Apsidal motion and light a curve solution \\ for eighteen SMC eccentric eclipsing binaries
P. Zasche~\altaffilmark{1
{Aims: The Danish 1.54-meter telescope at the La Silla observatory was used for photometric monitoring of selected eccentric eclipsing binaries located in the Small Magellanic Cloud. The new times of minima were derived for these systems, which are needed for accurate determination of the apsidal motion. Moreover, many new times of minima were derived from the photometric databases OGLE and MACHO. Eighteen early-type eccentric-orbit eclipsing binaries %OGLE-SMC-ECL-0720, OGLE-SMC-ECL-0781, %OGLE-SMC-ECL-0888, OGLE-SMC-ECL-1001, OGLE-SMC-ECL-1298, OGLE-SMC-ECL-1407, OGLE-SMC-ECL-2186, %OGLE-SMC-ECL-2225, OGLE-SMC-ECL-2251, OGLE-SMC-ECL-2524, OGLE-SMC-ECL-2534, OGLE-SMC-ECL-3594, %OGLE-SMC-ECL-3677, OGLE-SMC-ECL-3951, OGLE-SMC-ECL-4955, OGLE-SMC-ECL-5233, OGLE-SMC-ECL-5422, and %OGLE-SMC-ECL-5434 were studied. {Methods: Their $O-C$\ diagrams of minima timings were analysed and the parameters of the apsidal motion were obtained. The light curves of these eighteen binaries were analysed using the program {\sc PHOEBE, giving the light curve parameters. For several systems the additional third light also was detected. {Results: We derived for the first time and significantly improved the relatively short periods of apsidal motion %of 28.8, 108.1, 39.9, 19.0, 25.5, 48.5, 70.5, 41.9, 47.6, 45.0, 63.3, 142.1, 98.7, 64.3, 114.4, 26.1, 99.4, and 38.1 from 19 to 142 years for these systems. %The internal structure constants log $k_2$ were computed, %but these are still affected by large errors due to missing spectroscopy of the stars. The relativistic effects are weak, up to 10\, \% of the total apsidal motion rate. For one system (OGLE-SMC-ECL-0888), the third-body hypothesis was also presented, which agrees with high value of the third light for this system detected during the light curve solution. {
Smc_zasche.tex
% Version 0: Feb 14, 2013
% Version 1: Mar, Apr 2013
%
\documentclass{emulateapj}
%\documentclass[referee]{aa}
%\usepackage{graphicx}
%\sloppy

\shorttitle{Apsidal motion and LC solution for 18 SMC eccentric EBs} \shortauthors{Zasche et al.}

\begin{document}

\title{\textbf{Apsidal motion and light a curve solution \\ for eighteen SMC eccentric eclipsing binaries}\thanks{Based on data collected with the Danish 1.54-m telescope at the ESO La Silla Observatory.
       Tables \ref{minima} are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via
       http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/ } }

\author{P. Zasche~\altaffilmark{1}
    \and M. Wolf~\altaffilmark{1}
    \and J. Vra\v{s}til~\altaffilmark{1}
    \and J. Li\v{s}ka~\altaffilmark{2}
    \and M. Skarka~\altaffilmark{2}
    \and M. Zejda~\altaffilmark{2} }

\email{zasche@sirrah.troja.mff.cuni.cz}

\affil{
 \altaffilmark{1} Astronomical Institute, Charles University in Prague, Faculty of Mathematics and Physics, \\
 CZ-180~00 Praha 8, V~Hole\v{s}ovi\v{c}k\'ach 2, Czech Republic\\
 \altaffilmark{2} Department of Theoretical Physics and Astrophysics, Masaryk University, Kotl\'a\v{r}sk\'a 2, 611 37 Brno, Czech Republic }

\date{Received \today}

\begin{abstract}
{Aims: The Danish 1.54-meter telescope at the La Silla observatory was used for photometric
monitoring of selected eccentric eclipsing binaries located in the Small Magellanic Cloud. The new
times of minima were derived for these systems, which are needed for accurate determination of the
apsidal motion. Moreover, many new times of minima were derived from the photometric databases OGLE
and MACHO. Eighteen early-type eccentric-orbit eclipsing binaries %OGLE-SMC-ECL-0720, OGLE-SMC-ECL-0781,
%OGLE-SMC-ECL-0888, OGLE-SMC-ECL-1001, OGLE-SMC-ECL-1298, OGLE-SMC-ECL-1407, OGLE-SMC-ECL-2186,
%OGLE-SMC-ECL-2225, OGLE-SMC-ECL-2251, OGLE-SMC-ECL-2524, OGLE-SMC-ECL-2534, OGLE-SMC-ECL-3594,
%OGLE-SMC-ECL-3677, OGLE-SMC-ECL-3951, OGLE-SMC-ECL-4955, OGLE-SMC-ECL-5233, OGLE-SMC-ECL-5422, and
%OGLE-SMC-ECL-5434
were studied. }

 {Methods: Their $O-C$\ diagrams of minima timings were analysed and the parameters
of the apsidal motion were obtained. The light curves of these eighteen binaries were analysed
using the program {\sc PHOEBE}, giving the light curve parameters. For several systems the
additional third light also was detected. }

 {Results: We derived for the first time and
significantly improved the relatively short periods of
apsidal motion %of 28.8, 108.1, 39.9, 19.0, 25.5, 48.5, 70.5, 41.9, 47.6, 45.0, 63.3, 142.1, 98.7, 64.3, 114.4, 26.1, 99.4, and 38.1
from 19 to 142 years for these systems. %The internal structure constants log $k_2$ were computed,
%but these are still affected by large errors due to missing spectroscopy of the stars.
The relativistic effects are weak, up to 10\, \% of the total apsidal motion rate. For one system
(OGLE-SMC-ECL-0888), the third-body hypothesis was also presented, which agrees with high value of
the third light for this system detected during the light curve solution.}
 {}
 \end{abstract}

