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\IBVShead{4647}{3 November 1998}

\IBVStitletl{A Period Study of the Eclipsing Binary System}{ W Ursae Minoris}

\IBVSauth{Yasuhisa NAKAMURA$^{1,2}$, Kazuaki ASADA$^3$ and Ryuta SATO$^2$}

\IBVSinst{Konkoly Observatory of the Hungarian Academy of Sciences, 
PO Box 67, Budapest XII, H-1525, Hungary}
\IBVSinst{Department of Science Education, Faculty of Education,
Fukushima University, Fukushima, 960-1296 Japan,
e-mail: nakamura@educ.fukushima-u.ac.jp}
\IBVSinst{Kohken Junior High School, Fukuyama, Kohriyama, Fukushima, 
963-8071 Japan}

\IBVSabs{The variation of the period of W UMi is investigated.  It is }
\IBVSabs{shown that a sudden period decrease occurred in this system.}

\SIMBADobj{W UMi}
\IBVStyp{ EA/SD }
\IBVSkey{binaries: eclipsing}
\IBVSkey{binaries: period change}

\begintext

Since the discovery by Astbury (1913) and by Davidson (Dyson 1913), W
Ursae Minoris (BD +86\deg 244), a bright eclipsing binary quite close
to the celestial north pole, had attracted much interest in earlier
days, particularly among the photometrists.  Spectroscopic
observations were performed by Joy and Dustheimer (1935) and Sahade
(1945), who both gave single-lined radial velocity curves for the
system.  The most comprehensive study of the system was performed by
Devinney et al. (1970), where two sets of photometric light curves were
solved by the rectification method to yield the photometric elements.
They derived the absolute dimensions and confirmed that W~UMi is a
semi-detached system of Algol-type.  Mardirossian et al. (1980)
reanalyzed five light curves of Devinney et al. with the Wood's model.

  Occasional monitoring for the times of minima have been done for the
system.  As to the period study, the following ephemerides for Min I,
e.g., have been published.
\begin{center}
\begin{tabular}{ll}
Dyson
(1913): 		   & HJD 241 9487.850 + 1\fday 7012$E$ \\
Martin and Plummer (1918): & HJD 242 1219.685 + 1\fday 70116$E$ \\
McLaughlin (1926): 	   & HJD 242 2813.605 + 1\fday 70116$E$ \\
Dugan (1930): 		   & HJD 242 4999.604 + 1\fday 70116$E$ \\
Himpel (1937): 		   & HJD 242 7624.485 + 1\fday 70116$E$ \\
Nason and Moore (1951):    & HJD 243 3457.761 + 1\fday 7011576$E$ \\
Devinney et al. (1970):    & HJD 243 9758.846 + 1\fday 7011576$E$ \\
SAC 66 (1995): 		   & HJD 244 6614.481 + 1\fday 7011576$E$ \\
\end{tabular}\\
 (SAC = {\it Rocznik
Astronomiczny Observatorium Krakowskiego}) 
\end{center}
As these show,
almost everybody considered that the period had been constant, and
they devoted in revising the epoch and getting more precise period.
The only two exceptions were Gadomski (1926) and Payne-Gaposchkin
(1952), who suggested that the period was variable.  However, these
were not confirmed by others.

  As we noticed that the primary minimum did not occur at the predicted
time, we observed W~UMi in order to know the possible variation of its
orbital period.  Photoelectric observations of the system were done
with the Multichannel Polarimetric Photometer attached to the 91cm
reflector at Dodaira Station of the National Astronomical Observatory
of Japan and also with a photometer (PMT: 1P21) attached to the 45cm
telescope  at Fukushima University.  Their features are described in
other publications (Nakamura et al. 1991a, b).  The comparison and
check stars were BD +86\deg 245 and BD +86\deg 246 for Dodaira
observations and 23 and 24 UMi for Fukushima observations,
respectively.  The estimated times of the primary minimum are listed in Table 1.  The observed data at Fukushima are the mean of B and V light curves and those at Dodaira are averaged over four channels.  The new observations showed large negative $O-C$ values.

\begin{table} 
\caption{New Photoelectric Observations} 
\begin{center} 
\begin{tabular}{clllcrcr} 
\hline 
Obs.\ HJD (Min I) & Site & Observer & $E^1$ & $O-C^1$ & $E^2$ & $O-C^2$ \\ 
\hline
2449770.0722 & Dodaira & Y. Nakamura &5885 &--0.0863 &4429 &0.0018 \\
2450464.131:$^3$ & Fk.\ Univ. & K. Asada &6293 &--0.0998 &4837 & --0.0039 \\
2450487.9460 &  Fk.\ Univ. & K. Asada &6307&--0.1010&4851 &--0.0048\\
2450857.0866 & Fk.\ Univ. & R. Sato & 6524& --0.1116& 5068&--0.0112\\
\hline 
\end{tabular} 
\end{center}
$^1$ These values are based upon the ephemeris of Devinney et al.\
(1970).\\ 
$^2$ These are based upon the new linear ephemeris (4).\\
$^3$ This observation provided rather different moments for the minimum
in B and V bands.  However, the mean value seems reasonable.
\end{table}


