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\begin{document}

\IBVShead{5774}{31 May 2007}

\IBVStitle{AD CM\lowercase{i}} 

\IBVSauth{Hurta, Zs.$^{1,2}$; P\'ocs, M.D.$^2$; Szeidl, B.$^2$}

\IBVSinst{E\"otv\"os Lor\'and University, Department of Astronomy, P.O.
Box 32, H-1518 Budapest, Hungary; e-mail: zhurta@gmail.com}

\IBVSinst{Konkoly Observatory of the Hungarian Academy of Sciences, P.O.
Box 67, H-1525 Budapest, Hungary; e-mail: pocs@konkoly.hu, szeidl@konkoly.hu}

\SIMBADobj{AD CMi}
\GCVSobj{AD CMi}

\IBVStyp{RRab}
\IBVSkey{Variable stars}
\IBVSabs{CCD BVIc observations of AD CMi are presented}

\begintext

The variability of AD CMi was discovered by Hoffmeister (1934). Abhyankar (1959) observed the
star during five nights in 1959 and showed the star to be a short period pulsating variable
with a period of 0.12297 day.

Since the correct identification of the type of variability of AD CMi a great number of
photoelectric and CCD observations have been obtained by different observers and more than
seventy times of maximum light are given in the literature (Abhyankar, 1959; Agerer \&
H\"ubscher, 1997, 1998, 2000, 2003; Agerer et al., 2001; Anderson \& McNamara, 1960; Balona \&
Stobie, 1983; Breger, 1975; Burchi et al., 1993; Epstein \& Epstein, 1973; Fu \& Jiang, 1996;
H\"ubscher, 2005; H\"ubscher et al., 1994; Jiang, 1987; Klingenberg et al., 2006; Langford,
1976; Rodr\'{\i}guez et al., 1988, 1990; Yang et al., 1992). The period change of AD CMi was
studied by Jiang (1987), Rodr\'{\i}guez et al.\ (1988, 1990), Yang et al.\ (1992) and Fu \&
Jiang (1996). Fu \& Jiang remarked that the groups of data points distributed above and below
the parabolic fit curve which seemed to suggest a trigonometric function type period
variation. They came to the conclusion that light time effect caused by orbital motion might
explain the sine like variation and deduced a period of $P_B = 10965$ days $\approx 30$ years
and eccentricity $e = 0.59$ of the elliptical orbital motion and a rate of increase in the
pulsation period $(1/P)(dP/dt) = 1.1\times10^{-8}~{\rm yr}^{-1}$.

Radial velocity measurements could give further evidence for binary nature. Abhyankar (1959)
and Balona \& Stobie (1983) published radial velocity curves of AD CMi. Abhyankar (1959) gave
mean radial velocity of the star as 34.5 km/s, while from the radial velocity data of Balona
\& Stobie (1983) obtained in 1977 and 1978 Rodr\'{\i}guez et al.\ (1988) deduced a mean value
of 38.8 km/s. Recently, Derekas et al.\ (2006) reported new radial velocity measurements and
deduced 35 km/s for the mean radial velocity of AD CMi.

During the past thirty-five years AD CMi was observed with the different instruments of the
Konkoly Observatory on 11 nights. Different combination of the $UBVR_CI_C$ filters were used.
Throughout the photoelectric observations the comparison star was GSC 00181-00490 (except for
the nights 2453451 and 2453452 when GSC 00184-00604 was used) while for the CCD photometry the
comparison star was GSC 00181-00708. All the photometric observations are given electronically
through the IBVS website as files 5774-t3.txt, 5774-t4.txt, 5774-t5.txt, 5774-t6.txt and
5774-t7.txt.
\IBVSedata{5774-t3.txt}
\IBVSdataKey{5774-t3.txt}{AD CMi}{light curve}
\IBVSedata{5774-t4.txt}
\IBVSdataKey{5774-t4.txt}{AD CMi}{light curve}
\IBVSedata{5774-t5.txt}
\IBVSdataKey{5774-t5.txt}{AD CMi}{light curve}
\IBVSedata{5774-t6.txt}
\IBVSdataKey{5774-t6.txt}{AD CMi}{light curve}
\IBVSedata{5774-t7.txt}
\IBVSdataKey{5774-t7.txt}{AD CMi}{light curve}

