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\begin{document}
\IBVShead{5906}{17 September 2009}

\IBVStitle{Brightness Variations of SAO 53210}
 
\IBVSauth{Guerrero, G.}

\IBVSinsto{INAF Osservatorio Astronomico di Brera via E.Bianchi 46- 23807 Merate (LC) - Italy;\\ e-mail:giannantonio.guerrero@brera.inaf.it}
          
\SIMBADobjAlias{V454 And}{EXO 235330+4555.4}
\IBVStyp{ BY }
\IBVSkey{photometry}
\IBVSabs{New light curve of the star SAO 53210 is given}
\IBVSabs{The data analysis shows a possible double wave.}   


\begintext

\vspace*{-1cm}

With the aim to test the physical nature of some of the stellar serendipitous
X-ray sources detected by EXOSAT (Giommi et al., 1991), our group collected,
during the years 1990-1992, several photometric and spectroscopic observations
at the Observatorio Astronomico National, UNAM (San Pedro Martir, BC, Mexico).
For each star of our sample only few observations were obtained, but in many
cases they were sufficient to point out the presence of some photoelectric
variability (Cutispoto et al., 2000).
So we decided to plan, during the following years, further observations
to determine more precisely the variation characteristics and
possibly the nature of the stars.

The X-ray source SAO 53210 (EXO 233530.1+4555.4) is classified as BY Dra
type variable, with the name V454 And, in the 78th Name List of Variable
Stars (Kazarovets et al., 2006), on the basis of our Mexican observations.
%%(full data set are available at the CDS via {\tt http://cdsweb.u-strasb.fr/Abstract.html}).
These observations were very limited:
in total five data points on August 1990 and six on October 1991, distributed in seven
days for both observing runs. As a consequence, the period suggested
in Cutispoto et al. (2000) was inevitably very tentative.  The new data discussed here completely superseed this earlier attempt.

Following the ADS Abstract Service (Centre de Donn\'ees Astronomiques
de Strasbourg), no other report about the photometric variability of this star
has been published after Cutispoto et al. (2000), except an analysis by Percy 
(1993), which suggests a variability of SAO 53210 up to 0\fmm05 in $V$ and $B$
on a timescale of months.

The colours derived by the Hipparcos Catalogue are consistent with the spectral
type G3/4V.

SAO 53210 was observed during 30 nights in September-October 1992 at the
Brera Astronomical Observatory in Merate, using a digital photon-counting
photometer at the 50 cm. reflector and a Stromgren {\it y} filter.
The comparison and check stars were SAO 53147 and SAO 53149, respectively.
For details on the observing technique and data handling, see Cereda et al., 1988.
As a rule, about ten observations of the variable were performed in
alternation with the comparison star: these $\Delta${\it m}   magnitudes have
been averaged to give one or two {\it y}-normal points for every night.

Table~1 shows these {\it y}-normal points ({\it y}-np) with the observational 
times and the standard errors $\sigma$. 
Also the Mexican observations: J.D.\,\dots126-\dots133 and J.D.\,\dots556-\dots563, related to August 
1990 and October 1991 respectively, are reported in this Table. 

Figure~1 presents the light curves derived from our 1992 observations: the magnitude
differences {\it variable minus comparison} (top) is compared, in the same scale,
with the difference {\it check minus comparison} (bottom).

\begin{table}[!ht]
\centerline{Table 1. {\it y}-normal points ({\it y}-np) with observational times and 
standard errors $\sigma$}
%\normalsize
\vskip 3mm
\begin{center}
\begin{tabular}{llllll}
\hline
J.D.(8000+)  &  {\it y}-np  &  $\sigma$  & J.D.(8000+)  &  {\it y}-np  &  $\sigma$ \\
\hline
126.8610 & 0.352 & 0.003 & 892.4853 & 0.336 & 0.001 \\
127.8660 & 0.356 & 0.001 & 893.4015 & 0.339 & 0.003 \\
130.7910 & 0.356 & 0.003 & 893.5812 & 0.339 & 0.001 \\
132.8370 & 0.351 & 0.001 & 894.4886 & 0.344 & 0.002 \\
133.7990 & 0.345 & 0.001 & 896.4068 & 0.347 & 0.003 \\ 
556.7710 & 0.338 & 0.001 & 896.5714 & 0.349 & 0.001 \\
558.7450 & 0.340 & 0.004 & 898.4044 & 0.323 & 0.001 \\
559.7390 & 0.345 & 0.002 & 898.4634 & 0.323 & 0.004 \\
560.8400 & 0.327 & 0.003 & 899.6105 & 0.325 & 0.002 \\
562.8360 & 0.329 & 0.002 & 901.3950 & 0.344 & 0.001 \\
563.7190 & 0.334 & 0.001 & 901.5980 & 0.348 & 0.003 \\
870.5428 & 0.341 & 0.003 & 909.4569 & 0.331 & 0.002 \\  
871.5931 & 0.347 & 0.002 & 911.3985 & 0.320 & 0.002 \\
872.6163 & 0.349 & 0.002 & 911.5500 & 0.325 & 0.001 \\
873.5012 & 0.337 & 0.001 & 914.3890 & 0.345 & 0.002 \\
882.5884 & 0.342 & 0.004 & 914.5420 & 0.364 & 0.003 \\
883.4500 & 0.350 & 0.002 & 915.4653 & 0.339 & 0.004 \\
883.5963 & 0.351 & 0.003 & 917.4243 & 0.332 & 0.002 \\
884.4430 & 0.345 & 0.002 & 918.4039 & 0.340 & 0.001 \\
884.6137 & 0.347 & 0.001 & 918.5315 & 0.338 & 0.003 \\
885.5330 & 0.331 & 0.003 & 919.4419 & 0.348 & 0.005 \\
887.4850 & 0.325 & 0.001 & 920.3918 & 0.346 & 0.001 \\
887.5830 & 0.326 & 0.002 & 920.5290 & 0.343 & 0.002 \\
888.5705 & 0.333 & 0.004 & 922.3873 & 0.322 & 0.002 \\
889.5380 & 0.349 & 0.002 & 923.3940 & 0.322 & 0.002 \\
890.4740 & 0.347 & 0.002 & 923.5355 & 0.325 & 0.003 \\
890.6200 & 0.346 & 0.002 & 925.4335 & 0.340 & 0.001 \\
\hline
\end{tabular}
\end{center}
\end{table}

