the opportunity to identify pulsation modes in 2 different ways: Stellar
rotation splits non-radial modes, allowing us to discern radial from non-radial
pulsations. With an
orbital period of 2.4 hours, we may assume a tidally locked system, providing a
known rotational splitting. Additionally, primary eclipse covers
about half of the pulsator. This allows
 us the
opportunity to resolve pulsations across it's surface during primary eclipse.
The increased coverage, signal to noise, and
time resolution of the Whole Earth Telescope will allow us to find rotationally-split components and use the eclipses to unambiguously identify pulsation
modes.
\end{abstract}

\section{Justification}

Asteroseismology is a technique in which the interior structure of pulsating stars is deduced from their pulsation properties. The pulsation frequencies generally depend very
sensitively on the equilibrium stellar structure (ESS). By making ESS models which match the observed pulsation characteristics, we hope to learn details of the inner structure and
composition of the star. Asteroseismology has produced spectacular results for the Sun and for numerous pulsating white dwarfs (e.g. Winget et al. 1991, 1994). 

Subdwarf B (sdB) stars are extreme horizontal branch stars which are believed to be comprised of 0.5 solar masses of He (and the usual admixture of metals) with a very thin (less than 2\%
by mass) layer of H, chemically segregated from the He and heavier elements by settling in the star's large gravitational field. The evolution of the progenitors of these stars is not well
understood, relying on unknown mass loss mechanisms on the giant branch to remove almost all the H envelope of the progenitor at the same time as increasing the He core to the
mass needed to ignite He burning in the He flash. Fortunately the discovery in the past few years of pulsating sdB stars (the EC14026 stars) (Kilkenny et al. 1997)
has opened the prospect of using asteroseismology to examine the interiors of these stars. Understanding this stage in stellar evolution is important for distance calibrations (being
similar to RR~Lyrae stars) and population synthesis studies (to explain
the UV excesses in globular clusters and elliptical galaxies).

PG1336 is a partially
eclipsing binary that pulsates in at least 15 modes (Reed et al 1999).
It has a binary period of ~2.4 hours and the companion is an M4-5 star
of approximately the same radius but considerably fainter (Kilkenny et al. 1998).
As such, the
companion contributes little light to the system (except via a strong reflection
effect)(see Figure 1), yet the orbit is close enough to assume that it is tidally locked.
This provides us with a known rotation period, from which we can search
for rotationally split modes, a sign of non-radial pulsations. At an inclination
of ~81 degrees, we effectively view the stars equator-on and the primary
eclipse covers approximately half of the sdB star. Because of this
changing viewing geometry
the pulsation amplitudes will also change through the eclipse.
In an equator-on system, l=1, m=0 modes should show reduced net 
amplitude because of
geometric cancelation across the star's surface (see Figure 2). However, during eclipse, this
mode is rendered visible as one hemisphere is temporarily blocked. 
The same is true for l=2, m=+/-1 modes. While the
amplitude of nearly every non-radial mode will be affected (some minimally), 
any radial modes will remain unaffected. As such, PG1336 offers a unique
opportunity to identify pulsation modes in an sdBV star.

We propose to observe PG1336-018 with the Whole Earth Telescope (WET).
The WET (Nather et al. 1990) is a collaboration of astronomers who agree to
observe a target star in such a way that observations can continue around
the globe, from site to site, 24 hours a day.  The continuous coverage offered
by the WET is the only way to separate real rotationally-split modes from
aliases caused by data gaps, or in this case, orbital sidebands.  The increased
data density also provides a significantly higher signal to noise ratio than
is possible from a single site observing over a similar timespan.  We find we
typically need 2 weeks of coverage from the network to obtain a resolution
and signal to noise ratio high enough for accurate mode identification.
With a Vmag of 13.4, PG1336 is easily visible from 1m class telescopes,
but the real observed signal is not the mean level of the star, but the
deviations around that mean due to the stellar pulsations.  With the fairly
low amplitudes of this star (we are expecting modes of 0.003 mag or less),
2m class telescopes are really more appropriate. This class of telescope also
allows us a higher time resolution through the 900 second primary eclipse.
  We are requesting time at telescopes around the globe, including:
2.6m, Beijing Astrophysical
Observatory 2.16m, SAAO 1.9m, McDonald 2.1m, Observatoire de Haute Provence 1.9m, SAAO
1.9m,  Moletai 1.65m, Itajuba 1.6m, CTIO 1.5m, Calar Alto 1.2m, Mt. John 1.0m,
Siding Spring 1.0m, Naini Tal 1.0m, Wise Observatory 1.0m, and Mt. Suhora 1.0m.

