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\IBVShead{5202}{20 November 2001}
\IBVStitletl{Photoelectric observations of the complex}{ low-amplitude red variable, UX D\lowercase{ra}}

\IBVSauth{Lloyd, C.$^{1}$; West, K.$^{2}$}
\IBVSinst{Space Science \& Technology Department, Rutherford Appleton
Laboratory, Chilton, Didcot, Oxon. \\ 
\indent OX11 0QX, UK, e-mail: {\tt cl@astro1.bnsc.rl.ac.uk}}
\IBVSinst{5 Edward Street, Ryde, Isle of Wight, PO33 2SH, UK, e-mail: {\tt kevinwest@beeb.net}}

\SIMBADobjAliasJ2000{UX Dra}{HIP 95154}{19 21 35.5 +76 33 35}
\IBVStyp{ SRa }
\IBVSkey{LPV - photometry - multiperiod}
\IBVSabs{Photoelectric V-band observations of the carbon star and low-}
\IBVSabs{amplitude variable UX Dra show periods of 175+/-1 and 334+/-2}
\IBVSabs{days when combined with the Hipparcos data. The 175 day period is}
\IBVSabs{very stable over 11 years but the longer period shows some}
\IBVSabs{variation.}


\begintext

UX Dra (HD 183556, SAO 9404, HIP 95154) is a luminous carbon star with Tc
(Little et al. 1987) and has a spectral type of C5\,II. According to the
Combined GCVS (Kholopov et al. 1998), following earlier editions, it
is an SRa variable with a period of 168 days. From times of minimum,
Vetesnik (1983) found a constant lengthening of the period but more
extensive photographic data suggested that this was part of a long term
cycling of the period between 155 and 185 days, over about 5000 days. At
the end of each cycle the period would apparently glitch back to the
lower value. From an analysis of the historical visual data Kiss et al.
(1999) found UX Dra to be a biperiodic variable, in common with about
half of their sample, with periods of $176\pm1$ and $317\pm2$ days.

\vskip 11pt
UX~Dra has been observed almost continuously since mid-1994 as part of a
programme to investigate known and suspected, small-amplitude red
variables. Early observations covering the first two years data have been
discussed previously by Lloyd \& West (1996, Paper I). The observations
were made using an SSP3 photometer and nominal V filter on a 20-cm
Newtonian reflector using a 2\arcm\ aperture. Each observation consisted
of 2 or 3 sets of 3$\times$10 second integrations. Differential
extinction corrections were applied but these are small and are
comparable to the errors. Details of the comparison stars are given in
Table~1. The photometric data are taken from the compilation of
Mermilliod et al. (1997) and are very similar to the values derived from
Hp, $V_T$ and $B_T$. HR~7199 = CCDM 18535+7547 is a close double star
with a separation of 6\arcs\ and magnitude difference of 0\fmm6 at V. The
revised magnitudes of the comparison stars are now in much better
agreement with the observed magnitude difference, $\Delta V=-0\fmm 231\pm 0\fmm 017$ than was the case in
Paper 1.

\begin{table}[!b]\centering
\caption{UX Dra comparison stars information}
\begin{tabular}{cccc}
\hline
Comparison & $V$ & $B-V$ & Sp \\
\hline
HR 7199 = HD 176795 & 6.33 & 0.01 & A1\,V \\
HR 7247 = HD 178089 & 6.55 & 0.38 & F2\,V  \\
\hline
\end{tabular}
\end{table}

\IBVSfig{8cm}{5202-f1.eps}{The V-band light curve of UX Dra from 1994 --
2000 relative to HR~7199, with the 178 and 359 day period fit over
plotted.}

The new V-band light curve of UX Dra is shown in Figure 1 and covers
about four times the period reported in Paper I. Consequently the general
behavior of the star is rather clearer, but no simpler. The full range
of variation during this time is nearly 0\fmm6, but the vast majority of
the light curve covers less than 0\fmm3. The periodogram shows a main
period of 178 days with a second period of approximately twice this
value. There is very little difference in the fit to the light curve if
the shorter period is treated as the first harmonic of the longer period,
however, as will be seen the relationship between them is not fixed. A
two-period fit to the data yields periods of $178\pm1$ and $359\pm3$ days
and after these have been removed a period of $\sim$ 665 days, and a
long-term trend, remain above the general noise level. Including this
additional period makes no obvious improvement in the fit to the light
curve. Of the two principal periods the shorter one is very similar to
that found in the historical visual data but the longer period is rather
different, 359 as opposed to 317 days.