  \keywords {stars: binaries: eclipsing -- stars: early-type %-- stars:
%individual: (\object{OGLE-SMC-ECL-0720}, \object{OGLE-SMC-ECL-0781}, \object{OGLE-SMC-ECL-0888},
%\object{OGLE-SMC-ECL-1001}, \object{OGLE-SMC-ECL-1298}, \object{OGLE-SMC-ECL-1407},
%\object{OGLE-SMC-ECL-2186}, \object{OGLE-SMC-ECL-2225}, \object{OGLE-SMC-ECL-2251},
%\object{OGLE-SMC-ECL-2524}, \object{OGLE-SMC-ECL-2534}, \object{OGLE-SMC-ECL-3594},
%\object{OGLE-SMC-ECL-3677}, \object{OGLE-SMC-ECL-3951}, \object{OGLE-SMC-ECL-4955},
%\object{OGLE-SMC-ECL-5233}, \object{OGLE-SMC-ECL-5422}, \object{OGLE-SMC-ECL-5434})
 -- stars:
fundamental parameters -- Magellanic Clouds}




\section{Introduction}

Other galaxies have become the most prominent battlefields in current astrophysical research,
mainly due to the large and long-lasting photometric surveys. These surveys like MACHO or OGLE have
discovered thousands of new eclipsing binaries in the Magellanic Clouds, hence, we know only about
twice more eclipsing binaries in our own Milky Way than in other galaxies (see
Pawlak et al. 2013, or Graczyk et al. 2011).                                                %   number of EBs: 26121 LMC, 6138 SMC, 11589 Gal.Disk, only OGLE! + KEPLER (cca 2000), atd.

On the other hand, the chemical composition of the Magellanic Clouds differs from that of the solar
neighborhood (e.g. Ribas 2004), and the study of the massive and metal-deficient stars in the SMC
checks our evolutionary models for these abundances. All eclipsing binaries analysed here have
properties that make them important astrophysical laboratories for studying the structure and
evolution of massive stars (Ribas 2004).

Eccentric eclipsing binaries (hereafter EEBs) with an apsidal motion can provide us with an
important observational test of theoretical models of stellar structure and evolution. A long-term
collection of the times of EEBs minima observed for several years throughout the apsidal motion
cycle and a consecutive detailed analysis of the period variations of EEB can be performed,
yielding both the orbital eccentricity and the period of rotation of the apsidal line with high
accuracy (Gim\'enez 1994). Many different sets of stellar evolution models have been published in
recent years, such as for Maeder (1999), or Claret (2005); however, to distinguish between them and
to test, which one is more suitable, it is still rather difficult. The internal structure
constants, as derived from the apsidal motion analysis, could serve as one independent criterion.
On the other hand, only stellar parameters for EEBs with an accuracy of 1\,\% can be used to
discriminate between the models.

Here, we analyse the observational data and rates of apsidal motion for eighteen SMC detached
eclipsing systems. All these systems are early-type objects, having eccentric orbits, which also
exhibits an apsidal motion. Similar studies of LMC EEBs have been presented by Michalska \&
Pigulski (2005), by Michalska (2007), and recently also by Zasche \& Wolf (2013). As far as we
know, only several eclipsing binaries with apsidal motion were analysed in SMC galaxy until now:
SC3 139376, SC5 311566 (Graczyk 2003), and nine other systems by North et al. (2010).



\section{Observations of minimum light}

Monitoring of faint EEBs in external galaxies became almost routine nowadays with quite moderate
telescopes of 1 - 2m class, which are equipped with a modern CCD camera. However, a large amount of
observing time is needed, which is usually unavailable at larger telescopes. During the last two
observational seasons, we have accumulated 2660 photometric observations and derived 29 precise
times of minimum light for selected eccentric systems. New CCD photometry was obtained at the La
Silla Observatory in Chile, where the 1.54-m Danish telescope (hereafter DK154) with the CCD camera
and \textit{R} filter was used (remotely from the Czech Republic).

All CCD measurements were reduced in a standard way using the bias frames and then the flat fields.
The comparison star was chosen to be close to the variable one and with similar spectral type. A
synthetic aperture photometry and astrometry software developed by M.~Velen and P.~Pravec {\sc
Aphot}, was routinely used for reducing the data. No correction for differential extinction was
applied because of the proximity of the comparison stars to the variable and the resulting
negligible differences in air mass and their similar spectral types.

The new times of primary and secondary minima and their respective errors were determined by the
classical Kwee-van Woerden (1956) method or by our new approach (see the section \ref{Method}). All
new times of minima are given in the appendix Tables \ref{minima}.


\section{Photometry and light curve modelling}

The core of our analysis lies on the huge photometric data sets, as obtained during the {\sc Macho}
(Faccioli et al. 2007), {\sc Ogle II} (Wyrzykowski et al. 2004), and {\sc Ogle III} (Graczyk et al.
2011) surveys. These photometric data were used both for minima time analysis and for light curve
analysis. The method of how the individual times of minima for the particular system were computed
is presented in section \ref{Method}. Our new observations obtained at the Danish 1.54-m telescope
were used only for deriving the times of minima for the selected targets.

The analysis of the light curves (hereafter LC) for the systems was carried out using the program
{\sc PHOEBE}, ver. 0.31a (Pr{\v s}a \& Zwitter 2005), which is based on the Wilson-Devinney
algorithm (Wilson \& Devinney 1971) and its later modifications, but some of the parameters have to
be fixed during the fitting process. The albedo coefficients $A_i$ remained fixed at value 1.0, the
gravity darkening coefficients $g_i = 1.0$. The limb darkening coefficients were interpolated from
the van Hamme�s tables (van Hamme 1993),  %. A problem arises with the synchronicity parameters ($F_i$) due to poor
%coverage of the RV data near the eclipses and low quality of the light curves used for the LC analysis, hence
and the synchronicity parameters ($F_i$) were also kept fixed at values of $F_i = 1$. The
temperature of the primary component was derived from the photometric indices or other sources (see
below). The problematic issue of the mass ratio was solved by fixing $q=1$ because no spectroscopy
for most of these selected systems exists, and for detached eclipsing binaries the LC solution is
almost insensitive to the photometric mass ratio (see e.g. Terrell \& Wilson 2005).


