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\begin{document}

\IBVShead{4950}{5 September 2000}

\IBVStitle{Period Variation of XX~Cygni Revisited}


\IBVSauth{Kiss, L.L.; Derekas, A.}

\IBVSinsto{Department of Experimental Physics and Astronomical Observatory,
University of Szeged\\ \indent
e-mail: l.kiss@physx.u-szeged.hu}

\SIMBADobjAlias{XX Cyg}{HIP 98737}


\IBVStyp{ SX Phe }
\IBVSkey{CCD photometry}
\IBVSabs{New CCD observations are presented and the period variation}
\IBVSabs{of XX Cygni is discussed. Five new times of maxima were determined}
\IBVSabs{and the most recent O-C diagram was created by collecting}
\IBVSabs{all available epochs of maximum. We did not find evidence of}
\IBVSabs{possible period change since that jump in 1942 described in details}
\IBVSabs{by Szeidl & Mahdy (1981). A new accurate ephemeris is given.}

\begintext

The light variation of XX~Cygni (= HIP 98737, spectral type A5--F5,
$\langle V \rangle = 11\fmm7$, $P\approx0\fday1349$, $\Delta
V=0\fmm80$) was discovered by Ceraski (1904).  While Shapley \& Shapley
(1915) referred to XX~Cyg as ``the shortest-period variable star
known'', McNamara \& Feltz (1980) highlighted the importance of XX~Cyg
by noting the fact, that this star has longer period than any other
high-velocity variables of this type. The single periodic nature of the
star was recognized by Nijland (1923) and the follow-up studies
regarding the description of the light variation concentrated on
detecting small, secular changes of the light curve shape or the
period.  A full set of physical parameters was determined by Joner
(1982).  Szeidl \& Mahdy (1981) published a very thorough period study
concluding that the period of XX~Cyg suffered a sudden change by
$+87\times10^{-9}$ day ($\Delta P/P=6\times10^{-7}$) in 1942 and was
constant otherwise. Since then a few times of maxima have been
published in almost every observing season, but there has been no paper
dealing with the very recent behaviour of the period change.  For this
purpose, we made new CCD observations, collected all available epochs
of maximum and analysed the resulting $O-C$ diagram.

\IBVSfig{8cm}{4950-f1.eps}{The unfiltered light curve of XX Cygni obtained
on August 1, 2000}

\vskip-11pt
Unfiltered CCD observations were carried out at University of Szeged on
three subsequent nights (July 31--August 2, 2000). The applied instrument was the 0.28-m
Schmidt--Cassegrain-type telescope located in the very center of the
city of Szeged. The detector was an SBIG ST--9E CCD camera ($512\times512$
pixels) giving an angular resolution of about 2\arcs/pixel. The exposure
time was 20 seconds and the frames were obtained almost uninterruptedly
enabling a very good phase coverage during every cycle.

The data were reduced with standard tasks in IRAF\@. We made aperture
photometry with IRAF/DIGIPHOT\@. Two nearby stars were chosen as
comparison and check stars (comp = GSC 3948-2542, 10\fmm4, check =
GSC 3948-2105, 10\fmm9).  Throughout the observations we did not find
significant differential brightness variations larger than 0\fmm015
implying a photometric accuracy of the same order. A single-night light
curve is shown in Fig.~1. The whole dataset contains 826 individual
data points obtained on three nights. They are available upon request
from the first author. All data were phased with the finally adopted
ephemeris (see later) and the corresponding phase diagram is plotted in
Fig.~2.

Five new times of maxima were determined from the individual cycles
by fitting low-order (3--5) polynomials to the top part of the
light curves. The estimated accuracy is about 0.0003 days.
To construct the updated $O-C$ diagram, we collected all available
data from the literature. Szeidl \& Mahdy (1981) gave a full
compilation until 1980, therefore, we had only to add new data
published by Romano \& Perissinotto (1982), Joner (1982),
Sadun \& Ressler (1986), Rodr\'{\i}guez et al.\  (1993), Kim \& Joner (1994)
and Agerer \& H\"ubscher (2000). In cases when the authors listed
only the photometric data, we determined the individual
epochs of maximum with the same fitting procedure.
We have to note that the typical light curve sampling is less dense
than ours, therefore, some of the determined epochs are of lower
quality.