Our goals for this WET
run are to: 
1) Obtain 2 weeks of continuous coverage of PG1336 to beat down daily aliases
inherent in single-site data.
2) Use the known orbital period, assume the stars are tidally locked and search
for rotationally split modes as a sign of non-radial pulsations.
3) With an inclination of 81 degrees, the primary eclipse covers roughly half
of the pulsating star. This allows us to observe modes (during eclipse) that
we would not see otherwise.
4) Compare the amplitudes of pulsation seen in-eclipse to those out of eclipse
 to make a 
positive identification of pulsation modes, which may then be used to constrain
models.

It is very likely that, in a binary this close, the rotation of the pulsator will be phase-locked to the orbital motion. If so, non-radial pulsations will be split according to the Ledoux
formula: $
f_{klm} = f_0 + m*(1-C_{lk})*F_{rot}$
with Frot=1/2.4hr, the star's rotation frequency. The rotational splitting coefficient C(kl) is a function of the structure of the star, and is estimated from pulsation models for the sdB
stars developed by Kawaler (ISU) to be between 0.05 and 0.4, significantly NON-zero. It is inevitable from the shape of the light curve (eclipses, reflection effect) that a frequency
splitting equal to the orbital frequency will be seen in the pulsations. But rotational splitting would be resolved from this in ~3-20 binary periods provided C(kl) is in the expected range.
Since these stars pulsate in a range where we expect to see both radial
and non-radial pulsations, detection of rotational splitting would aleviate
some of this ambiguity.

The data from such a WET run will have some additional complexities over normal
observations of variable stars. However, we already have software in place that
has been tested. We are thus able to effectively remove the reflection effect
from the light curve as well as extract and flatten the primary eclipse for
use in pulsation analysis (Figure 3). 
Where other multi-site campaigns have found an abundance
of pulsation modes in pulsating sdB stars, this
WET campaign may be the first real opportunity to identify modes, rather
than just detect them.

\begin{figure}[h]
\centerline{\psfig{figure=beaut.ps,width=3in}}

\caption{Sample light curve of PG~1336 showing primary and secondary eclipses. 
\label{fig02} }
\end{figure}

\begin{figure}[h]
\centerline{\psfig{figure=fig1.ps,width=3in}\psfig{figure=fig2.ps,width=3in}}

\caption{Left: Sample model images (at 200 second intervals) and light curves fo
r simulations of PG~1336.
Right: Light curves from simulations of non-radial pulsations. The pulsations
have been corrected by the constant curve on the bottom.
\label{fig01} }
\end{figure}

\begin{figure}[h]
\centerline{\psfig{figure=fig3b.ps,width=3in}}

\caption{
Top: Extracted eclipse with correcting contour (line) offset by -0.2.
Bottom: Flattened eclipse showing obvious pulsations.
\label{fig03} }
\end{figure}


\section{References}
Kawaler, Steven D., 1999, A.S.P. Conf. Ser. Vol 169, 158 \\
Kilkenny D., et al.,   1997, MNRAS, 285, 640 \\
Kilkenny D., et al.,   1998, MNRAS, 296, 329    \\
Nather, R.E., et al.,  1990, ApJ,   361, 209 \\
Reed, M.D. et al., 1999, Balt.A. 9, 183 \\
Winget D.E., et al.,   1991, ApJ,   378, 326  \\
Winget D.E., et al.,   1994, ApJ,   430, 839 \\


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