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\centerline{\ft THE PULSATION FREQUENCIES OF $\beta$~CMa}
\vspace{8mm}

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$\beta$~CMa is one of the brightest $\beta$~Cep stars in the sky.  As such, it is a
difficult object to observe without the use of neutral density filters or
other techniques of preventing saturation of the photomultiplier.  This
perhaps explains why there are no photometric observations since those of
Shobbrook (1973).

 $\beta$~CMa is the second brightest object in the sky in
the spectral range 500 - 700 \AA\ (the brightest being $\epsilon$~CMa).
Observations of $\epsilon$~CMa in the EUV are presented by Cassinelli et al. 
(1995); results of observations of $\beta$~CMa in the EUV by
the same group are in press.  It turns out that there are several anomalies
regarding the continuum of $\beta$~CMa at these short wavelengths.  It is
possible that this may have something to do with the re-distribution of
pulsational energy.  The link between the EUV excess and pulsation
is being studied further by Cassinelli and co-workers.  Since the EUV and the
optical portions of the spectrum form at different heights in the
atmosphere, it is important to obtain contemporaneous optical photometry for
the star.

Str\"{o}mgren $uvby$ photometry of $\beta$~CMa was obtained in 1996
January 2 -- 15 using the 0.5-m reflector of the SAAO.  A total of 106 data
points in all four colours was obtained.  A 2.5 mag neutral
density filter was employed. As comparison stars we used the nearby B-type
stars HR~2266 and HR~2271.  These were observed without neutral density
filters to maximise the signal.  The ND filter was calibrated by observing
one of these stars with and without the filter through each of the four
bands.  In addition, we included in the analysis 40 $uvby$
measurements made with the same telescope and equipment in 1987
November 5 -- 15.  The same comparison stars were used.

A periodogram of the 1987 data shows the main pulsation at $f_2 = 3.99$ cycles
d$^{-1}$ having a semi-amplitude of $11.0 \pm 1.2$ mmag.  There is no sign
of additional periods in our data with semi-amplitudes in excess of 3.5
mmag.  The results for the 1996 data are the same: there is a strong
peak in the periodogram at $f_2 = 3.98$ d$^{-1}$, but nothing further with a
semi-amplitude in excess of 3 mmag.  The periodograms of the $b$ data for
the two seasons are shown in Fig.~1. Shobbrook (1973) obtains the following
frequencies and semi-amplitudes: $f_2 = 3.979331(\pm 5), A_2 = 10.5;
f_1 = 3.9995(\pm6), A_1 = 2.2; f_3 = 4.1834(\pm7), A_3 = 1.5$ (cycles
d$^{-1}$ and mmag respectively).  The time span within our two separate runs
is too short to resolve $f_1$ and $f_2$, but is sufficient to resolve $f_3$. 
Evidently, our observations are of too short a duration to reduce the noise
level to a point where $f_1$ and $f_3$ become visible.

The frequency of $f_2$ determined by Shobbrook (1973) fits the combined data
from 1987 and 1996 very well if the frequency is revised slightly to $f_2 =
3.979326$ d$^{-1}$.  We obtain the following ephemeris for maximum light in
all four colours (there is no appreciable phase shift between any two
colours): $T_{max} = JD\,2450000.0591 + 0\fd 2512988E.$  The following semi-amplitudes
are obtained (in mmag): $A_y = 8.8 \pm 0.7$; $A_b = 10.3 \pm 0.8$;
$A_v = 11.2 \pm 0.9$;  $A_u = 23.4 \pm 2.9$.  There is a very large increase
in amplitude in the $u$-band, but at the\break 