\begin{table}[!hr]
\centerline{Table 2. The two solutions for the light curve of SAO 53210}
\vskip 3mm
\begin{center}
\begin{tabular}{|llll|}
%1)1992 observations only & & \\
\hline
Epoch & Period  &  Amplitude  &  Phase \\
\hline
1992 only      & {\it P$_1$}=11.8d $\pm 0.1$  & 0\fmm0060 $\pm 0.0005$ &  $-$3.125 $\pm 0.085$ \\
1992 only      & {\it P$_2$}=5.9d  $\pm 0.2$  & 0\fmm0100 $\pm 0.0004$ &  $-$2.596 $\pm 0.056$\\
\hline
1990+1991+1992 & {\it P$_1$}=12.1d $\pm 0.01$  & 0\fmm0069 $\pm 0.0009$ &  $-$2.993 $\pm 0.130$ \\
1990+1991+1992 & {\it P$_2$}=6.1d  $\pm 0.02$  & 0\fmm0009 $\pm 0.0008$ &  $-$2.592 $\pm 0.100$\\
\hline
\end{tabular}
\end{center}
\end{table}

\begin{table}[!hr]
\centerline{Table 3. Details of the frequency analysis for the two different epochs of observation}
\vskip 3mm
\begin{center}
\begin{tabular}{|lllll|}
%1)1992 observations only & & \\
\hline
Epoch & $T_o$ & Initial {\it r.m.s.} res. & Final {\it r.m.s.} res. & Total variance \\
\hline
1992 only      & JD2448899.5450& 0\fmm0096 & 0\fmm0031 & 89\% \\
1990+1991+1992 & JD2448899.5450& 0\fmm0099 & 0\fmm0041 & 83\% \\
\hline
\end{tabular}
\end{center}
\end{table}

\clearpage
\IBVSfig{10cm}{5906-f1.eps}{The light curves derived from our 1992 observations: the magnitude
differences {\it variable minus comparison} (top) is compared
with the difference {\it check minus comparison} (bottom).}
\IBVSfigKey{5906-f1.eps}{SAO 53210}{light curve}

The data of Table~1 were analysed in two steps: at first considering only the 
more meaningful group of 1992 observations and then all the data
together (1990+1991+1992). The analysis was performed by means of the
``Multifre code'' (Bossi et al., 2009), which searches for the least squares best fit of a time series using a finite number of sinusoids.

In Figure 2 the periodogram related to the complete data set is presented,
while Tables~2 and 3 show the results of the two separate analyses.

Finally, Figure 3 shows the synthetized light curve and the phased {\it y}-normal points,
computed according to the data of Tables 2 and 3, and related to the whole set of observations
reported in Table~1. Here open and filled circles represent the 1990 and 1992 measures,
while crosses describe the 1991 data. A similar plot using only the 1992 observations does not show
significant differences.

As a preliminary conclusion, Table~2 and 3 show that the light curve parameters
based on the 1992 observations represent quite well also the 1990 and 1991 light variations.
This could indicate that the same periodic physical phenomenon acted continuously 
over at least three years.

As a second important point, the light variations of SAO 53210 are satisfactorily
explained by means of a double wave in which the two frequencies are not independent,
but represent the fundamental frequency and its first harmonic. 

The deviations of the 1990 observations (open circles in Figure~2) from the fit
could be explained by a modulation of the light variation amplitude.

This picture seems to agree with the classification of SAO 53210 as a BY Dra  
type variable (Kazarovets et al., 2006), or as some other type of rotating
variable stars. Further observations would clearly be important in order to improve the model of the star. 

\newpage

\IBVSfig{7cm}{5906-f2.eps}{The periodogram of the complete set of observations}
\IBVSfigKey{5906-f2.eps}{SAO 53210}{periodogram}

\IBVSfig{7cm}{5906-f3.eps}{The light curve of SAO53210. The solid line
is the synthetized light curve obtained according to to the data of Tables 2 and 3,
and related to the whole set of observations.
The open and filled circles represent the 1990 and 1992 observations,
while the crosses correspond to 1991 data.}
\IBVSfigKey{5906-f3.eps}{SAO 53210}{light curve}


\references

Bossi, M., Nunez, N., 2009, {\it private communication}

Cereda, L., Mist\'o, A., Niarchos, P.G., and Poretti, E., 1988, {\it A\&AS}, {\bf 76}, 255

Cutispoto, G., Pastori, L., Guerrero, G. et al., 2000, {\it A\&A}, {\bf 364}, 205

Giommi, P., Tagliaferri, G., Beuermann, K. et al., 1991, {\it ApJ}, {\bf 378}, 77

Kazarovets, E.V., Samus, N.N., Durlevich, O.V., 2006, {\it IBVS}, {\bf 5721}, 1

Percy, J.R., 1993, {\it PASP}, {\bf 105}, 1422


\endreferences
\end{document}

