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\IBVShead{4629}{8 September 1998}

\IBVStitletl{Variations of Luminosity, Radius, and Temperature of}{ the Pulsating Red Supergiant CE Tauri} 

\IBVSauth{ Rick WASATONIC, Edward F. GUINAN}
\IBVSinsto{Department of Astronomy and Astrophysics, Villanova University, Villanova, PA\,19085, USA}

\SIMBADobj{CE Tau}

\begintext

  CE Tauri (HD\,36389; HR\,1845; 119 Tau) is a bright semi-regular
pulsating M2 Iab-Ib variable star. It is easily observable
with a mean V-mag = +4.45 and B$-$V = +2.07.  Although CE Tau may 
be a possible twin to the SRc M2 Iab supergiant $\alpha$ Orionis,  
it has been the target of few long-term photometric studies.
Boyd et al. (1984) found the star to have a nearly sinusoidal 
visual light curve with an amplitude of 0.25 mag and a half-period
of nearly 80 days.  This estimate corresponds well with
the AAVSO reported period of 165 days.  Several V-band measures
have also been published by Krisciunas (1986).  Recent measurements
by the Hipparcos satellite yield a parallax of 1.7 $\pm$ 0.8 mas,
which corresponds to a distance of about 588 $\pm$ 277 pc. Morever,
near-IR interferometric measurements by Quirrenbach et al. (1993)
and Dyck et al. (1996), and lunar occultation measurements
by Di Benedetto et al. (1993) yield an average angular diameter
of 10.3 mas.  This corresponds to a stellar radius of 
R =  654 $R_{\odot}$ or 3.04 AU, based on the given Hipparcos 
distance.
  
   Because CE Tau is a cool M2 star, its maximum energy output 
is in the near-infrared and its spectrum is dominated by temperature
dependent TiO molecular bands.  For these reasons, and because of a 
lack of long-term photometric monitoring, CE Tau is an excellent 
candidate for Wing (1992) near-IR TiO photometry. Furthermore, using the 
Wing near-IR photometry presented here, and methods developed by us 
(see, e.g., Morgan et al. 1997; Mahler et al. 1997), it is possible to 
estimate the temperature, radius, and luminosity changes of CE Tau
over its pulsation cycle. Hence, CE Tau was added to our program of 
V-band and Wing (1992) near-IR photometry of bright red giants and 
supergiants being carried out at the Wasatonic and Villanova 
observatories.

   Two seasons of variability are discussed, covering 12 nights from 
November 1996 to March 1997 and 17 nights from November 1997 to March 
1998.  Differential photometry of CE Tau was carried out with a 20 cm 
Schmidt-Cassegrain telescope coupled to 
an Optec silicon PIN-photometer.  The comparison star was HD 35802
and HD 35296 served as the check star.  No significant light variations 
were found between the comparison and check stars.  In addition,
$\epsilon$ Tau served as a near-IR Wing standard star (Wing, 1979).

  The photometry was conducted using a filter closely matched to the 
Johnson V-band system and the Wing near-IR three filter system, 
which uses near-IR intermediate-band filters centered at 719 nm, 
754 nm, and 1024 nm.  These filters are designated as A, B, and C by
Wing (1992), respectively.  TiO-indices, near-IR color indices, and IR 
apparent magnitudes are calculated from the observations. As defined, 
a numerical increase in the TiO-index corresponds to an increase in 
TiO absorption at 719 nm.  For M-type stars the C(1024) magnitude closely
approximates the apparent bolometric magnitude (m$_{bol}$).  Wing (1992) gives
a detailed description of the three-color near-IR photometric system.