\centerline{2}
\vskip 1mm
\centerline{Table 1. Str\"{o}mgren photometry of $\beta$~CMa}
\begin{center}
\begin{tabular}{rrrrrrrrrr}\hline
HJD    &  $V$  & $b$   &  $v$  &  $u$ & HJD    &  $V$  & $b$   &  $v$  &  $u$ \\
\hline
\\
2447104.3852 & 1.991 & 1.878 & 1.849 & 1.813 & 2447114.5511 & 1.993 & 1.887 & 1.863 & 1.822\\
2447104.4252 & 1.997 & 1.880 & 1.854 & 1.827 & 2447114.5695 & 1.989 & 1.883 & 1.858 & 1.817\\
2447104.4597 & 1.997 & 1.893 & 1.868 & 1.821 & 2447114.5874 & 1.982 & 1.888 & 1.859 & 1.814\\
2447104.4965 & 1.992 & 1.885 & 1.866 & 1.812 & 2450085.3337 & 1.994 & 1.908 & 1.881 & 1.740\\
2447104.5513 & 1.981 & 1.874 & 1.853 & 1.797 & 2450085.3666 & 2.002 & 1.907 & 1.885 & 1.736\\
2447104.5815 & 1.982 & 1.873 & 1.847 & 1.800 & 2450085.4016 & 1.999 & 1.905 & 1.890 & 1.758\\
2447104.5985 & 1.970 & 1.874 & 1.848 & 1.798 & 2450085.4350 & 1.995 & 1.897 & 1.878 & 1.745\\
2447105.4095 & 1.984 & 1.886 & 1.869 & 1.823 & 2450085.4676 & 1.989 & 1.895 & 1.872 & 1.738\\
2447105.4336 & 1.994 & 1.895 & 1.864 & 1.810 & 2450086.3619 & 1.999 & 1.907 & 1.895 & 1.780\\
2447105.4728 & 1.988 & 1.893 & 1.873 & 1.821 & 2450086.3895 & 1.994 & 1.900 & 1.879 & 1.767\\
2447106.3517 & 2.013 & 1.863 & 1.847 & 1.807 & 2450086.4642 & 1.980 & 1.888 & 1.865 & 1.731\\
2447106.3907 & 1.973 & 1.875 & 1.864 & 1.831 & 2450086.4885 & 1.988 & 1.890 & 1.869 & 1.741\\
2447107.3600 & 1.982 & 1.861 & 1.836 & 1.829 & 2450086.5121 & 1.978 & 1.889 & 1.859 & 1.727\\
2447107.3851 & 1.985 & 1.864 & 1.856 & 1.806 & 2450086.5387 & 1.988 & 1.894 & 1.867 & 1.708\\
2447107.4094 & 1.988 & 1.868 & 1.857 & 1.804 & 2450086.5758 & 2.007 & 1.915 & 1.883 & 1.683\\
2447107.4376 & 1.989 & 1.883 & 1.865 & 1.823 & 2450087.4432 & 2.002 & 1.912 & 1.897 & 1.759\\
2447107.4621 & 1.996 & 1.898 & 1.866 & 1.822 & 2450087.4677 & 1.983 & 1.886 & 1.867 & 1.722\\
2447107.4902 & 1.999 & 1.896 & 1.873 & 1.829 & 2450087.4891 & 1.981 & 1.889 & 1.861 & 1.739\\
2447107.5163 & 1.997 & 1.885 & 1.869 & 1.823 & 2450087.5298 & 1.974 & 1.881 & 1.863 & 1.688\\
2447107.5446 & 1.988 & 1.885 & 1.859 & 1.821 & 2450087.5618 & 1.996 & 1.901 & 1.893 & 1.711\\
2447107.5699 & 1.984 & 1.876 & 1.855 & 1.808 & 2450088.3642 & 1.990 & 1.897 & 1.870 & 1.771\\
2447107.6046 & 1.973 & 1.878 & 1.851 & 1.796 & 2450088.3877 & 1.998 & 1.905 & 1.880 & 1.743\\
2447113.3505 & 2.013 & 1.858 & 1.833 & 1.814 & 2450088.4105 & 1.996 & 1.901 & 1.885 & 1.734\\
2447113.3765 & 1.978 & 1.876 & 1.853 & 1.810 & 2450088.4319 & 1.992 & 1.906 & 1.877 & 1.754\\
2447113.4013 & 1.982 & 1.876 & 1.865 & 1.804 & 2450088.4540 & 2.011 & 1.912 & 1.887 & 1.767\\
2447113.4278 & 1.979 & 1.875 & 1.853 & 1.796 & 2450088.4760 & 1.986 & 1.891 & 1.868 & 1.735\\
2447113.4530 & 1.995 & 1.879 & 1.855 & 1.813 & 2450088.4965 & 1.986 & 1.888 & 1.861 & 1.732\\
2447113.4788 & 1.997 & 1.887 & 1.863 & 1.815 & 2450088.5191 & 1.996 & 1.895 & 1.862 & 1.716\\
2447113.5031 & 1.999 & 1.897 & 1.866 & 1.820 & 2450088.5406 & 1.990 & 1.892 & 1.863 & 1.701\\
2447113.5269 & 1.999 & 1.888 & 1.869 & 1.818 & 2450088.5572 & 1.988 & 1.890 & 1.866 & 1.703\\
2447113.5501 & 1.992 & 1.886 & 1.869 & 1.815 & 2450088.5731 & 1.999 & 1.901 & 1.871 & 1.683\\
2447114.3537 & 1.968 & 1.880 & 1.851 & 1.826 & 2450089.2962 & 1.973 & 1.883 & 1.857 & 1.681\\
2447114.3765 & 1.983 & 1.878 & 1.850 & 1.812 & 2450089.3157 & 1.984 & 1.895 & 1.862 & 1.681\\
2447114.3997 & 1.972 & 1.880 & 1.850 & 1.800 & 2450089.3418 & 1.992 & 1.895 & 1.862 & 1.714\\
2447114.4236 & 1.990 & 1.885 & 1.857 & 1.813 & 2450089.4320 & 2.000 & 1.903 & 1.877 & 1.747\\
2447114.4474 & 2.007 & 1.891 & 1.859 & 1.822 & 2450089.4701 & 1.995 & 1.894 & 1.866 & 1.699\\
2447114.5327 & 1.999 & 1.886 & 1.867 & 1.826 & 2450089.4932 & 1.991 & 1.892 & 1.864 & 1.703\\