\IBVSfig{8cm}{4950-f2.eps}{The phase diagram of all unfiltered observations
calculated with the adopted ephemeris ($E_0={\rm HJD}~2451757.3984$,
$P=0.134865123$ days)}

\vskip-11pt
The final sample including times of maxima from Szeidl \& Mahdy (1981)
contains 88 points. The $O-C$ values were calculated with the same
formula as in Szeidl \& Mahdy (1981):  ${\rm Hel.~JD_{max}} =
2430671.1010+0.134865070 \times E$.  Six discordant points which were
obviously bad had to be rejected. The remaining 82 points were used to
form yearly means of the cycle numbers and $O-C$ values.  The resulting
diagram is plotted in Fig.~3.

\begin{table}
\caption{Times of maxima of XX~Cyg (HJD${}-{}$2400000). References:
(1) Romano \& Perissinotto (1982), (2) Joner (1982), (3) Sadun \& Ressler
(1986), (4) Rodr\'{\i}guez et al.\  (1993), (5) Kim \& Joner (1994),
(6) Agerer \& H\"ubscher (2000). Cycle numbers and $O-C$ values 
were calculated with the ephemeris of Szeidl \& Mahdy (1981)}
\vskip 3mm
\begin{center}
\begin{tabular}{llrl|llrl}
\hline
Hel.\ JD  &  $E$ &  $O-C$ & Ref. & Hel.\ JD & $E$ & $O-C$ & Ref. \\
\hline
38939.4210 & 61308  &    0.0123 & (1) & 46631.7142 & 118345 & 0.0065 & (5) \\
38961.3960 & 61471  &    0.0043 & (1) & 46951.6171 & 120717 & 0.0094 & (4) \\
40124.3460 & 70094  &    0.0128 & (1) & 46999.4899 & 121072 & 0.0051 & (4) \\
40152.2470 & 70301  & $-$0.0033 & (1) & 46999.6249 & 121073 & 0.0053 & (4) \\
44437.8645 & 102078 &    0.0069 & (2) & 47001.5153 & 121087 & 0.0076 & (4) \\
44440.8298 & 102100 &    0.0052 & (2) & 47001.6508 & 121088 & 0.0082 & (4) \\
44456.7445 & 102218 &    0.0058 & (2) & 47004.4814 & 121109 & 0.0066 & (4) \\
44461.7353 & 102255 &    0.0066 & (2) & 47360.7955 & 123751 & 0.0072 & (5) \\
44461.8705 & 102256 &    0.0069 & (2) & 47361.7374 & 123758 & 0.0051 & (5) \\
44513.6594 & 102640 &    0.0076 & (2) & 50674.4279 & 148321 & 0.0049 & (6) \\
45901.6893 & 112932 &    0.0062 & (3) & 50677.3965 & 148343 & 0.0064 & (6) \\
45906.6798 & 112969 &    0.0067 & (3) & 50677.5315 & 148344 & 0.0066 & (6) \\
45928.6638 & 113132 &    0.0077 & (3) & 51305.4641 & 153000 & 0.0074 & (6) \\
45941.7467 & 113229 &    0.0087 & (5) & 51757.3984 & 156351 & 0.0088 & this paper \\
45945.7926 & 113259 &    0.0086 & (5) & 51757.5342 & 156352 & 0.0098 & this paper \\
46581.8129 & 117975 &    0.0053 & (5) & 51758.3432 & 156358 & 0.0096 & this paper \\
46583.8378 & 117990 &    0.0072 & (5) & 51758.4773 & 156359 & 0.0088 & this paper \\
46627.5333 & 118314 &    0.0064 & (4) & 51759.4214 & 156366 & 0.0089 & this paper \\
\hline                                                              
\end{tabular}
\end{center}
\end{table}