\section{Methods used for the analysis} \label{approach}

\subsection{Apsidal motion analysis}

For the analysis, we used the approach as presented below.

 \begin{enumerate}
   \item At the beginning, all of the available photometric data were analysed, resulting in a set
   of minima times. Preliminary apsidal motion parameters were derived (with the assumption $i=90^\circ$).\\[-1mm]

   \item Secondly, the eccentricity ($e$), argument of periastron ($\omega$), and apsidal motion
   rate ($\dot \omega$) that resulted from the apsidal motion analysis were used for the preliminary
   light curve analysis.\\[-1mm]

   \item As the third step, the inclination ($i$) from the LC analysis was used for the final apsidal motion
   analysis.\\[-1mm]

   \item Finally, the resulted $e$, $\omega$, and $\dot \omega$ values from the apsidal motion
   analysis were used for the final LC analysis.\\[-1mm]
 \end{enumerate}

Moreover, this simple approach was a bit complicated because the minima times were also derived
using the light curve template (see the AFP method in Section \ref{Method}). Hence, the LC solution
from step 2 allows us to derive the better times of minima for the step 3. The whole process run
iteratively until the changes are negligible (usually it was enough to run these four steps two
times).

%\section{Apsidal motion analysis}
%
%The motion of the apsis of an eclipsing binary star is a direct consequence of the finite size of
%its components. The rate of the apsidal motion is dependent on the internal structure of each
%component. Determination of the characteristics of a binary thus provides an observational test of
%the theory of stellar structure and evolution (see e.g. Claret \& Gim{\'e}nez 2010).

The \oc\ diagrams of all available times of minima were analysed using the method presented by
Gim\'enez \& Garc\'{\i}a-Pelayo (1983). This is a weighted least-squares iterative procedure,
including terms in the eccentricity up to the fifth order. There are five independent variables
$(T_0, P_s, e, \dot{\omega}, \omega_0)$ determined in this procedure. The periastron position
$\omega$ is given by the linear equation

\medskip
\noindent $ \omega = \omega_0 + \dot{\omega}\ E $,

\medskip
\noindent where $\dot{\omega}$ is the rate of periastron advance, $E$ is the epoch, and the
position of periastron for the zero epoch $T_0$ is denoted as $\omega_0$. The relation between the
sidereal and the anomalistic period, $P_s$ and $P_a$, is given by

\medskip
\noindent $ P_s = P_a \,(1 - \dot{\omega}/360^\circ) $

\medskip
\noindent and the period of apsidal motion by $ U = 360^\circ P_a/\dot{\omega} $.

All new precise CCD times of minima were used with a weight of 10 in our computation; some of our
less precise measurements were weighted by a factor of five, while the poorly covered minima were
given a weight of 1.


\subsection{Method of minima fitting} \label{Method}

We developed and routinely used a method for deriving the times of minima for selected stars
observed during the {\sc MACHO} and {\sc OGLE} surveys. This semi-automatic fitting procedure
(hereafter AFP) has harvested the fact that the number of data points obtained during these two
photometric surveys is large (typically thousands of data points) but obtained during many orbital
revolutions of the close pair (a so-called sparse photometry).

Therefore, we can construct the phased light curve of the eclipsing binary in different time
epochs. If the apsidal motion is prominent in the system, the shape of the light curve also
slightly varies between the different epochs.

The first step is to divide the whole data set of photometry into several different ``subsets'',
which are used for constructing the individual light curves. Then, we usually choose the data set
closest to the half of the time interval covered with observations and use these data points for
constructing the light curve to be analysed.

Then, this light curve is analysed using the {\sc PHOEBE} code, and the theoretical light curve
template is being constructed. This LC model is then being used for deriving the individual times
of minima easily by fitting this phased light curve to the phased light curves for the individual
data sets. The best fit is obtained with the simplex algorithm and the least squares fitting method
by only shifting the theoretical and observed light curve in two axis (phase and magnitude). If the
star has constant magnitude over the whole time range of our data, there is no need to fit the
magnitude shift, and only one free parameter is computed. When we find the best fit, then the times
of minima are computed easily according to the ephemerides for a particular data set. Of course,
for eccentric orbit binaries, both primary and secondary minima are being computed separately.

For the input, there are the data points, the time intervals, the ephemerides, and also parameters
of the method. These are the duration of eclipse (how large portion of the phase curve around
minima is being used for computing), minimum number of data points (if lower, the minimum is not
computed), and the depth of minima. If $1/5$ of the depth of minima is covered with data points,
then this particular minimum is being computed.

Hence, by using this technique, we can usually obtain both primary and secondary minima for each
data subset from an original photometry file. Moreover, this method can also be used in these
cases, where the minimum is covered only very poorly, or only a descent to the minimum is covered.
In these cases, the classical Kwee-van Woerden method would not work properly, so we can obtain
more useful data points. On the other hand, we would like to emphasize that the method is suitable
only for systems with low eccentricity, where the shape of the light curve is changing only
slightly. Otherwise, we have to construct a separate light curve template for each of the data
subset.

