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\begin{document}
\IBVShead{5967}{25 January 2011}

\IBVStitle{New Multicolour CCD Photometric Analysis of BI CM\lowercase{i}}


\IBVSauth{LIAKOS, A.; NIARCHOS, P.}

\IBVSinsto{Department of Astrophysics, Astronomy and Mechanics,
University of Athens, GR 157 84, Zografos,\\ Athens, Hellas,
e-mail: alliakos@phys.uoa.gr, pniarcho@phys.uoa.gr}


\SIMBADobjAlias{BI CMi}{HD 66853}

\IBVStyp{ DSCT }

\IBVSkey{CCD photometry, oscillating variables, frequency
analysis}

\IBVSabs{A new frequency analysis of the delta Sct type pulsating star}
\IBVSabs{BI CMi is presented.}
\IBVSabs{The multicoloured data are analysed with the PERIOD04 software.}
\IBVSabs{The results are compared with ones of other studies.}


\begintext


BI CMi (=HD 56167) was discovered as a $\delta$ Sct type pulsator
by Kurpinska-Winiarska~et al. (1988), with a period of
$\sim$0.1194660 days, a $V_{mag}$ of 9.279, and a $B-V$ index of
0.359. Mantegazza \& Poretti (1994) performed a frequency analysis
on their photoelectric data and resulted in 10 pulsation modes.
The most complete study of the star was made by Breger et al.
(2002) who included the star into a multisite photometric and
spectroscopic campaign. They found 29 pulsation frequencies in the
data of two observing seasons, calculated its rotational velocity
and proposed a spectral type of F2.

The observations of the star were made at the Gerostathopoulion
Observatory of the University of Athens, from January to March
2010 for 9 nights in a time span of 45 days, with a 20-cm
Newtonian reflector telescope (f/5) and the ST-8XMEI CCD equipped
with the Bessel B, V, R, I photometric filters. The differential
photometry method was applied to the data using the software
\emph{MuniWin} v.1.1.26 (Hroch, 1998). TYC~194-498-1
($V_{mag}=10.293$ and $B-V=0.379$ mag) and TYC~194-292-1
($V_{mag}=10.604$ and $B-V=0.503$) were used as comparison and check
stars, respectively. In this study, although the amount of data is
less than the ones in the studies of Mantegazza \& Poretti (1994)
and Breger et al. (2002), we present for the first time 4-band
photometry of the star based completely on CCD observations. In
Fig. 1 the data of all nights in $B$-filter are illustrated.

\IBVSfig{10cm}{5967-f1.eps}{The observed light curves of BI CMi in
$B$-filter.} 
\IBVSfigKey{5967-f1.eps}{BI CMi}{light curve}

\vspace*{-0.4cm}

The frequency analysis was made with the software \emph{PERIOD04}
v.1.2 which is based on the classical Fourier analysis (Lenz \&
Breger, 2005). Since our data cover less time span than the ones of
Mantegazza \& Poretti (1994) and Breger et al. (2002) we tried to
find a solution based on their results. Initially, we performed
frequency-search of all the available observational points in the
interval from 8 to 9 c/d in order to detect the frequency
$f_1\sim$8.25 c/d reported as the dominant one by the previous
authors. The latter, after the removal of this frequency, we
continued to search for another ones in the interval 5-80 c/d
(typical range for $\delta~Scuti$ stars; Breger, 2000). In
addition, we searched for frequencies in the range 0-1 c/d, which
potentially could be caused from atmospheric reasons or
observational drifts. These frequencies are indicated as f* in
Table 1. After the first frequency computation, the residuals were
subsequently prewhitened for the next one. The calculations
stopped when the detected frequency had a signal-to-noise~ratio~$\sim$4 and its amplitude reached our magnitude error limit
($\sim$4.5 mmag in $B$ and $V$ and $\sim$5~mmag in $R$ and $I$ filters).
The results of the frequency search for all filters are given in
Table 1, where we list: the identification number of the frequency
(\emph{No}), the frequency (\emph{F}) value, its corresponding
amplitude (\emph{A}) and phase ($\Phi$) and the signal-to-noise
ratio (\emph{S/N}) after prewhitening for the previous
frequency(ies). The sum of the squared residuals ($\chi^{2}$)
derived from a multi-parameter least-squares fit of sinusoidal
functions, is also given for each case. The Fourier fits on the
observational points for the longest (data) sets of observations
are presented in Figs 2 and 3, respectively, and the frequency spectra for $B$-filter is plotted in Fig. 4. \\



\IBVS2fig{7.5cm}{5967-f2.eps}{The Fourier fit on the B data.}{5967-f3.eps}{The Fourier fit on the V data.}
\IBVSfigKey{5967-f2.eps}{BI CMi}{fitted light curve}
\IBVSfigKey{5967-f3.eps}{BI CMi}{fitted light curve}

\IBVSfig{8.5cm}{5967-f4.eps}{The periodogram in B-filter after the
removal of $f_1$, where the detected frequencies are
indicated.} 
\IBVSfigKey{5967-f4.eps}{BI CMi}{periodogram}

\begin{table}[!hr]
\centerline{Table 1. The pulsational frequencies of BI CMi for all
filters} \vskip 3mm
\begin{center}
\begin{tabular}{ c | c c c c | c c c c}