\IBVSfig{8cm}{4950-f3.eps}{The mean $O-C$ diagram of XX~Cyg}

\vskip-11pt
The two well-defined linear branches give further support to the main
conclusion by Szeidl \& Mahdy (1981) that the period of XX~Cyg suffered
a sudden change in 1942 and since then it has remained constant. The
amount of period change is $(+92.8\pm9.8)\times10^{-9}$ days, or
$\Delta P/P=6.9\times10^{-7}$.  This is somewhat larger than the value
determined by Szeidl \& Mahdy (1981) --- $87\times10^{-9}$ days ---
that can be attributed to our longer dataset allowing higher accuracy.
Our work extends the results of Szeidl \& Mahdy (1981) by a further
20-year long period of time and thanks to the relatively large number
of observations, we could determine a very accurate ephemeris for
XX~Cyg. By a least-squares linear fit of the second branch of the $O-C$
diagram, we obtained the following formula:
$$
{\rm Hel.~JD_{max}} =2451757.3984+0.13486513(5) \times E.
$$

The reason of the abrupt period change has remained essentially unknown
since its detection.  Recently, Breger \& Pamyatnykh (1998) shortly
discussed the observed period changes in SX~Phe stars concluding that
sudden jumps cannot be described in terms of long-term stellar
evolution, but they are most likely in connection with nonlinear
effects in pulsation. Similar conclusion was also reached by
Rodr\'{\i}guez et al.\  (1995). Mixing events in the semiconvective
zone or slight overshooting at the convective core edge predicted by
Sweigart \& Renzini (1979) are the most widely accepted theoretical
explanations.  Follow-up observations are crucial to monitor the
constancy of the period and to detect further possible sudden
change(s).

This research was supported by the ``Bolyai J\'anos'' Research
Scholarship of LLK from the Hungarian Academy of Sciences,
Hungarian OTKA Grant \#T032258 and Szeged Observatory Foundation.
The observations were acquired during the course of Summer Training
Programme for students of astronomy at University of Szeged.
The NASA ADS Abstract Service was used to access data and references.
This research has made use of Simbad Database operated at CDS, Strasbourg,
France.

\references

Agerer, F., H\"ubscher, J., 2000, {\it IBVS}, No.\ 4912

Breger, M., Pamyatnykh, A.A., 1998, {\it A\&A}, {\bf 332}, 958

Ceraski, W., 1904, {\it AN}, {\bf 165}, 61

Joner, M.D., 1982, {\it PASP}, {\bf 94}, 289

Kim, C., Joner, M.D., 1994, {\it Ap\&SS}, {\bf 218}, 113

McNamara, D.H., Feltz, K.A., 1980, {\it PASP}, {\bf 92}, 195

Nijland, A.A., 1923, {\it Utrecht Rech.\ Astr.}, {\bf 8}, 144

Rodr\'{\i}guez, E., Rolland, A., L\'opez de Coca, P., 1993, {\it A\&AS}, {\bf 100}, 571

Rodr\'{\i}guez, E., L\'opez de Coca, P., Mart\'{\i}n, S., 1995, {\it A\&A}, {\bf 299}, 108

Romano, G., Perissinotto, M., 1982, {\it IBVS}, No.\ 2161

Sadun, A.C., Ressler, M.E., 1986, {\it PASP}, {\bf 98}, 504

Shapley, H., Shapley, M.B., 1915, {\it ApJ}, {\bf 42}, 148

Sweigart, A.V., Renzini, A., 1979, {\it A\&A}, {\bf 71}, 66

Szeidl, B., Mahdy, H.A., 1981, {\it Comm.\ Konkoly Obs.}, No.\ 75
\BIBCODE{1981CoKon..75....1S}

\end{document}