The whole method is graphically shown in Fig. \ref{MethodObr}, where an illustrative example of
OGLE-SMC-ECL-0720 is being presented. All of the derived times of minima are stored in the
online-only Tables \ref{minima}. There are also given the errors of individual minima times, which
are being computed also by AFP in the following way. The set of different solutions was computed
for a particular minimum with different parameters of the code (length of interval around each
minimum used for the analysis, number of data points according to their precision, etc.), yielding
a set of times of minima, which is usually more than 10. From these minima data set, an average and
its variance were computed,. The variance is then taken as an approximate error estimation for the
particular minimum.

\begin{figure}
 \includegraphics[width=0.48\textwidth]{Method.eps}
% \includegraphics[width=0.98\textwidth]{Method.eps}
 \caption[]{How the AFP method works.} \label{MethodObr}
\end{figure}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\begin{table*}[h!]
\caption{Relevant information for the analysed systems.}  \label{InfoSystems}  \scriptsize
\begin{tabular}{lcccccccccl}
   \hline\hline\noalign{\smallskip}
 System   & OGLE II$^{*}$ &  MACHO     &          RA           &             DE                              & $I_{\rm max}$ & $(B-V)$ & $(U-B)$ & $(B-V)_0$ & Sp.type$^{**}$ & Ref. \\
  \hline\noalign{\smallskip}
 $\#$0720 & SC3 139376 & 213.15620.12  & 00$^h$44$^m$08$^s$.67 & -73$^\circ$14$^\prime$18$^{\prime\prime}$.5 &  14$^{\rm m}\!\!.$47       &  -0.16  & -0.91   & -0.26     & B0(IV)       & 1 , 2      \\
 $\#$0781 & SC3 157218 & 212.15624.89  & 00$^h$44$^m$39$^s$.73 & -72$^\circ$59$^\prime$58$^{\prime\prime}$.5 &  17$^{\rm m}\!\!.$03       &  -0.10  & -0.78   & -0.23     & \emph{B2}    & 1          \\
 $\#$0888 & SC4 29231  & 212.15680.18  & 00$^h$45$^m$30$^s$.72 & -73$^\circ$03$^\prime$29$^{\prime\prime}$.7 &  15$^{\rm m}\!\!.$52       &  -0.09  & -0.82   & -0.25     & O9V          & 1 , 2      \\
 $\#$1001 &            & 208.15744.1836& 00$^h$46$^m$11$^s$.29 & -72$^\circ$35$^\prime$17$^{\prime\prime}$.3 &  18$^{\rm m}\!\!.$44       &  -0.31  & -0.58   & -0.12     & \emph{late B/early A} & 3 \\
 $\#$1298 & SC4 163754 & 212.15848.1258& 00$^h$47$^m$52$^s$.73 & -73$^\circ$16$^\prime$34$^{\prime\prime}$.0 &  17$^{\rm m}\!\!.$22       &  -0.04  & -0.89   & -0.29     & \emph{B0}    & 1          \\
 $\#$1407 &            & 208.15861.734 & 00$^h$48$^m$19$^s$.26 & -72$^\circ$21$^\prime$40$^{\prime\prime}$.2 &  17$^{\rm m}\!\!.$02       &  -0.04  & -0.67   & -0.21     & \emph{B3}    & 1          \\
 $\#$2186 & SC5 311566 & 208.16083.86  & 00$^h$51$^m$34$^s$.84 & -72$^\circ$45$^\prime$46$^{\prime\prime}$.4 &  16$^{\rm m}\!\!.$06       &  -0.04  & -0.79   & -0.25     & B0+B0-3      & 1 , 4      \\
 $\#$2225 & SC6 72782  & 208.16084.117 & 00$^h$51$^m$41$^s$.80 & -72$^\circ$41$^\prime$06$^{\prime\prime}$.1 &  16$^{\rm m}\!\!.$71       &  -0.128 &         & -0.22     & \emph{B3}    & 5 , 6      \\
 $\#$2251 & SC6 61418  &               & 00$^h$51$^m$46$^s$.64 & -72$^\circ$51$^\prime$21$^{\prime\prime}$.7 &  16$^{\rm m}\!\!.$23       &  -0.14  & -0.91   & -0.27     & \emph{B1}    & 1          \\
 $\#$2524 & SC6 158178 & 208.16141.60  & 00$^h$52$^m$42$^s$.32 & -72$^\circ$41$^\prime$27$^{\prime\prime}$.9 &  16$^{\rm m}\!\!.$53       &  -0.176 & -0.86   & -0.24     & \emph{B2}    & 3          \\
 $\#$2534 &            & 208.16147.22  & 00$^h$52$^m$43$^s$.85 & -72$^\circ$18$^\prime$08$^{\prime\prime}$.6 &  16$^{\rm m}\!\!.$57       &  -0.04  & -0.81   & -0.26     & \emph{B1}    & 1          \\ %Evans et al. (2004) published sp.type B0-5(IV)
 $\#$3594 & SC7 255621 & 207.16428.1423& 00$^h$57$^m$26$^s$.41 & -72$^\circ$36$^\prime$46$^{\prime\prime}$.2 &  16$^{\rm m}\!\!.$26       &  -0.21  & -0.72   & -0.19     & B1+B1-3      & 1 , 4      \\
 $\#$3677 & SC8 52815  & 207.16490.6   & 00$^h$57$^m$49$^s$.25 & -72$^\circ$16$^\prime$55$^{\prime\prime}$.7 &  15$^{\rm m}\!\!.$11       &  -0.16  & -0.84   & -0.24     & \emph{B2}    & 1 , 7      \\ %earlyB+earlyB from Bonanos et al. 2010
 $\#$3951 & SC8 160725 &               & 00$^h$59$^m$14$^s$.98 & -72$^\circ$11$^\prime$35$^{\prime\prime}$.3 &  15$^{\rm m}\!\!.$90       &  -0.18  & -0.84   & -0.24     & B1V          & 8 , 9      \\
 $\#$4955 & SC10 94636 & 206.16886.52  & 01$^h$04$^m$59$^s$.18 & -72$^\circ$25$^\prime$29$^{\prime\prime}$.3 &  17$^{\rm m}\!\!.$11       &  -0.16  & -0.68   & -0.19     & \emph{B3}    & 1          \\ %B0-5(V) dle Evans et al.(2004)
 $\#$5233 &            & 206.17061.14  & 01$^h$07$^m$12$^s$.54 & -72$^\circ$11$^\prime$42$^{\prime\prime}$.0 &  15$^{\rm m}\!\!.$34       &  -0.08  & -0.91   & -0.28     & \emph{B0}    & 1          \\
 $\#$5422 & SC11 111907& 206.17170.8   & 01$^h$08$^m$45$^s$.74 & -72$^\circ$31$^\prime$22$^{\prime\prime}$.4 &  14$^{\rm m}\!\!.$99       &  -0.22  & -0.93   & -0.26     & \emph{B1}    & 1          \\ %B0-5(II) dle Evans et al. (2004)
 $\#$5434 & SC11 118966& 206.17173.10  & 01$^h$08$^m$50$^s$.47 & -72$^\circ$17$^\prime$26$^{\prime\prime}$.1 &  15$^{\rm m}\!\!.$56       &  -0.11  & -0.86   & -0.26     & \emph{B1}    & 1          \\ %B1-5(III) dle Evans et al. (2004)
 \noalign{\smallskip}\hline
\end{tabular}
\scriptsize Note: [*] - The full name from OGLE II survey should be OGLE SMC-SCn nnnnnn, [**] -
Spectral types given in italics were only estimated from the photometric indices for the first time
in the present paper. References: [1] - Massey (2002), [2] - Evans et al. (2004), [3] - Zaritsky et
al. (2002), [4] - Hilditch et al. (2005), [5] - Udalski et al. (1998), [6] - Massey et al. (1995),
[7] - Bonanos et al. (2010), [8] - Massey et al. (1989), [9] - Massey et al. (2012).
\end{table*}