\vskip 11pt
Not surprisingly the near-harmonic two-period fit produces a light curve
with oscillating maxima and minima. The phasing of the fit throughout this
time is relatively good but it does occasionally wander off, and there
are clearly very significant deviations in amplitude of both the maxima
and minima. Also, as was reported in Paper I, but is not clearly visible in
Figure 1, the behavior at the start of the observations is rather
different. The amplitude is much lower, $<0\fmm1$, and the characteristic
time scale of the variations is $\sim 75$ days, which is close to the
second harmonic of the long period. The reduction in amplitude at this
time is typical of the beating together of two periods but the time scale
of the variations should not change. It is possible that other,
low-amplitude variations may be revealed at these times, but if they are
always present then they should also appear in the periodograms, and
there are no consistent features above the noise at periods $<100$ days.

\IBVSfig{8cm}{5202-f2.eps}{The Hipparcos light curve of UX Dra from 1990 --
1992, with the 179 and 322 day period fit over plotted.}

\newpage

Hipparcos has also observed UX Dra, for approximately three years about two
years prior to the start of the V-band observations. The Hipparcos
light curve is shown in Figure 2 and the general behavior is very
similar to that in Figure 1. The periodogram of the Hipparcos data also
reveals similar periods; the best fit is with 179$\pm1$ and 322$\pm5$
days. The shorter period is practically identical to that of the V-band data
and both are close to the values found in the historical visual data. Any
remaining periods are dominated by a long-term trend in the data.

\vskip 11pt
The two data set have been combined by subtracting their respective
means, which are also very close to the zero points of their two-period
fits. The combined data yields best fit periods of $175\pm1$ and
$334\pm2$ days but the periodogram does not offer an unambiguous choice
of second period. It also shows other periods remaining above the noise
after the principal periods have been removed, the two most prominent
being at 186 and 301 days. Interestingly, when these two periods are
included in the fit to the data, their amplitudes are essentially
identical to that of the 334 day period, at 0\fmm05. The amplitude of the
dominant period, 175 days, is 0\fmm10. Another curious feature of
including these additional two periods is that the frequency spacing of
the longer and shorter pairs is identical, 0.00032 cycles\,day$^{-1}$,
corresponding to 3125 days. Similarly, the alternative pairings give
frequency spacings of 0.00238 cycles\,day$^{-1}$, corresponding to 420
days. Neither of these time scales have any apparent correspondence in
the data, nor do the periods appear clearly in the periodograms of the
individual data sets, although the 301-day period does appear weakly in
the V-band data. The significance, or otherwise, of these additional
periods and the frequency spacings they generate, is at present unclear,
but tests have shown that they are not due to the misalignment of the
two data sets.

\IBVSfig{8cm}{5202-f3.eps}{The autocorrelation function of the combined
data set showing the stability of the 175 day period.}

UX Dra appears to have two dominant periods but it is clear that a
stationary solution, even with several additional periods will not
adequately describe the light curve. Shifting periods, and phase changes,
are a recognized feature of long-period variable light curves but within
the data studied here the shorter period, 175 days, seems to have been
the more stable. The autocorrelation function of the combined data set is
shown in Figure 3 and clearly demonstrates the stability of this period
over eleven years. On the other hand the longer period does differ
between the two data sets, and the long term visual value. It seems
likely that the interaction of the two periods, along with some
instability can account for the changing behavior seen by Vetesnik (1983).
However, variation of the longer period will not account for the large,
and relative short time scale, of the amplitude variations, which cause
the main discrepancy between the observed and modelled light curve. These
seem to be on the time scale of the 175 day period or shorter, as do the
variations at the beginning of the V-band data described earlier. While
it may possible to explain some of the residuals by shifts in period or
phase, the main difficulty in describing the large excursions in
amplitude in the context of multiperiodic variations, is the lack of any
periods $<100$ days.

\references

Kholopov P.N., Samus N.N., Frolov M.S., Goranskij V.P., Gorynya N.A.,
Karitskaya E.A., Kazarovets E.V., Kireeva N.N., Kukarkina N.P., Kurochkin
N.E., Medvedeva G.I., Pastukhova E.N., Perova N.B., Rastorguev A.S.,
Shugarov S.Yu., 1998, The Combined General Catalogue of Variable Stars,
4.1 Edition

Kiss L.L., Szatm\'{a}ry K., Cadmus Jr. R.R., Mattei J.A., 1999, {\it
A\&A}, {\bf 346}, 542

Little S.J., Little-Marenin I.R. \& Bauer W.H., 1987, {\it AJ}, 94, 981

Lloyd C., West K., 1996, {\it IBVS} No. 4335 (Paper 1)

Mermilliod J.-C., Hauck B., Mermilliod M., 1997, {\it A\&AS}, {\bf 124},
349, {\it The General Catalogue of Photometric Data}, \\
{\tt http://obswww.unige.ch/gcpd/gcpd.html}

Vetesnik M., 1983, {\it IBVS} No. 2329

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