On the whole 10 times of maximum light (Table~1) could be determined from our observations.
Each light maximum was derived as an average over the $B$ and $V$ bands since the times of
maximum for these colour bands are not perceptibly shifted to each other. The typical error of
maximum times derived from our observations is about 1 minute.

\begin{table}
\normalsize
\centerline{Table 1. Observations at Konkoly Observatory}
\begin{center}
\vskip 4mm
\begin{tabular}{clcc}
\hline
times of maximum & telescope & detector & observation \\
HJD 2400000+ &  &  & duration \\
\hline
41681.5258 & 50-cm Cassegrain & pe & $.4537-.5860$ \\
41682.5090 & 50-cm Cassegrain & pe & $.4589-.5277$ \\
42461.4291 & 60-cm Newton & pe & $.3485-.4492$ \\
43572.3810 & 60-cm Newton & pe & $.3480-.3838$ \\
43936.2635 & 60-cm Newton & pe & $.2658-.3322$ \\
46775.6235 & 1-m RCC & pe & $.5159-.6498$ \\
48254.5171 & 1-m RCC & pe & $.4410-.6281$ \\
53452.2795 & 1-m RCC & pe & $.2673-.3880$ \\
54165.2862 & 60-cm Newton & CCD & $.2343-.4510$ \\
54172.2961 & 60-cm Newton & CCD & $.2343-.4186$ \\
\hline
\end{tabular}
\end{center}
\end{table}

From the ASAS (Pojmanski, 2005) and NSVS (Wo\'zniak et al., 2004) datasets normal maxima were
derived through third order Fourier fits (The NSVS observations have been subject to
heliocentric correction).

The Hipparcos database provides one useful time of maximum light. Since heliocentric
corrections have not been applied to these data we determined a new epoch of maximum taking
the heliocentric correction into account.

Kilambi \& Rahman (1993) and Kim \& Joner (1994) published photometry of AD CMi, which made
the determination of ten further times of maximum light possible.

All the published and newly determined times of maximum light are given in Table~2 (available
only in the electronic version on the IBVS website as 5774-t2.txt.)
\IBVSedata{5774-t2.txt}
\IBVSdataKey{5774-t2.txt}{AD CMi}{maxima times}
The $O-C$ values have been calculated by the formula:
 $$
 C = {\rm J.D.}~2436601.82736 + 0\fday12297451 \times E.
 $$
 We attempted to fit the $O-C$ diagram by the sum of a quadratic and a trigonometric function,
assuming that the $O-C$ diagram is a product of a slow linear period change and light time
effect caused by binary motion:
 $$
 O-C = a + bE + cE^2 + A\sin\varphi + B\cos\varphi.
 $$ 
 $\varphi$ is the solution of the Kepler equation:
 $$\varphi - e \sin\varphi = 2\pi P_{\rm orb}^{-1}(PE - T)$$
 where $e$ is the eccentricity, $T$ the time of the periastron of the assumed elliptical orbit 
and $P_{\rm orb}$ is the orbiting period. The deduced parameters are:
 $$a=-0.00002\pm0.00018, \qquad  b=(-2.95\pm0.02)\times10^{-7}, \qquad c =
(1.93\pm0.03)\times10^{-12},$$
 $$A=-0.00440\pm0.00012,\qquad B=0.00056\pm0.00042, \qquad e=0.71\pm0.05,$$
 $$P_{\rm orb}=15660\pm300, \qquad T=13870\pm150.$$
Figure~1 shows the $O-C$ diagram fitted by the above formula.