\begin{table*}[h!]
\caption{Light curve parameters for the analysed systems.} \label{LCparam} \tiny
\begin{tabular}{lcccccccccc}
  \hline\hline\noalign{\smallskip}
   System          &   $T_1$ [K]   &  $T_2$ [K]  &  $i$ [deg]   &  $\Omega_1$   &  $\Omega_2$   &  $L_1$ [\%]  &  $L_2$  [\%] & $L_3$ [\%] \\
  \hline\noalign{\smallskip}
 $\#$0720 & 31500 (fixed) & 31700 (400) & 84.57 (0.30) & 5.524 (0.061) & 7.356 (0.085) & 66.87 (0.83) & 33.13 (0.68) &  0 \\
 $\#$0781 & 23100 (fixed) & 16700 (300) & 85.08 (0.18) & 7.265 (0.086) & 8.690 (0.120) & 71.90 (1.25) & 28.10 (0.98) &  0 \\
 $\#$0888 & 33200 (fixed) & 38100 (1100)& 77.77 (0.38) & 6.119 (0.101) & 6.128 (0.112) & 22.01 (1.85) & 26.94 (3.46) & 51.05 (4.98) \\
 $\#$1001 & 11000 (fixed) &  9700 (500) & 79.13 (0.92) & 5.064 (0.204) & 6.661 (0.397) & 67.48 (1.37) & 32.52 (1.02) &  0 \\
 $\#$1298 & 30000 (fixed) & 19900 (700) & 74.68 (0.45) & 6.364 (0.138) & 6.701 (0.174) & 70.46 (1.32) & 29.54 (0.77) &  0 \\
 $\#$1407 & 19000 (fixed) & 19100 (700) & 75.60 (0.50) & 5.907 (0.147) & 6.833 (0.177) & 56.26 (1.06) & 39.10 (1.00) &  4.64 (1.87) \\
 $\#$2186 & 30100 (fixed) & 28500 (300) & 87.02 (0.22) & 6.843 (0.058) & 8.040 (0.097) & 62.73 (3.14) & 36.00 (1.25) &  4.03 (2.59) \\
 $\#$2225 & 11600 (fixed) &  7100 (200) & 80.33 (0.53) & 5.678 (0.100) &11.334 (0.490) & 60.98 (2.87) &  4.58 (0.57) & 34.45 (1.55) \\
 $\#$2251 & 26200 (fixed) & 30600 (900) & 79.62 (0.26) & 6.149 (0.080) &10.184 (0.184) & 48.35 (3.02) & 17.91 (1.26) & 33.73 (4.05) \\
 $\#$2524 & 23100 (fixed) & 24600 (600) & 83.32 (0.37) & 6.128 (0.085) & 7.165 (0.112) & 56.63 (1.26) & 41.53 (2.03) &  1.85 (5.76) \\
 $\#$2534 & 26200 (fixed) & 18300 (300) & 76.23 (0.28) & 5.690 (0.050) & 6.150 (0.052) & 61.67 (1.79) & 28.64 (1.58) &  9.69 (2.63) \\
 $\#$3594 & 25500 (fixed) & 22000 (200) & 83.60 (0.41) & 7.095 (0.040) & 6.668 (0.055) & 50.50 (1.56) & 48.00 (1.03) &  1.49 (1.96) \\
 $\#$3677 & 23100 (fixed) & 25100 (300) & 73.60 (0.22) & 5.029 (0.029) & 7.833 (0.064) & 74.51 (1.07) & 25.49 (0.94) &  0 \\
 $\#$3951 & 26200 (fixed) & 24400 (200) & 78.50 (0.24) & 6.699 (0.055) & 6.789 (0.056) & 53.76 (0.97) & 46.24 (1.16) &  0 \\
 $\#$4955 & 19000 (fixed) & 17400 (500) & 80.01 (0.31) & 7.868 (0.165) & 8.591 (0.180) & 58.97 (0.75) & 41.03 (0.79) &  0 \\
 $\#$5233 & 30000 (fixed) & 29400 (300) & 80.52 (0.21) & 8.762 (0.098) & 7.843 (0.093) & 44.09 (1.02) & 55.91 (0.93) &  0 \\
 $\#$5422 & 26200 (fixed) & 20400 (300) & 79.18 (0.33) & 7.076 (0.098) & 7.070 (0.102) & 54.69 (2.34) & 36.51 (4.57) &  8.80 (7.82) \\
 $\#$5434 & 26200 (fixed) & 24200 (400) & 71.72 (0.40) & 5.400 (0.061) & 5.516 (0.059) & 53.49 (1.14) & 43.86 (1.62) &  2.65 (2.01) \\
 \noalign{\smallskip}\hline
\end{tabular}
\end{table*}



