\documentstyle[paasms4,pptwocol]{preprint}

\input pub.sty

\def\OVI{\ion{O}{6}}
\def\msun{M_{\odot}}

\begin{document}

\title{ASTEROSEISMOLOGICAL OBSERVATIONS OF THE CENTRAL STAR OF THE 
PLANETARY NEBULA NGC~1501}

\author{
Howard~E.~Bond,\thanks{Space Telescope Science Institute, 3700 San Martin 
Drive, Baltimore, MD 21218; bond@stsci.edu}\morethanks{Guest Observer, Kitt 
Peak National Observatory, National Optical Astronomy Observatories, operated 
by AURA under contract with NSF}
Steven D.~Kawaler,\thanks{Dept.~of Physics and Astronomy, Iowa State 
University, Ames, IA  50011; sdk@iastate.edu}
Robin Ciardullo,\thanks{Dept.\ of Astronomy \& Astrophysics, Pennsylvania State 
University, 525 Davey Lab., University Park, PA  16802; rbc@astro.psu.edu}
R.~Stover,\thanks{UCO/Lick Observatory, University of California, Santa Cruz, 
CA  95064; richard@ucolick.org}
T.~Kuroda,\thanks{Nishi-Harima Observatory (NHAO), Sayo-cho, Hyogo 679-53, 
Japan; kuroda@nhao.go.jp}\\
%
\centerline{\it T.~Ishida,\samethanks{6}
T.~Ono,\samethanks{6}
S.~Tamura,\thanks{Okayama Astrophysical Observatory, Kamogata-cho, 
Asakuchi-gun, Okayama 719-02, Japan}\morethanks{Astronomical Institute, 
Tohoku University, Sendai, Japan 980-77; tamura@ astroa.astr.tohoku.ac.jp}
H.~Malasan,\samethanks{7}\morethanks{current address: Bosscha Observatory, 
Lembang, Bandung 40391, Indonesia; HAKIM@as.itb.ac.id}
A.~Yamasaki,\samethanks{7}\morethanks{Department of Geoscience, National 
Defense Academy, Yokosuka, Japan 238; yamasaki@cc.nda.ac.jp}}\\
%
\centerline{\it O.~Hashimoto,\samethanks{7}\morethanks{Department of 
Technology, Seikei University, Musashino-shi, Tokyo, Japan 180; 
hasimoto@aps.seikei.ac.jp}
E.~Kambe,\samethanks{7}\moresamethanks{10}
M.~Takeuti,\samethanks{7}\moresamethanks{8}
T.~Kato,\thanks{Ouda Observatory, Japan; 
tkato@kusastro.kyoto-u.ac.jp}\morethanks{Department of Astronomy, Faculty 
of Science, Kyoto University,
Sakyo-ku, Kyoto 606-01, Japan; tkato@kusastro.kyoto-u.ac.jp}
M.~Kato,\samethanks{12}\moresamethanks{13}}\\
%
\centerline{\it J.-S.~Chen,\thanks{Beijing Astronomical Observatory, Chinese 
Academy of Sciences, Zhongguancun, Beijing 100080, China}
E.~M.\ Leibowitz,\thanks{Wise Observatory and School of 
Physics \& Astronomy, Sackler Faculty of Exact Sciences, Tel Aviv University,
Ramat Aviv, Tel Aviv 69978, Israel; elia@wise1.tau.ac.il}
M.~M.\ Roth,\thanks{Universit\"ats-Sternwarte M\"unchen, Scheinerstr.~1, 
81679 M\"unchen, Germany; soffner@ usm.uni-muenchen.de}\morethanks{Current 
address: Astrophysikalisches Institut Potsdam, An
der Sternwarte 16, 14482 Potsdam, Germany; mmroth@aip.de}
T.~Soffner,\samethanks{16} and
W.~Mitsch\/\samethanks{16}}
\vspace{6pt}}
\tobe{December 1996}{Astronomical Journal}
\recacc{4 June 1996}{22 August 1996}

\maketitle

\abstract{
We report on a global CCD time-series photometric campaign to decode the
pulsations of the nucleus of the planetary nebula NGC~1501.  The WC4 central
star is an extremely hot, hydrogen-deficient, ``\OVI''-type object, with some
spectroscopic characteristics similar to those of the pre-white-dwarf
PG~1159$-$035 stars.  NGC~1501 shows pulsational brightness variations of a
few percent with numerous individual periods ranging from 19 to 87~minutes.
The pulsation amplitudes and periods are highly variable, suggesting a
complex pulsation spectrum that requires a long unbroken time series to
resolve.  To that end, we obtained CCD photometry of the central star over a
two-week period in 1991 November, using a network of observatories around the
globe.  We obtained nearly continuous coverage over an interval of almost one
week in the middle of the run.  With this data set, we have identified 10
independent pulsation periods, ranging from 5235~s down to 1154~s. The
pulsation modes changed amplitude significantly during the course of the run,
indicating either real amplitude variations, or that the modes are not fully
resolved over the two-week interval. We find strong evidence that the modes
we see in this star are indeed nonradial $g$-modes.  The ratios of the
frequencies of the largest-amplitude modes agree closely with those expected
for modes that are trapped by a density discontinuity in the outer layers.
This conclusion is strengthened by including single-site observations of this
star, obtained during previous years, in our analysis.  We offer a model for
the pulsation spectrum that includes a common period spacing of 22.30~s and a
stellar rotation period of 1.17~days; the period spacing allows us to assign
a preliminary asteroseismological mass of $0.55\pm0.03 \msun$.  However,
several factors complicate the analysis. Aside from the proximity of the
rotational splitting to 1 cycle per day, this frequency splitting corresponds
closely to {\it period\/} spacings near 20 seconds near the dominant
frequencies of the star.  Thus, the period spacing and frequency spacings are
nearly degenerate.}