\hline
\end{tabular}
\end{center}
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\centerline{3}
\vskip 1mm
\centerline{Table 1 (continued)}
\begin{center}
\begin{tabular}{rrrrrrrrrr}
\hline
      HJD    &  $V$  & $b$   &  $v$  &  $u$ & HJD    &  $V$  & $b$   &  $v$  &  $u$\\
\hline
\\
2450089.5146 & 1.990 & 1.892 & 1.858 & 1.673 & 2450095.3130 & 1.981 & 1.883 & 1.857 & 1.679\\
2450089.5306 & 1.987 & 1.884 & 1.850 & 1.655 & 2450095.3339 & 1.984 & 1.889 & 1.865 & 1.711\\
2450089.5441 & 1.977 & 1.871 & 1.850 & 1.654 & 2450095.3828 & 1.999 & 1.896 & 1.873 & 1.736\\
2450089.5577 & 1.984 & 1.890 & 1.859 & 1.678 & 2450095.4033 & 2.007 & 1.905 & 1.879 & 1.734\\
2450090.2922 & 1.972 & 1.873 & 1.854 & 1.665 & 2450096.3565 & 1.988 & 1.889 & 1.866 & 1.743\\
2450090.3135 & 1.988 & 1.889 & 1.869 & 1.707 & 2450096.3830 & 1.997 & 1.907 & 1.880 & 1.752\\
2450090.3362 & 1.995 & 1.899 & 1.870 & 1.698 & 2450096.4089 & 2.002 & 1.907 & 1.883 & 1.748\\
2450090.3593 & 2.000 & 1.904 & 1.871 & 1.720 & 2450096.4682 & 1.992 & 1.903 & 1.876 & 1.736\\
2450090.3788 & 2.002 & 1.902 & 1.879 & 1.720 & 2450096.4907 & 1.989 & 1.888 & 1.871 & 1.714\\
2450090.4074 & 2.003 & 1.902 & 1.871 & 1.753 & 2450096.5097 & 1.985 & 1.885 & 1.864 & 1.689\\
2450090.4350 & 2.002 & 1.900 & 1.867 & 1.743 & 2450096.5234 & 1.982 & 1.881 & 1.860 & 1.693\\
2450090.4543 & 1.995 & 1.895 & 1.864 & 1.700 & 2450096.5401 & 1.984 & 1.882 & 1.859 & 1.660\\
2450090.4722 & 1.996 & 1.891 & 1.850 & 1.714 & 2450096.5573 & 1.994 & 1.882 & 1.866 & 1.667\\
2450090.4921 & 1.991 & 1.890 & 1.855 & 1.685 & 2450097.3112 & 1.976 & 1.886 & 1.859 & 1.734\\
2450090.5177 & 1.990 & 1.885 & 1.847 & 1.681 & 2450097.3584 & 1.986 & 1.898 & 1.873 & 1.670\\
2450090.5333 & 1.988 & 1.884 & 1.845 & 1.664 & 2450097.3826 & 1.996 & 1.899 & 1.875 & 1.740\\
2450090.5457 & 1.991 & 1.876 & 1.850 & 1.654 & 2450097.4060 & 1.997 & 1.914 & 1.887 & 1.752\\
2450090.5591 & 1.988 & 1.872 & 1.854 & 1.653 & 2450097.4679 & 1.992 & 1.901 & 1.867 & 1.720\\
2450090.5761 & 1.994 & 1.889 & 1.872 & 1.647 & 2450097.4929 & 1.998 & 1.899 & 1.860 & 1.726\\
2450091.3059 & 1.981 & 1.881 & 1.854 & 1.706 & 2450097.5171 & 1.994 & 1.896 & 1.863 & 1.705\\
2450091.3676 & 1.999 & 1.909 & 1.877 & 1.732 & 2450097.5322 & 1.981 & 1.887 & 1.853 & 1.662\\
2450091.4199 & 2.005 & 1.902 & 1.868 & 1.725 & 2450097.5459 & 1.990 & 1.923 & 1.893 & 1.740\\
2450091.4449 & 1.998 & 1.897 & 1.862 & 1.693 & 2450098.3078 & 1.970 & 1.882 & 1.867 & 1.728\\
2450091.4732 & 1.993 & 1.896 & 1.859 & 1.706 & 2450098.3256 & 1.976 & 1.881 & 1.857 & 1.721\\
2450091.5027 & 1.986 & 1.888 & 1.852 & 1.684 & 2450098.3427 & 1.981 & 1.893 & 1.864 & 1.720\\
2450091.5235 & 1.997 & 1.892 & 1.857 & 1.644 & 2450098.3603 & 1.987 & 1.891 & 1.867 & 1.726\\
2450091.5362 & 1.993 & 1.888 & 1.852 & 1.666 & 2450098.3803 & 1.989 & 1.892 & 1.872 & 1.738\\
2450091.5540 & 1.989 & 1.883 & 1.853 & 1.658 & 2450098.4006 & 1.997 & 1.902 & 1.880 & 1.760\\
2450091.5713 & 1.995 & 1.901 & 1.855 & 1.638 & 2450098.4237 & 2.003 & 1.905 & 1.880 & 1.753\\
2450092.4729 & 2.001 & 1.897 & 1.868 & 1.732 & 2450098.4440 & 2.001 & 1.906 & 1.882 & 1.764\\
2450092.5187 & 1.995 & 1.889 & 1.865 & 1.705 & 2450098.4640 & 2.003 & 1.907 & 1.880 & 1.705\\
2450092.5595 & 1.992 & 1.891 & 1.862 & 1.649 & 2450098.4845 & 1.997 & 1.901 & 1.876 & 1.718\\
2450093.4104 & 2.003 & 1.912 & 1.887 & 1.731 & 2450098.5037 & 1.996 & 1.895 & 1.855 & 1.682\\
2450093.4597 & 2.008 & 1.915 & 1.891 & 1.759 & 2450098.5250 & 1.989 & 1.891 & 1.856 & 1.666\\
2450093.4969 & 1.988 & 1.894 & 1.863 & 1.695 & 2450098.5485 & 1.984 & 1.887 & 1.855 & 1.692\\
2450093.5530 & 1.988 & 1.885 & 1.853 & 1.670 \\
\hline
\end{tabular}
\end{center}
\vfill \eject