   Nightly means were formed from the individual observations 
and plotted against Julian Day Number in Figure 1.  The V-mag, 
TiO-index, and the near-IR C(1024)-mag are plotted.  As shown in 
the figure, the star varies with time on a time-scale of several 
months.  During the 1996-97 observing season CE Tau has a nearly
sinusoidal light variation in which the V-mag varies from 
V$_{max} = +4.29$ mag to V$_{min} = +4.46$ mag. Fitting the data with a 
sinusoid suggests a characteristic period of about 140d for 
this interval. Also during the 1997/98 season the light variations 
are less regular and the light ranges slightly smaller. 
The observed V-mag amplitude of about 0.20 mag during 1996/97
is smaller than the total V-mag range of 0.40 mag found from 
Hipparcos photometry of CE Tau secured from 1990 to 1993. 

   Variations in the TiO-index are shown in the second panel of 
Figure 1.  The TiO-index varies inversely in phase with the V-mag 
light variations. During 1996/97 the TiO-index reaches its minimum 
value of +0.54 during light maximum and reaches its maximum value 
of +0.64 near light minimum.  These values correspond to spectral 
types of about M2.0 Iab to M2.4 Iab, respectively.  From the TiO-index 
the star (at least during 1996/97) is hottest at light maximum, and 
coolest at light minimum. As shown in Fig.1, the mean seasonal 
TiO-index is more positive during 1997/98, than during 1996/97. This 
indicates that the mean TiO absorption is stronger during the second 
season, corresponding to an overall decrease in the mean temperature 
over the two years. 
 
   The C(1024) mag is plotted against time in the bottom panel of 
Figure 1. As shown, the C(1024) mag varies in a similar manner 
to the V-mag, but with an amplitude only  $\approx$ 0.05 mag.  
From observations of standard stars with reliable bolometric magnitudes, 
the C(1024) mag was transformed to apparent bolometric magnitude 
(m$_{bol}$) by adding 1.10 to the C-mags. From prior TiO 
Index--temperature calibrations using near-IR standard star  
information supplied by Wing (1978), the T$_{eff}$ of CE Tau
was determined for each night.  These effective temperatures 
are plotted in the
top panel of Figure 2.  Using these temperature and m$_{bol}$
values, and adopting the Hipparcos distance, the luminosity 
($L_\star$) and radius ($R_\star$) of the star were computed for each
nightly data set. The resultant values of $L_\star$/$L_\odot$ and
$R_\star$/$R_\odot$ are plotted in Figure 2. In converting from  
M$_{bol}$ to $L_\star$/$L_\odot$, the value of $(M_{bol})_\odot$
= +4.75 mag was adopted.

  As shown in Fig. 2, for 1996/97 the temperature and luminosity 
variations of CE Tau are correlated but there appears to be no 
corresponding correlated changes in the stellar radius. As shown, 
the star is hottest at a time when it is most luminous and vice versa. 
However the radius of the star appears to increase 
systematically from $R_\star$/$R_\odot$ = 553 to about 
$R_\star$/$R_\odot$ = 570 over the 1996/97 observing season.
The apparent systematic increase in the star's radius appears to 
continue over the 1997/98 observing season. By the end of the 1997/98
season, the inferred stellar radius is $R_\star$/$R_\odot$ = 580. 
This change is accompanied by an apparent decrease in the T$_{eff}$
over the two years.  These systematic changes in $R_\star$ and
T$_{eff}$ could be part of a long-term pulsation cycle lasting a
few years.  $\alpha$ Ori shows similar long-term behavior (Morgan 
et al. 1997).

  It is interesting that the 140d light variation seen during 1996/97 is
driven chiefly by temperature changes without the expected accompanying
radius changes expected from pulsation. This suggests that the 140-160d
light variation arises chiefly from the growth and decay of huge 
granulation cells over the star's surface rather than from primary 
pulsation (see Schwarzschild, 1975).
\vskip 5mm
  \IBVSfig{9.5cm}{4629-f1.ps}{CE Tau visual light curve, TiO index, and IR magnitudes for the 1996/97 and 1997/98 observing seasons}

\IBVSfig{9.5cm}{4629-f2.ps}{CE Tau derived effective temperature, luminosity,
and radius variations for the 1996/97 and 1997/98 observing seasons}


