COMMISSION 27 OF THE I. A. U.
              INFORMATION BULLETIN ON VARIABLE STARS
                           Number 3670

                                                   Konkoly Observatory
                                                   Budapest
                                                   9 October 1991

                                                   HU ISSN 0374 - 0676


           THE PHOTOMETRIC VARIABILITY OF KX ANDROMEDAE


Introduction.  KX And (HD 218393) is a bright (V = 6.9 - 7.1), active Be star
which shows remarkable variations in light, colour and spectrum; see Stefl et
al.  (1990) for a recent, comprehensive review.  There are (i) short-term
variations with a possible time scale of 0.35 day (Pavlovski and Ruzic 1989) or
0.4716 and/or 4.8635 days (Stagg et al. 1988), due to pulsation or perhaps
rotation; (ii) medium-term variations on a well-established time scale of
38.919 days (Stefl et al. 1990), which bear some resemblance to what is observed
in strongly-interacting binaries; and (iii) long-term variations on time scales
of months to years, due to the changing amount of gas in the circumstellar
disc.  In an effort to disentangle these variations, we have subjected a large
body of existing photometric data to a simple form of period analysis.

Observations.  The input data consisted of several hundred UBV observations
made between 1974 and 1986, mostly at Hvar Observatory (Stefl et al. 1990), and
several dozen BV observations made during the 1980's at the University of
Toronto (Percy et al. 1988).

Analysis.  The autocorrelation of the observations was studied on time
intervals ("lags") of 0 to 2 days and 0 to 40 days.  Each interval was divided
into approximately 40 bins.  All pairs of observations ((m_i,t_i,), (m_j,t_j))
for which t_j-t_i, fell in a given bin were averaged:  <|(m_j-m_i)|>, and the
averages plotted against the time difference (Figures 1, 2).  If the magnitude
was periodic with period P, the curves would show minima of level sigma (the
observational scatter) at lags of 0, P, 2P, 3P etc., and maxima of level sigma
+ about 1.2 Delta m (Delta m is the semi-amplitude) at lags of 0.5P, 1.5P, 2.5P
etc.

Results.  The results are shown in Figures 1 (V data) and 2 (U data); the
results for the B data are very similar to those for the V data, indicating
that variations of (B-V) colour are small.  The 38.919-day variations are
dominant.  There is little or no evidence in Figures 1 and 2 (top panels) for
maxima or minima corresponding to 0.35 day, 0.4716 day, or any other short
period (except possibly ~ 1.2 days); the amplitude of any such short-term
variability must be 0.02m at most.  The 38.919-day variations, on the other
hand, show up clearly in Figures 1 and 2 (bottom panels).  The maxima
correspond to full amplitudes of 0.13m in V, and 0.33m in U, indicating that
variations in (U-B) colour are large, in good agreement with the phase diagrams
shown by Stefl et al.  (1990).  The rather unusual shape of the autocorrelation
diagram for the U data suggests that the variations are non-sinusoidal.  Note
that Stefl et al.  (1990) found strong cycle-to-cycle changes in the light
curve, especially in U.  In particular, there were two distinct shapes of the U
light curve, with different depths of minimum.  The fact that Figures 1 and 2
(bottom panels) show clear, low minima at 39 days indicates that the long-term
variations are insignificant on time scales of about a month; this is confirmed
by light curves for individual years.  We attempted to study the long-term
variations in V by subtracting the "average" 38.919-day variation, but we found
that the amplitude of this variation changed markedly from cycle to cycle, by
factors of two or more.  The long-term variations seem to have a typical range
of 0.1m, and a time scale of a year or more.


                                   [FIGURE 1]

 Figure 1. Autocorrelation diagram for V observations of KX And. Top panel:
 "lags" of 0 to 2 days; note the lack of clear maxima and minima. Bottom
 panel: "lags" of 0 to 40 days; note the maxima and minima corresponding to
 the 39 day period.

                                   [FIGURE 2]

 Figure 2. Autocorrelation diagram for U observations of KX And. Top panel:
 "lags" of 0 to 2 days; bottom panel: "lags" of 0 to 40 days.


We have since used the simple autocorrelation method to study other stars with
complex, irregular variations, and have found it to be very useful for
analyzing the time scales, amplitudes and irregular and irregularities in such
stars.

Acknowledgements.  We are very grateful to Drs. S. Stefl, P. Harmanec and
the other authors of Stefl et al.  (1990) for making their photometric data
available to us in machine-readable form, and to Dr. P. Harmanec for his
useful comments.  Li Sen (Northern Secondary School) was a participant in the
University of Toronto Mentorship Program, which enables outstanding senior high
school students to work on research projects with university faculty members.


JOHN R. PERCY and LI SEN
Department of Astronomy and
Erindale Campus
University of Toronto
Mississauga, Ontario
Canada L5L 1C6

References:

Pavlovski, K. and Ruzic, Z. 1989. Ap.Sp.Sci. 152, 35 [BIBCODE 1989Ap&SS.152...35P ]
Percy, J.R., Coffin, B.L., Drukier, G.A., Ford, R.P., Plume, R., Richer, M.G.
   and Spalding, R. 1988. PASP 100, 1555. [BIBCODE 1988PASP..100.1555P ]
Stagg, C.R., Bozic, H., Fullerton, A.W., Gao, W.S., Guo, Z.H., Harmanec, P.,
   Horn, J., Huang, L., Iliev, L.H, Koubsky, P., Kovachev, B.Z., Pavlovski,
   K., Percy, J.R., Schmidt, F., Stefl, S., Tomov, N.A. and Ziznovsky, I.
   1988. MNRAS 234, 1021. [BIBCODE 1988MNRAS.234.1021S ]
Stefl, S., Harmanec, P., Horn, J., Koubsky, P., Kriz, S., Hadrava, P., Bozic,
   H. and Pavlovski, K. 1990. Bull.Astron.Inst. Czechoslovakia 41,29 [BIBCODE 1990BAICz..41...29S ]