\centerline{4}
\epsfysize=8cm
\centerline{\epsffile{4313-f1.ps}}
\begin{center}
Figure 1. Periodograms of the $b$ data for $\beta$~CMa.  Left panel: the 1987
data; right panel: the 1996 data.  The frequency is in cycles d$^{-1}$ and
the amplitude in mmag.
\end{center}
\vskip 5mm



\noindent same time the photometric accuracy
is much worse owing to the poor properties of the ND filter.

One can also adopt the three periods as known components and attempt to fit
the combined 1987 and 1996 data with these periods.  In that case we find
semi-amplitudes of 1 -- 2 mmag for $f_1$ and $f_3$ in the $y$, $b$ and $v$
bands.  However, the amplitude of $f_1$ increases to 20.6 mmag in $u$ and is
in fact larger than $f_2$ (16.7 mmag).  Because $f_1$ and $f_2$ are not
resolved in either of the two seasons, we view this result with suspicion. 
It is possible that the large rise in amplitude of $f_2$ in the $u$-band may
not be entirely real, but could be aided by an even steeper rise in the
unresolved component $f_1$.  It is interesting to note that while $f_2$ has
a much larger amplitude than $f_1$ in optical photometry, the two have
comparable radial velocity amplitudes (Kubiak 1980).

\vskip 1cm

\beginauthors
\authorsrightcol
L.A. BALONA$^{\star}$
L. BREGMAN$^{\star\star}$, B.A. LETSAPA$^{\star\star}$,
B.T. MAGORO$^{\star\star}$, S.E. WALSH$^{\star\star}$
\endauthors

\vspace{8mm}

\noindent
$^{\star}$ South African Astronomical Observatory, P.O. Box 9, Observatory 7935\\
Cape Town, South Africa; e-mail: lab@saao.ac.za\\

\noindent
$^{\star\star}$ SAAO Summer School Student\\


\references

Shobbrook, R.R., 1973, {\it MNRAS}, {\bf 161}, 257

Cassinelli et al., 1995, {\it ApJ}, {\bf 438}, 950

Kubiak, M., 1980, {\it Acta Astr.}, {\bf 30}, 41

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