  Wing photometry of $\alpha$ Ori has also been carried out by us with 
the same equipment; the observed temperature, luminosity, and radius 
changes are slightly larger than those of CE Tau. From the TiO-indices 
$\alpha$ Ori is on average about 80 deg K warmer than CE Tau.  Also 
$\alpha$ 
Ori appears somewhat larger and more luminous than CE Tau but the large 
uncertainty in CE Tau's parallax makes these comparisons less reliable. 
The mean photometric and physical properties of CE Tau and $\alpha$ Ori  
are listed in Table 1 for comparison. At face value, CE Tau is a close 
match to $\alpha$ Ori. 


\begin{center}
Table 1: Averaged common properties and parameters
\end{center}

\begin{center}
\begin{tabular}{|l|c|c|c|l}\hline
Avg. Properties&Alpha Ori&CE Tau&Comments \\ \hline \hline

Spec. Type     &  M2 Iab          & M2 Iab - Ib         &     \\
V-Mag.         & +0.50            & +4.45               &  Data from current photometry   \\
d(pc)          & 131 $\pm$ 30     & 588 $\pm$ 287       &  From Hipparcos \\
(B$-$V)        & +1.85            & +2.07               &     \\
E(B$-$V)       & $\approx$ 0.05   & $\approx$ 0.25      &  Using A$_{\rm V}$ = 3.2E(B$-$V)  \\
A$_{\rm V}$    & $\approx$ 0.16   & $\approx$ 0.80      &     \\
M$_{\rm V}$    & $-$5.24          & $-$5.20             &     \\
TiO Index      & 0.73             & 0.60                &  Data from current photometry.  \\
T$_{\rm eff}$  & 3430K            & 3510K               &  Data from current photometry  \\
Ang. Diameter  & 55.0 mas         & 10.3mas             &     \\
Radius         & 775 $R_\odot$    & 654 $R_\odot$       &     \\
Luminosity     & 69000 $L_\odot$  & 44500 $L_\odot$     &  Data from current photometry.  \\
Period(s)      & $\approx$ 400d   & $\approx$ 140d-165d &  Data from current photometry\\
 &$\approx$ 4.05yr & $ > $ 2 yrs.        &  P = 140d from 1996/97 photometry\\         \hline
\end {tabular}
\end {center}
\vskip 5mm

The authors would like to thank Dr. Robert Wing for his advice
and support.  We also acknowledge the use of the SIMBAD database
and the Hipparcos Main Catalog.  This research is supported by
NSF grants AST-9315365 to Villanova University and AST-9528506
to the Four College Consortium.

\references
 
Boyd, L.J., Genet, R.M., Hall, D.S., 1984, {\it IBVS}, No.\,2563

Di Benedetto, G.P., 1993, {\it A\&A}, {\bf 270}, 315

Dyck H.M., Benson J.A., Van Belle G.T., Ridgway, S.T.,
          1996, {\it AJ}, {\bf 111}, 1705

Krisciunas, K.L., 1986, {\it JAAVSO}, {\bf 15}, 15

Mahler, T., Wasatonic, R.P., Guinan, E.F., 1997, {\it IBVS}, No.\,4500

Morgan, N., Wasatonic, R.P., Guinan, E.F., 1997, {\it IBVS}, No.\,4499

Quirrenbach, A. et al., 1993, {\it ApJ}, {\bf 406}, 215

Schwarzschild, M., 1975, {\it ApJ}, {\bf 195}, 137

Wing, R.F. 1978 in Spectral Classification and Color Temperatures for 280 Bright Stars in the Range K4 - M8, Astronomy Department, Ohio State University

Wing, R.F., 1979, Standard Stars for Eight-Color Photometry, Dudley Obs. Report 14, ed.  A.G. Davis Philip
          

Wing, R.F., 1992, {\it JAAVSO}, {\bf 21}, 42

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