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\input ibvs2.sty

\begin{document}
\IBVShead{4577}{3 April 1998}

\IBVStitle{A note on the period behaviour of BL Eridani}

\IBVSauth{Petr Molik$^{1,2}$}

\IBVSinst{Petrin Hill Observatory,
Strahovska 205, 118 46 Prague 1,
Czech Republic,
 e$-$mail: observat@ms.anet.cz}

\IBVSinst{Dept. of Astronomy, Charles University, 180 00 Prague
8, V Holesovickach 2, Czech Republic}

\SIMBADobj{BL Eri}
\IBVStyp{ EW }
\IBVSkey{period study}

\begintext

BL Eri (= BD $-$12\deg 0818, HV 6277; Max: 11.5 mag P, Min: 12.2 mag P)
is an eclipsing binary of the W UMa-type which had been neglected for
a long time but recently it has attracted attention of observers.
Its preliminary light elements based on photographic observations are
given in GCVS4:

\begin{equation}
Min.I = JD(hel)\;\; 24 29 232.082 + 0\fday 4162 \times E
\end{equation}

First photoelectric photometry of BL Eri was done by Kern and Bookmyer
(1986) in December, 1980, and January, 1981. They obtained four times
of minimum light and published the improved elements:

\begin{equation}
Min.I = JD(hel)\;\; 24 44 606.5914 + 0\fday 41696010 \times E
\end{equation}

Yamasaki et al. (1988) observed this star photoelectrically in November,
1982, and in November, 1986. Their light elements

\begin{equation}
Min.I = JD(hel)\;\; 24 44 606.5901 + 0\fday 41691339 \times E
\end{equation}
fitted observations from 1982 (three minima timings) as well as previous
times of minima. But observations from 1986 did not agree with these
elements so the authors suspected a change (increase) in the orbital
period. They calculated other elements which were also suitable for
their observations from 1986:

\begin{equation}
Min.I = JD(hel)\;\; 24 44 606.5880 + 0\fday 41691506 \times E
\end{equation}

They supposed that the period change occurred within the interval
of years 1980-1986.

Quingyao et al. (1994) obtained two photoelectric minima timings and
derived the light elements:

\begin{equation}
Min.I = JD(hel)\;\; 24 44 606.5884 + 0\fday 41691591 \times E
\end{equation}

Qingyao et al. (1996) confirmed the period increase. Shengbang et al.
(1996) on the basis of two new and nine old photoelectric times of
minima and the light elements by Kern and Bookmyer (1986) came to the
conclusion that the increase in period is continuous and can be described
by the following elements with a quadratic term:

\begin{equation}
Min.I = JD(hel)\;\; 24 44 606.5833 + 0\fday 41691786 \times E + 4\fday 286 \times
10^{-9} \times E^2
\end{equation}

Recently, Paschke (1997) analyzed all available times of minima of
BL Eri including his nine visual and CCD minima timings and calculated
the following linear ephemeris:

\begin{equation}
Min.I = JD(hel)\;\; 24 44 606.5928 + 0\fday 416916 \times E
\end{equation}

He agreed with Shengbang et al. (1996)
that the O$-$C values had parabolic course
but according to him the increase in period was 20 times slower in
comparison to Shengbang's elements. He also noted that five O$-$C values
(Nos 1, 8, 18, 26, and 27 in Table) extremely deviated
from the others. They had to be excluded from the data set used for
calculation of the elements. All published times of minimum light of
BL Eri are listed in Table 1.

\vskip 1cm

\centerline{Table 1. List of minima timings of BL Eri}
\vskip 3mm
\begin{center}
\begin{tabular}{rrrrll}
\hline
No. & JD hel 2400000+ & Epoch & O$$-$$C & Method & Reference \\
\hline
 1 & 29232.0820 & $-$36877.0 &  0.1005 & pg  & Kholopov et al., 1985 \\
 2 & 43515.3150 &  $-$2617.5 & $-$0.0002 & vis & Locher, 1978a \\
 3 & 43544.2970 &  $-$2548.0 &  0.0062 & vis & Locher, 1978a \\
 4 & 43749.6310 &  $-$2055.5 &  0.0090 & vis & Locher, 1978b \\
 5 & 43764.6460 &  $-$2019.5 &  0.0151 & vis & Locher, 1979 \\
 6 & 43773.6030 &  $-$1998.0 &  0.0084 & vis & Locher, 1979 \\
 7 & 43783.6030 &  $-$1974.0 &  0.0024 & vis & Locher, 1979 \\
 8 & 43812.5390 &  $-$1904.5 & $-$0.0373 & vis & Locher, 1979 \\
 9 & 44603.6709 &     $-$7.0 & $-$0.0035 & pe  & Kern, Bookmyer, 1986 \\
10 & 44604.7146 &     $-$4.5 & $-$0.0021 & pe  & Kern, Bookmyer, 1986 \\
11 & 44606.5894 &      0.0 & $-$0.0034 & pe  & Kern, Bookmyer, 1986 \\
12 & 44607.6328 &      2.5 & $-$0.0023 & pe  & Kern, Bookmyer, 1986 \\
13 & 45298.8745 &   1660.5 & $-$0.0073 & pe  & Yamasaki et al., 1988 \\
14 & 45299.9170 &   1663.0 & $-$0.0071 & pe  & Yamasaki et al., 1988 \\
15 & 45300.9599 &   1665.5 & $-$0.0065 & pe  & Yamasaki et al., 1988 \\
16 & 47118.4950 &   6025.0 & $-$0.0167 & vis & Paschke, 1988a \\
17 & 47141.4400 &   6080.0 & $-$0.0021 & vis & Paschke, 1988a \\
18 & 47151.4150 &   6104.0 & $-$0.0331 & vis & Paschke, 1988a \\
19 & 47207.3160 &   6238.0 &  0.0012 & vis & Paschke, 1988b \\
20 & 47535.4270 &   7025.0 & $-$0.0007 & vis & Paschke, 1989 \\
21 & 48286.2900 &   8826.0 & $-$0.0034 & CCD & Paschke, 1991 \\
22 & 48602.1026 &   9583.5 & $-$0.0047 & pe  & Quingyao et al., 1994 \\
23 & 48603.1452 &   9586.0 & $-$0.0044 & pe  & Quingyao et al., 1994 \\
24 & 48652.3420 &   9704.0 & $-$0.0037 & CCD & Paschke, 1992 \\
25 & 49698.3920 &  11213.0 &  0.0041 & CCD & Paschke, 1995 \\
26 & 50096.6707 &  13168.5 & $-$0.0804 & pe  & Shengbang et al., 1996 \\
27 & 50099.5889 &  13175.5 & $-$0.0807 & pe  & Shengbang et al., 1996 \\
28 & 50114.2715 &  13210.5 &  0.0099 & CCD & Agerer, Huebscher, 1996 \\
29 & 50480.3220 &  14088.5 &  0.0081 & CCD & Paschke, 1997 \\
30 & 50485.3256 &  14100.5 &  0.0087 & CCD & Paschke, 1997 \\
\hline
\end{tabular}
\end{center}

