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\IBVShead{4325}{16 April 1996}

\centerline{\ft HAS THE DELTA SCUTI STAR AD CMi A COMPANION?}
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\begintext

AD CMi is a $\delta$ Scuti type variable with an amplitude of 0.30 magnitude and
stable light curve. Jiang (1987) and Rodr\'{\i}guez et al. (1988)
published many observations and suggested an increasing period change.
Rodr\'{\i}guez et al. (1990) and Yang et al. (1992) reported some
new times of light maxima, with the linear and quadratic solutions.

To check how the star's period varies with time, the authors observed AD CMi
again in three nights, from 15 to 17 February, 1994, in Yunnan Astronomical
Observatory. The telescope used is a 1 meter reflector with a conventional
single-channel photoelectric photometer plus a Johnson V filter. From the
new observational data, three new maximum times of AD CMi were determined.
Table 1 lists all the times of light maxima collected from the literature and
derived from our new observations. For all the data, the linear fit is used
to determine the calculated times of light maxima,
$ T_{max}=T_{01}+P_{01}\times E $. The results of fitting
are: $T_{01}=$ HJD $2436601.8210$, $P_{01}= 0.12297449$ $days$. And the
$(O-C)_{l}$ are listed in table 1. Then a
parabolic curve is used to fit the data as:  $ T_{max}=T_{02}+P_{02} \times
E + 0.5 \beta \times E^{2} $. Thus, we got the fitting parameters as: $T_{02}=$
HJD\,$2436601.8223$ $days$, $P_{02}=0.12297433$ $days$, $\beta=1.7 \times
10^{-12}$ $days/cycle$. Figure 1 shows the $O-C$ diagram and the fit curve
using the parabolic function.

Because many groups of data point distribute above or below the fit curve
in Figure 1, which seems to suggest that there is a trigonometric function
type variation, we tried to use the following formula
to fit the individual maxima, $ T_{max}=T_{03}+P_{03} \times  E + 0.5
\beta \times E^{2} +A \sin \varphi + B \cos \varphi $. The last two terms
correspond to possible light-time effect caused by the orbital motion,
whereas $\varphi$ is the solution of the equation: $\varphi - e \sin \varphi =
2 \pi f ( P_{03} \times E - \tau )$, in which
$e$ is the eccentricity of the elliptical orbit; $f$, the orbital
frequency; $\tau$ , the time of periastron. Figure 2 shows the derived
$O-C$ residuals and the fit curve using both the parabolic and the
trigonometric function. The related parameters thus obtained are as below:

\normalsize
\begin{center}
\begin{tabular}{cccccccc}
\hline
~~T$_{03}$(HJD)~~&P$_{03}$(days)&$\beta$(day/cycle)&A(days)&B(days)&
$f$(day$^{-1}$)&$e$&res(days)\\
\hline
2436601.8203&0.12297446&4.6$\times$10$^{-13}$&0.0010&0.0026&
0.0000912&0.5898&2.6$\times$10$^{-3}$\\
\hline
\end{tabular}
\end{center}
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\centerline{2}
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\centerline{Figure 1. The O$-$C diagram and the fit curve using the
parabolic function}
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\begin{center}
Figure 2. The O$-$C diagram and the fit curve using the parabolic
function and the trigonometric function
\end{center}
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Based on the fit above, the authors tend to think that the model of explaining
the discrepancies between the observed and calculated times of maximum light
as the consequence of a continuously changing (increasing) period, combined
with the light-time effect caused by the orbital motion of AD CMi around the
mass center of a binary system with an unseen companion, is reasonable.
The orbital period here obtained is about 30.0 years. The rate
of the period change, $\beta$, is now in agreement with the forecast of the
stellar evolution theory, both in the direction of the period changes
(increase) and the value of the  rate of change ($\sim  0.46 \times 10^{-12}$
day/cycle). However, we should mention that due to the limitation of
the number of data points, the solution provided here corresponds to that with
the smallest residual among many possible solutions with different parameter
values. It is necessary to obtain more observations, especially radial
velocity information, to check our new model and determine the parameters
in the end.