In order to study the long-term behaviour of the period variation, we
have collected observed minima timings, including ours, from the
literature and from B.R.N.O. (Brno Regional Network of Observers) and
BAV Databases, which are all for the primary eclipse.  Devinney et al.
(1970) observed primary minima, whose central times are, however, not
described explicitly in their paper.  The mean of the two minima times
observed by them is instead given, hence we employed it as useful
information.  A total of 160 observed times of primary minima (147
visual, 4 photographic and 9 photoelectric) were collected and are
plotted in Figure 1 according to the ephemeris by Devinney et al.
There is a large scatter in the observed times of minima.  Despite such
a large scatter, it may be concluded that the orbital period of the
system had been constant before $E\sim +1000$.  However, recent primary
minima have occurred definitely earlier than predicted.




Because the ephemeris by Devinney et al. (1970) was derived with only
the limited data up to 1970, we derived another linear ephemeris using
all data.  In deriving this, we omitted six data which show the large
$O-C$ residuals in Figure 1, and we put weight 10 on the photoelectric
estimates, 3 on photographic ones, and 1 to visual ones.  If the datum
is denoted to be uncertain, we set the weight to its half value.  Thus,
we have $$
   {\rm Min ~I} = {\rm HJD} ~244 3392.4794(\pm13) + 1\fday
   70115182(\pm22)~E.     \eqno(1) $$ The $O-C$ residuals based upon
this ephemeris are shown in Figure 2.



  We have examined two possibilities for the period change of the
  system:  one is a constant period change (decrease) and the other a
sudden period decrease.  For the first possibility, the ephemeris
should be quadratic.  We calculated such a formula as $$
   {\rm Min~I} = {\rm HJD}~244 3392.4924(\pm\ 7) + 1\fday
   70114548(\pm18)~E -8\fday 80(\pm21) \times
10^{-10}~E^2.                  \eqno(2) $$ This quadratic ephemeris is
shown with the dash-dot curve in Figure 2.

We next sought for the two linear ephemerides which fit for the sudden
period decrease shown in the figures.  The following ephemerides were
found to be good for the purpose:
$$
{\rm Min~I} = {\rm HJD}~244 2235.7289(\pm\ 8) + 1\fday 70115716(\pm22)~E \eqno(3) $$
before the sudden period decrease, and 
$$
{\rm Min~I} = {\rm HJD}~244 2235.7289(\pm16) + 1\fday
70113830(\pm45)~E      \eqno(4) 
$$
after the period change.  The
$O-C$ residuals based upon these ephemerides are shown in Figure 3.
The $\Sigma (O-C)^2$ values for all the data used are 0.032616 for the eq.\ (2) and 0.021577 for the eqs.\ (3)+(4), respectively.


\IBVSfig{75mm}{4647-f1.eps}{$O-C$ diagram for the primary minimum of
W~UMi.  The calculation is based on the ephemeris of Devinney et al.
(1970).}


\IBVSfig{75mm}{4647-f2.eps}{$O-C$ residuals based upon the new single
linear ephemeris.  The quadratic ephemeris is also represented with the dashed curve.}





Though we derived a quadratic ephemeris for W~UMi, the fitting by the
parabola is worse than the two linear ephemerides, and moreover it is
rather difficult to imagine a mechanism which derives constant period
decrease in such a semi-detached system as W UMi.  Therefore, we prefer
the interpretation of a sudden period decrease which is represented as
two straight lines in Figure 3.  According to this, the amount of
period decrease is $\Delta P / P = -1.11 \times 10^{-5}$, and this
change occurred nearly at JD2442236.  We think that mass loss from the
system is the most natural explanation for this phenomenon.

\IBVSfig{75mm}{4647-f3.eps}{$O-C$ diagram for the primary minimum of
W~UMi.  The observed data are fitted with the two linear ephemerides
(3) and (4).  The intersection is at JD 2442236.}


We are grateful to Dr.\ M. Zejda for sending the data in B.R.N.O. database and to Mr.\ F. Agerer in BAV database, which is based on the data collection by Mr.\ D. Lichtenknecker.  One of us (YN) acknowledges Mr.\ S. Narusawa at Nishi-Harima Astron.\ Obs.\  for his assistance in the observations at Dodaira.  He also heartily acknowledges the staff of Konkoly Observatory for their kind hospitality during his stay.

\references

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Himpel, K., 1937, {\it AN}, {\bf 261}, 233

Joy, A.H. and Dustheimer, O.L., 1935, {\it ApJ}, {\bf 81}, 479

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