\vskip 1cm

Explanations to the table: epochs and O$-$C residuals were calculated
with respect to the elements (7), method of observation is denoted by
abbreviations (pg = photographic, vis = visual, pe = classic
photoelectric (photomultiplier), CCD = CCD camera).

Remark: minima timings No. 26 and No. 27 have large deviation from the
preceding and following ones. The value of this deviation is close to
two hours and may have originated from incorrect transformation of
local time to universal time. An O$-$C diagram of BL Eri based on the
elements (7) is presented in Figure 1.

\IBVSfig{10cm}{4577-f1.ps}{O$-$C diagram of BL Eri}

There is a large gap between the first and the second O$-$C value but the
diagram is sufficient for evaluation of the period behaviour. It can be
seen that the general parabolic course suggested by Shengbang et al.
(1996) and Paschke (1997) is only a rough approximation. In reality,
there is one abrupt period increase by 0.46 second about JD 24 46 622
(July, 1986). Before and after this event the period remained constant.
Light elements for the corresponding time intervals are as follows:

\begin{equation}
Min.I = JD(hel)\;\; 24 44 606.5906 + 0.41691322 \times E \;\;\;  (1938-July, 1986)
\end{equation}

\begin{equation}
Min.I = JD(hel)\;\; 24 48 286.2880 + 0.41691855 \times E \;\;\;  (after July, 1986)
\end{equation}
These elements were derived from the minima timings Nos 1-3, 6, 7,
9-16, and Nos 21-30, respectively, with the use of the least squares
method. The values No. 26 and No. 27 were corrected by adding two
hours.

Now it is clear that the elements (2) have erroneous period value and
their use by Shengbang et al. (1996) prevented these authors from finding
out that their two minima timings are also in error. The linear elements
(4), (5), and (7) contain the period values that represent average values
for the two time intervals. They have never been valid. The elements (3)
are valid for the interval 1938-1986. For prediction of future minima
only the elements (9) should be used.

BL Eri is  interesting not only due to its period variation. It exhibits
also peculiar variations of the light curve. It belongs among a few
W UMa-stars which temporarily have flat (depressed) maxima that resemble
rather maxima of close detached binaries than maxima of contact systems
(cf. Yamasaki et al., 1988; Quingyao et al., 1994). There are also other
signs of non-contact configuration of BL Eri (see e.g. Yamasaki et al.,
1988). Yamasaki et al. have shown that the spectral type
of BL Eri is approximately G0 IV-V and not B5 as stated in GCVS4. Thus
BL Eri may be important from the evolutionary point of view (as a link
between detached or semi-detached and contact systems) and the aim of
this note is also to support Mr. Paschke's call for further observation
of this star.

\vskip 1cm

\references

Agerer F., Huebscher, J., 1996, {\it Inform. Bull. Var. Stars}, No.\,4383

Kern J.R., Bookmyer B.B., 1986, {\it Inform. Bull. Var. Stars}, No.\,2850

Kholopov, P.N. et al., 1985$-$1987, {\it General Cat. of Variable Stars},
4th ed., Moscow

Locher K., 1978a, {\it BBSAG Bull.}, No. 36

Locher K., 1978b, {\it BBSAG Bull.}, No. 38

Locher K., 1979, {\it BBSAG Bull.}, No. 39

Paschke A., 1988a, {\it BBSAG Bull.}, No. 86

Paschke A., 1988b, {\it BBSAG Bull.}, No. 88

Paschke A., 1989, {\it BBSAG Bull.}, No. 91

Paschke A., 1991, {\it BBSAG Bull.}, No. 97

Paschke A., 1992, {\it BBSAG Bull.}, No. 100

Paschke A., 1995, {\it BBSAG Bull.}, No. 110

Paschke A., 1997, {\it BAV Rundbrief}, {\bf 46}, No.3, 100

Qingyao L. et al., 1996, {\it Astron. Astrophys., Suppl. Ser.}, {\bf 118}, 453

Quingyao L. et al., 1994, {\it Inform. Bull. Var. Stars}, No. 4104

Shengbang Q. et al., 1996, {\it Inform. Bull. Var. Stars}, No. 4388

Yamasaki A., Jugaku J., Seki M., 1988, {\it Astron. J.}, {\bf 95}, 894

\end{document}