\IBVSfig{10.0cm}{5774-f1.ps}{$O-C$ diagram of AD CMi}
 \IBVSfigKey{5774-f1.ps}{AD CMi}{O-C diagram}

\IBVSfig{10.0cm}{5774-f2.ps}{$O-C$ diagram of AD CMi after the subtraction of the quadratic
function. The arrows indicate when radial velocity data were obtained}
 \IBVSfigKey{5774-f2.ps}{AD CMi}{O-C diagram}

\vspace{-24pt}
After subtracting the quadratic function the $O-C$ residual is presented in Figure~2 fitted
only with the trigonometric term. The satisfactory approximation indicates that the $O-C$
diagram of AD CMi can be interpreted by a slow increase in the pulsation period with a rate of
$(1/P)(dP/dt) = (9.32\pm0.11)\times10^{-8}~{\rm yr}^{-1}$ and by the light time effect caused
by binary motion on an elliptical orbit with orbiting period $P_{\rm orb} = 42.88\pm0.83$~yr,
eccentricity $e = 0.71\pm0.05$, projected semi major axis $a\sin i = 1.092\pm0.080$~AU and
the longitude of the periastron passage $\omega = 175\deg\pm4\deg$.

The slow increase in the pulsation period is in accord with evolutionary theories (Breger \&
Pamyatnykh, 1998).

The spectroscopic observations did not show any sign of a companion, therefore on the one hand
an upper limit can be given for the mass of the companion, on the other hand the mass function
provides a lower limit. The mass function is $f(M) \approx 7.2\times10^{-4}\ M_\odot$. If we
assume that the mass of AD CMi is around $2\ M_\odot$, the mass of the companion should be
between $0.15$ and $1\ M_\odot$. For the radial velocity (semi) amplitude $K \approx 1.1$~km/s can be
deduced. This value is not in conflict with the radial velocity data.

The authors express their gratitude to Dr.~Johanna Jurcsik for her assistance. The financial
support of OTKA grants T-046207 and T-048961 is acknowledged.

\references

Abhyankar, K.D., 1959, {\it ApJ}, {\bf 130}, 834

Agerer, F., H\"ubscher, J., 1997, {\it IBVS}, No.\ 4472

Agerer, F., H\"ubscher, J., 1998, {\it IBVS}, No.\ 4562

Agerer, F., H\"ubscher, J., 2000, {\it IBVS}, No.\ 4912

Agerer, F., H\"ubscher, J., 2003, {\it IBVS}, No.\ 5485

Agerer, F., Dahm, M., H\"ubscher, J., 2001, {\it IBVS}, No.\ 5017

Anderson, L.R., McNamara, D.H., 1960, {\it PASP}, {\bf 72}, 506

Balona, L.A., Stobie, R.S., 1983, {\it South African Astron.\ Obs.\ Circ.}, {\bf 7}, 19

Breger, M., 1975, {\it ApJ}, {\bf 201}, 653

Breger, M., Pamyatnykh, A.A., 1998, {\it A\&A}, {\bf 332}, 958

Burchi, R., de Santis, R., di Paolantonio, A., Piersimoni, A.M., 1993, {\it A\&AS}, {\bf
97}, 827

Derekas, A., Kiss, L.L., Cs\'ak, B., et al., 2006, {\it MmSAI}, {\bf 77}, 517

Epstein, J., Epstein, A.E.A., 1973, {\it AJ}, {\bf 78}, 83

ESA, 1997, {\it The Hipparcos and Tycho Catalogues}, ESA SP-1200

Fu, J.N., Jiang, S.Y. 1996, {\it IBVS}, No.\ 4325

Hoffmeister, C., 1934, {\it AN}, {\bf 253}, 195

H\"ubscher, J., 2005, {\it IBVS}, No.\ 5643

H\"ubscher, J., Agerer, F., Frank, P., Wunder, E., 1994, {\it BAV Mitt.}, No.\ 68

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

Kilambi, G.C., Rahman, A., 1993, {\it Bull. Astr. Soc. India}, {\bf 21}, 47

Kim, C., Joner, M.D., 1994, {\it Ap\&SS}, {\bf 218}, 113

Klingenberg, G., Dvorak, S.W., Roberts, C.W., 2006, {\it IBVS}, No.\ 5701

Langford, W.R., 1976, {\it Ph.\ Thesis}, Brigham Young Univ.

Pojmanski, G., 2005, {\it Acta Astr.}, {\bf 55}, 275

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

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

Wo\'zniak, P.R., Vestrand, W.T., Akerlof, C.W., et al., 2004, {\it AJ}, {\bf 127}, 2436

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

\endreferences

\end{document}