\begin{table*}[h!]
\caption{The parameters of the apsidal motion for the individual systems.} \label{OCparam}
\scriptsize
\begin{tabular}{lcccccccc}
\hline\hline\noalign{\smallskip}
  System           & $T_0 - 2400000$ [HJD] &  $P_s$ [days]   &   $e$       & $\dot{\omega}$ [deg$/\rm{cycle}$] & $\omega_0$ [deg] & $U$ [yr] \\% log k2
 \noalign{\smallskip}\hline\noalign{\smallskip}
 $\#$0720 & 53803.390 (21)        & 6.052322 (48) & 0.062 (16)& 0.2070 (300)                      & 67.6 (5.0)       & 28.8 (5.5)  \\ %-1.327-divne, chyba cca 0.15
 $\#$0781 & 52745.417 (32)        & 3.299923 (48) & 0.310 (75)& 0.0301 (37)                       & 244.4 (10.3)     & 108.1 (15.1)\\ %-1.907
 $\#$0888 & 53470.954 (15)        & 1.918337 (11) & 0.143 (34)& 0.0474 (193)                      & 89.3 (4.7)       & 39.9 (11.6) \\ %-2.118
 $\#$1001 & 53090.7643 (35)       & 1.1621122 (18)& 0.072 (14)& 0.0601 (69)                       & 94.5  (7.8)      & 19.0 (2.4)  \\ %-2.017
 $\#$1298 & 53501.194 (14)        & 1.7532121 (99)& 0.219 (42)& 0.0677 (93)                       & 130.0 (4.2)      & 25.5 (4.1)  \\ %-1.830
 $\#$1407 & 53470.497 (13)        & 2.100755  (11)& 0.151 (47)& 0.0427 (120)                      & 115.9 (3.9)      & 46.3 (18.0) \\ %-2.036
 $\#$2186 & 53470.314 (15)        & 3.291316  (20)& 0.227 (82)& 0.0258 (42)                       & 91.9 (2.6)       & 125.7 (24.5)\\ %-1.665-trochu divne
 $\#$2225 & 53089.914 (10)        & 1.491721  (8) & 0.187 (48)& 0.0351 (121)                      & 291.9 (8.8)      & 41.9 (21.8) \\ %-2.104
 $\#$2251 & 54179.695 (25)        & 2.336038 (33) & 0.271 (22)& 0.0484 (132)                      & 99.8 (5.6)       & 47.6 (17.8) \\ %-1.954
 $\#$2524 & 53471.664 (24)        & 2.169236 (23) & 0.263 (68)& 0.0475 (92)                       & 81.5 (6.5)       & 45.0 (10.8) \\ %-2.043
 $\#$2534 & 53277.1246 (72)       & 2.2967384 (72)& 0.078 (24)& 0.0357 (57)                       & 265.0 (3.4)      & 63.3 (11.9) \\ %-2.190
 $\#$3594 & 53280.315 (41)        & 4.330333 (80) & 0.194 (69)& 0.0300 (63)                       & 238.1 (9.9)      & 142.1 (38.9)\\ %-1.983
 $\#$3677 & 53278.036 (52)        & 5.241539 (117)& 0.153 (55)& 0.0554 (133)                      & 40.2 (4.6)       & 93.3 (33.6) \\ %-2.220
 $\#$3951 & 53277.2672 (75)       & 3.104291 (17) & 0.092 (20)& 0.0476 (165)                      & 92.9 (4.0)       & 64.3 (33.9) \\ %-1.684-trochu divne, chyba cca 0.22
 $\#$4955 & 54022.771 (52)        & 2.772183 (53) & 0.338 (48)& 0.0239 (84)                       & 143.3 (5.0)      & 114.4 (51.5)\\ %-1.951
 $\#$5233 & 52746.459 (45)        & 5.068362 (103)& 0.199 (57)& 0.1915 (321)                      & 7.0 (8.7)        & 26.1 (5.2)  \\ %-0.703-trochu divne
 $\#$5422 & 53656.966 (26)        & 3.040295 (31) & 0.199 (56)& 0.0301 (83)                       & 318.1 (6.0)      & 99.4 (37.9) \\ %-1.920-sp trida II ?
 $\#$5434 & 53478.7191 (72)       & 2.886936 (9)  & 0.051 (16)& 0.0747 (214)                      & 129.6 (3.4)      & 38.1 (15.2) \\ %-2.038
 \noalign{\smallskip}\hline
\end{tabular}
\end{table*}




\section{Notes on individual systems}


\begin{figure*}
 \includegraphics[width=\textwidth]{figs.eps}
 \caption[]{Light curves of the analysed systems, the data taken from the OGLE III survey, and the $I$
 filter.} \label{LCs}
\end{figure*}

\begin{figure*}
 \includegraphics[width=\textwidth]{figuresOC_OK.eps}
 \caption[]{\oc\ diagram for the times of minima for the analysed systems. The continuous and dashed
curves represent predictions for the primary and secondary eclipses, respectively. The individual
primary and secondary minima are denoted by dots and open circles, respectively. Larger symbols
correspond to the measurements, which were given higher weights.} \label{OCs}
\end{figure*}

All of the eclipsing systems were analysed using a similar approach, hence we cannot focus on every
star in detail. See Table \ref{InfoSystems} for information and cross-identification of these
stars. The abbreviations of the star names were used for all of the systems for a better brevity.
That is, OGLE-SMC-ECL-0720 was shortened as $\#$0720, etc. Only the most important results are
summarized below. The final light curve fits, and the $O-C$ diagrams are presented in Figs.
\ref{LCs} and \ref{OCs}; the parameters are given in Tables \ref{LCparam} and \ref{OCparam}. The
whole set of eighteen analysed systems can be divided into a few subsets according to available
spectral information.