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\centerline{3}
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\centerline{Table 1. Times of light maxima of AD CMi}
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\tabcolsep 1.35mm
\begin{tabular}{|r|rcrcc||r|rcrcc|}
\hline
$i$~ & ~~E$_{i}$~~ & T$_{i}$ & (O$-$C)$_{l}$ & W & Ref & $i$~ & ~~E$_{i}$~~
& T$_{i}$ & (O-C)$_{l}$ & W & Ref\\
\hline
1&0 & 36601.8228 & 0.0018 & 1.0 & Ab&24&74574 & 45772.5187 & $-$0.0019 & 1.0& R8\\
2&8 & 36602.8066 & 0.0018 & 1.0& Ab&25&79818 & 46417.3991 &  0.0003 & 0.5& Ji\\
3&9 & 36602.9296 & 0.0018 & 1.0& Ab&26&79825 & 46418.2596 & $-$0.0001 & 2.0& Ji\\
4&25& 36604.8971 & 0.0017 & 1.0& Ab&27&79826 & 46418.3825 & $-$0.0001 & 2.0& Ji\\
5&211 & 36627.7700 & 0.0014 & 1.0& Ab&28&79833 & 46419.2434 & $-$0.0001 & 2.0& Ji\\
6&219 & 36628.7538 & 0.0014 & 1.0& Ab&29&79834 & 46419.3663 & $-$0.0001 & 2.0& Ji\\
7&227 & 36629.7373 & 0.0011 & 1.0& Ab&30&80027 & 46443.1010 & 0.0005 & 1.0& Ji\\
8&228 & 36629.8602 & 0.0010 & 1.0& Ab&31&80028 & 46443.2243 & 0.0008 & 2.0& Ji\\
9&2683& 36931.7620 & 0.0004 & 1.0& An&32&80029 & 46443.3470 & 0.0005 & 2.0& Ji\\
10&2691 & 36932.7470 & 0.0016 & 1.0& An&33&80035 & 46444.0850 & 0.0007 & 1.0& Ji\\
11&2708 & 36934.8364 & 0.0005 & 1.0& An&34&80036 & 46444.2082 & 0.0009 & 2.0& Ji\\
12&2992 & 36969.7620 & 0.0013 & 1.0& An&35&80037 & 46444.3312 & 0.0009 & 2.0& Ji\\
13&35852 & 41010.6985 & $-$0.0039 & 0.5& La&36&86340 & 47219.4395 & 0.0010 & 2.0& R9\\
14&47389 & 42429.4582 & $-$0.0009 & 0.1& Ep&37&86340 & 47220.4228 & 0.0005 & 2.0& R9\\
15&53512 & 43182.4290 & $-$0.0029 & 2.0& Ba&38&97999 & 48653.2017 & 0.0037 & 1.0& Ya\\
16&56390& 43536.3488 & $-$0.0037 & 2.0& Ba&39&98023 & 48656.1511 & 0.0017 & 2.0& Ya\\
17&56391 & 43536.4714 & $-$0.0041 & 2.0& Ba&40&98024 & 48656.2762 & 0.0038 & 2.0& Ya\\
18&65406 & 44645.0877 & $-$0.0028 & 2.0& Ji&41&98486 & 48713.0884 & 0.0018 & 1.0& Ya\\
19&74524 & 45766.3713 & $-$0.0006 & 1.0& R8&42&98494 & 48714.0724 & 0.0020 & 1.0& Ya\\
20&74540& 45768.3377 & $-$0.0018& 1.0& R8&43&98518& 48717.0242 & 0.0024 & 1.0& Ya\\
21&74541 & 45768.4606 & $-$0.0019 & 1.0& R8&44&104065 & 49399.1625 & 0.0012 & 2.0& pp\\
22&74565 & 45771.4134 & $-$0.0004 & 1.0& R8&45&104073 & 49400.1462 & 0.0011 & 2.0& pp\\
23&74573 & 45772.3961 & $-$0.0015 & 1.0& R8&46&104081 & 49401.1320 & 0.0031 & 1.0& pp\\
\hline
\end{tabular}

\normalsize
\begin{tabular}{cl}
~*Ab &~Abhyankar, K.D., 1959, {\it Ap.J.}, {\bf 130}, 834\\
~*An &~Anderson, L.R., McNamara, D.H., 1961, {\it Publ. Astr. Soc. Pacific}, {\bf 94}, 289\\
~*La &~Langford, W.R., 1976, Ph. Thesis, Brigham Young University\\
~*Ep &~Epstein, I., Epstein, A.E.A., 1973, {\it A.J.}, {\bf 78}, 83\\
~*Ba &~Balona, L.A., Stobie, R.S., 1983, {\it South African  Astron. Obs.}, {\bf 7}, 19\\
~*Ji &~Jiang, S.Y., 1987, {\it Chin. Astron. Astrophys.}, {\bf 11}, 343\\
~*R8 &~Rodr\'{\i}guez, E., Rolland, A., L\'opez de Coca,  P., 1988, {\it Rev. Mex. Astron.  Astrofis.}, {\bf 16}, 7\\
~*R9 &~Rodr\'{\i}guez, E., Rolland, A., L\'opez de Coca, P., 1990, {\it IBVS}, No.\,3427\\
~*Ya &~Yang, D.W., Tang, Q.Q., and Jiang, S.Y., 1992, {\it IBVS}, No.\, 3770\\
~*pp &~ present paper\\
\end{tabular}
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This work was supported by the Natural Science Foundation of China and
JiangXi Province.
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\beginauthors
\authorsrightcol
FU JIAN-NING$^{1,2}$ 
JIANG SHI-YANG$^{1}$
\endauthors
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$^{1}$Beijing Astronomical Observatory, Chinese Academy of Sciences,
Beijing 100080,

China

$^{2}$Department of Physics, Nanchang University, Nanchang 330047, China

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\references

Jiang, S.Y., 1987, {\it Chin. Astron. Astrophys.}, {\bf 11}, 343

Rodr\'{\i}guez, E., Rolland, A., L\'opez de Coca, P., 1988, {\it Rev. Mex.  Astron. Astrofis.}, {\bf 16}, 7

Rodr\'{\i}guez, E., Rolland, A., L\'opez de Coca, P., 1990,
{\it IBVS}, No.\,3427

Yang, D.W., Tang, Q.Q., and Jiang S.Y., 1992, {\it IBVS}, No.\,3770

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