\hline
        &         \multicolumn{4}{c}{\textbf{B-filter}}       &        \multicolumn{4}{c}{\textbf{V-filter}}            \\
\hline
 $No$   &  \textbf{F}  & \textbf{A}&\textbf{$\Phi$}&\textbf{S/N}&\textbf{F} & \textbf{A}&\textbf{$\Phi$}&\textbf{S/N}   \\
        &     [c/d]    &   [mmag]  &      [deg]    &            &  [c/d]    &   [mmag]  &      [deg]    &               \\
\hline
$f_{1}$ &   8.2476(3)  &   33.5(6) &       335(1)  &   29.0     & 8.2464(4) &  23.3(7)  &      336(2)   &   12.0        \\
$f_{2}$ &   8.8675(3)  &   26.2(6) &       130(1)  &   20.5     & 8.8654(4) &  22.3(7)  &      147(2)   &   12.3        \\
$f_{3}$ &   10.4391(7) &   11.3(6) &       230(3)  &   5.7      &10.4358(11)&   7.3(7)  &      238(2)   &   4.8         \\
$f_{4}$ &   7.3966(7)  &   10.0(6) &        54(3)  &   7.6      & 7.4452(14)&   6.0(7)  &      345(5)   &   3.8         \\
$f_{5}$ &   5.6487(9)  &   7.9(6)  &       220(4)  &   4.2      &           &           &               &               \\
$f^{*}$ &   0.7579(3)  &   27.5(6) &       92(1)   &   5.8      & 0.2468(4) &  22.3(7)  &      285(6)   &   4.0         \\
\hline
$\chi^{2}$&              \multicolumn{4}{c}{0.017}              &                 \multicolumn{4}{c}{0.018}             \\
\hline
        &         \multicolumn{4}{c}{\textbf{R-filter}}         &          \multicolumn{4}{c}{\textbf{I-filter}}        \\
\hline
$f_{1}$ &   8.2463(6)  &   15.7(8) &       324(3)  &   12.0     & 8.2481(6) &  15.7(7)  &      317(3)   &   13.8        \\
$f_{2}$ &   8.8663(6)  &   16.6(8) &       136(3)  &   12.3     & 8.8669(7) &  16.6(7)  &      147(3)   &   12.5        \\
$f_{3}$ &   10.4343(18)&    5.4(8) &       254(8)  &   3.8      &10.4380(12)&   8.7(7)  &      227(6)   &   5.2         \\
$f_{4}$ &   7.3728(11) &    8.7(8) &        34(5)  &   4.8      & 7.3989(15)&   5.4(7)  &      11(7)    &   4.4         \\
$f^{*}$ &   0.6358(4)  &   22.9(8) &       249(2)  &   3.8      & 0.0581(6) &  22.9(7)  &      84(3)    &   3.9         \\
\hline
$\chi^{2}$&              \multicolumn{4}{c}{0.021}              &               \multicolumn{4}{c}{0.019}               \\
\hline

\end{tabular}
\end{center}
\end{table}

\vspace*{-1cm}

The multifilter photometry helps us to verify which of the
detected frequencies are physically originated, since they should
be present in all filter observations. By this method, frequencies
having a S/N$>$4 but not detected in all filter data, can be
easily distinguished and characterized as observational errors
(the lower ones) or residuals from a previous detected frequency
after prewhitening (values close to the already detected ones). In
the present work five pulsation frequencies in $B$-filter were found
for BI CMi. The first four of them were also detected in $V$, $R$ and
$I$ filter data. The Amplitude of the frequencies, as it is expected
from the spectral type of the star, is decreasing from $B$ to $I$
filter. The current frequencies $f_1$, $f_2$ and $f_4$ were also
detected by Mantegazza \& Poretti (1994) and Breger et al. (2002).
Our $f_3$ value is the almost the same with the $f_5$ (and $f_6$
as a close component) found by Breger et al. (2002). The frequency
$f_5$ in the $B$-data was not detected by the other authors, while
its signature was not traced also in the other filter data, a fact
that creates uncertainty for its real existence. \\
Another solution could be achieved if one does not confine the
initial search between 8-9 c/d, and search directly in the
interval 5-80 c/d. The dominant frequency then is found to be
$\sim$9.09 c/d and the $f_3$=8.51 c/d of Breger et al. (2002)
(=$f_4$ of Mantegazza \& Poretti 1994) is also detected. A
different value for the dominant frequency was also found by
Kurpinska-Winiarska et al. (1988) as $f_1$=8.37 c/d. \\
Concluding, we preferred to present the current solution (Table 1)
as the most possible one, since the amount of data of the other
authors is larger, and their solution describes more or less very
well our data in all filters.



\references

Breger, M., 2000, {\it ASPC}, {\bf 210}, 3
%\BIBCODE{2000ASPC..210....3B}

Breger, M., Garrido, R., Handler, G. et al., 2002, {\it MNRAS}, {\bf 329}, 531 
%\BIBCODE{2002MNRAS.329..531B}

Hroch, F., 1998, {\it Proceedings of the 29th Conference on Variable Star Research}, {\bf 30} 
\BIBCODE{1998stel.conf...30H}

Kurpinska-Winiarska, M., Winiarski, M., Zola, S., 1988, {\it IBVS}, 3275, 1 
%\BIBCODE{1988IBVS.3275....1K}

Lenz, P., Breger, M. 2005, {\it CoAst}, {\bf 146}, 53
%\BIBCODE{2005CoAst.146...53L}

Mantegazza, L., Poretti, E., 1994, {\it A\&A}, {\bf 281}, 66
%\BIBCODE{1994A&A...281...66M}

\endreferences

\IBVSedata{5967-t2.txt}
\IBVSdataKey{5967-t2.txt}{BI CMi}{photometry}

\end{document}