%\begin{itemize}

%XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

%\item[$\bullet$]

%SYSTEMS WITH NO SPECTRA:

The largest group in our sample of stars comprise these stars, which were never observed
spectroscopically, hence no spectral classification or radial velocity study was published so far.
These systems are $\#$0781, $\#$1001, $\#$1298, $\#$1407, $\#$2225, $\#$2251, $\#$2524, and
$\#$5233. Most of them were discovered as eclipsing binaries by Udalski et al. (1998), Wyrzykowski
et al. (2004), or Faccioli et al. (2007). Several of them were mentioned as eccentric ones with
apsidal motion in some of the above mentioned papers. Owing to having no information about their
spectra, we only roughly estimated the spectral types from the measurements in photometric filters,
as seen in Table \ref{InfoSystems}. These observations were usually taken from Massey (2002) and
from the dereddened photometric indices the spectral types were estimated (Popper 1980, Ducati et
al. 2001, or Cox 2000). For some of the systems, there resulted a non-negligible third light
contribution (e.g. $\#$2225, $\#$2251).


%XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

%\item[$\bullet$]

%SYSTEMS WITH SPECTRAL-TYPE ESTIMATION:

For some of the systems, the spectral types were published, so we can use them for a better primary
temperature estimation for a subsequent light curve analysis. These systems are $\#$0720, $\#$2534,
$\#$3677, $\#$4955, $\#$5422, and $\#$5434 (to this group of stars, two systems $\#$0888 and
$\#$3951 also belong, but these were given a special focus in the following subsections). These
binaries were also discovered by Udalski et al. (1998) and Faccioli et al. (2007); for some of
them, a short note about their apsidal motion was published. The spectral types for these systems
given by Evans et al. (2004) and Bonanos et al. (2010) are in good agreement with our spectral
types that are estimated from the dereddened photometric indices.



%XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

%SYSTEMS WITH PREVIOUS LC+RV SOLUTION:

%\item[$\bullet$]

\subsection{OGLE-SMC-ECL-2186}

Two systems, $\#$2186 and $\#$3594, were even published with their light and radial velocity curves
solutions. The first one ($\#$2186) was analysed by Wyithe \& Wilson (2001), who presented a
preliminary light curve solution with an eccentric orbit with $e=0.068$. Graczyk (2003) analysed
the LC of $\#$2186, yielding an eccentricity of 0.251, no third light, and the luminosity ratio of
$L_2/L_1=0.843$. Wyrzykowski et al. (2004) presented a note about its apsidal motion but with no
estimation of its period. Concerning the spectral type, Graczyk (2003) estimated the types of about
O9V+O9V but dealt only with the photometry. Later, Hilditch et al. (2005) published its spectral
type to be B0+B0-3 based on 15 spectra of the star. They also analysed the light curve, yielding a
value of the eccentricity of the orbit to be 0.063. However, their LC solution is not very
convincing due to poor fit of the secondary minimum.

\subsection{OGLE-SMC-ECL-3594}

The second system ($\#$3594) was also studied by Wyithe \& Wilson (2001), who included this star
into their sample of SMC eclipsing binaries with the light curve solution, which result in orbital
inclination of 88.9$^\circ$ and an eccentricity of 0.144. Hilditch et al. (2005) analysed the
system in more detail, resulting in an orbital eccentricity of 0.19 (based on photometry and
spectroscopy together) and the spectral types of both components as B1+B1-3.



%XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

%INTERESTING SYSTEMS:

%\item[$\bullet$]

\subsection{OGLE-SMC-ECL-0888}

The object $\#$0888 was first mentioned by Wyrzykowski et al. (2004), who also noted about its
apsidal motion. Its spectral type was derived to be about O9V by Evans et al. (2004). We found that
the pure apsidal motion is not able to describe the $O-C$ diagram in detail, hence another effect
has also to be included. We also tried to fit the parabolic fit to the ephemerides, with the
apsidal motion hypothesis (can be interpreted as a mass transfer between the components, despite
improbable for detached binary). However, this fit was also not very satisfactory. Therefore, we
used a different code that computes the apsidal motion parameters with the third-body orbit (a
so-called 'light travel time' effect), as seen in for example Irwin (1959) or Mayer (1990). Ten
parameters were fitted (five from the apsidal motion, five from the third body hypothesis); thus,
this approach led to an acceptable solution with the lowest sum of squares residuals. The final
parameters of the fit are given in Tables~\ref{OCparam} and \ref{LITE0888}; the complete \oc\
diagrams are shown in Figs.~\ref{OCs} and \ref{OC0888LITE}.

\begin{table}[b]
\caption{Third body orbit parameters for $\#$0888.} \label{LITE0888}
\begin{flushleft}
\begin{tabular}{lcccccc}
\hline\hline\noalign{\smallskip}
Parameter [Unit]     &   Value  \\
\noalign{\smallskip}\hline\noalign{\smallskip}
 $p_3$ [yr]        & 72.1 $\pm$ 28.0 \\
 $A_3$ [day]       & 0.030 $\pm$ 0.011  \\
 $T_3$ [HJD]       & 2454900 $\pm$ 8700  \\
 $e_3$             & 0.709 $\pm$ 0.247  \\
 $\omega_3$ [deg]  & 154.0 $\pm$ 15.6  \\
 \noalign{\smallskip}\hline
\end{tabular}
\end{flushleft}
\end{table}

\begin{figure}
\includegraphics[width=0.48\textwidth]{OGLE0888_OnlyLITE.eps}
\caption[ ]{\oc\ diagram of $\#$0888 after subtraction of the apsidal motion term.}
\label{OC0888LITE}
\end{figure}

From the third-body parameters, we could also compute the mass function of the distant component,
which resulted in $f(m_3) = 0.059 \pm 0.015~\mathrm{M_\odot}$. From this value, one can calculate a predicted
minimal mass of the third body (i.e. assuming coplanar orbits $i_3=90^\circ$), which resulted in
$m_{3,min} = 4.9~\mathrm{M_\odot}$. If we propose such a body in the system, one can ask whether it is
detectable somehow in the already obtained data. The period is long for continuous monitoring of
the radial velocity changes, but detecting the third light in the light curve solution would be
promising. Assuming a normal main sequence star, its luminosity would be of about only $L_{3,min} =
1-2$\,\% of the total system luminosity. Such a weak third light would be hardly detectable in our
poor-quality photometric data, but it is worth of try. Hence, we performed a new light curve
solution with a special focus on the value of the third light for a LC solution. The value was
really obtained, and its value is not negligible at all. As one can see from the parameters
presented in Table \ref{LCparam}, the third light represents about one half of the total light.
This finding naturally explains why both the eclipses are so shallow. On the other hand, one can
ask to which body the estimated spectral type of O9V belongs. If the third body is the dominant
source, this is probably the O9V component, but the primary temperature of 33200~K was assumed
using the O9V primary, which now seems to be incorrect. However, having no other relevant
information about the individual spectral types, one cannot easily assume a different primary
temperature. Thus, we can conclude that the third body is probably present and orbits around the EB
pair on orbit which is mildly inclined from the originally assumed 90$^\circ$. It is hard to say
anything more about such a body because of the high errors of the parameters (period, third light,
etc.). More precise photometry or radial velocities would be very welcome for a final confirmation
of our hypothesis.


%\item[$\bullet$]

\subsection{OGLE-SMC-ECL-3951}

The object $\#$3951 is a part of the SMC open cluster NGC 346. Its eclipsing nature and orbital
period was first presented by Udalski et al. (1998). Later, the star was classified as B1V by
Massey et al. (2012). From the period analysis, a weak quasi-periodic signal also on the residuals
after subtraction of the apsidal motion hypothesis (see Fig. \ref{OC3951resid}) resulted. However,
the variation is still too spurious for any final confirmation yet and we have not even try to fit
the data with any additional variation, as in the previous case.

\begin{figure}
\includegraphics[width=0.48\textwidth]{OGLE3951_Residuals.eps}
\caption[ ]{\oc\ diagram of $\#$3951 after subtraction of the apsidal motion term.}
\label{OC3951resid}
\end{figure}


%\end{itemize}




%\begin{table*}
% \caption{The internal structure constants $\log k_{\mathrm{2,obs}}$ as compared with the theoretical
% values from stellar evolution models together with the relativistic fraction of the total apsidal
% motion rate.}
% \label{logK2}
%% \small
% \centering \scalebox{0.9}{
% \begin{tabular}{c c c c || c c c c}
% \hline\hline
%  System & log $k_{\mathrm{2,obs}}$ & log $k_{\mathrm{2,theor}}$ & $\omega_{\mathrm{rel}}/\omega_{\mathrm{total}}$ &   System & log $k_{\mathrm{2,obs}}$ & log $k_{\mathrm{2,theor}}$ & $\omega_{\mathrm{rel}}/\omega_{\mathrm{total}}$  \\
% \hline
%  OGLE-SMC-ECL-0720 &  -1.33 $\pm$ 0.20 & -1.50 $\pm$ 0.05 & 0.7 \% &  OGLE-SMC-ECL-2524 &  -2.04 $\pm$ 0.20 & -1.87 $\pm$ 0.05 & 4.9 \% \\
%  OGLE-SMC-ECL-0781 &  -1.91 $\pm$ 0.20 & -1.87 $\pm$ 0.05 & 6.0 \% &  OGLE-SMC-ECL-2534 &  -2.19 $\pm$ 0.20 & -1.90 $\pm$ 0.05 & 6.9 \% \\
%  OGLE-SMC-ECL-0888 &  -2.05 $\pm$ 0.20 & -2.15 $\pm$ 0.05 & 8.3 \% &  OGLE-SMC-ECL-3594 &  -1.98 $\pm$ 0.20 & -1.90 $\pm$ 0.05 & 5.2 \% \\
%  OGLE-SMC-ECL-1001 &  -2.02 $\pm$ 0.20 & -2.03 $\pm$ 0.05 & 2.4 \% &  OGLE-SMC-ECL-3677 &  -2.25 $\pm$ 0.20 & -1.87 $\pm$ 0.05 & 2.3 \% \\
%  OGLE-SMC-ECL-1298 &  -1.84 $\pm$ 0.20 & -1.97 $\pm$ 0.05 & 5.4 \% &  OGLE-SMC-ECL-3951 &  -1.68 $\pm$ 0.20 & -1.90 $\pm$ 0.05 & 4.3 \% \\
%  OGLE-SMC-ECL-1407 &  -2.04 $\pm$ 0.20 & -1.88 $\pm$ 0.05 & 4.2 \% &  OGLE-SMC-ECL-4955 &  -1.95 $\pm$ 0.20 & -1.88 $\pm$ 0.05 & 6.8 \% \\
%  OGLE-SMC-ECL-2186 &  -1.67 $\pm$ 0.20 & -1.90 $\pm$ 0.05 & 8.1 \% &  OGLE-SMC-ECL-5233 &  -0.70 $\pm$ 0.20 & -2.15 $\pm$ 0.05 & 9.3 \% \\
%  OGLE-SMC-ECL-2225 &  -2.13 $\pm$ 0.20 & -1.99 $\pm$ 0.05 & 4.1 \% &  OGLE-SMC-ECL-5422 &  -1.92 $\pm$ 0.20 & -1.90 $\pm$ 0.05 & 7.0 \% \\
%  OGLE-SMC-ECL-2251 &  -1.95 $\pm$ 0.20 & -1.90 $\pm$ 0.05 & 5.4 \% &  OGLE-SMC-ECL-5434 &  -2.04 $\pm$ 0.20 & -1.87 $\pm$ 0.05 & 2.3 \% \\
%  \hline
% \end{tabular}}
%\end{table*}

% 0720 - starsi nezli 12 Myr (evolved, lum.tr IV)
% 0781 - nejlepe mladsi nezli 0.5 Myr, pp: 10 Myr
% 0888 - nejlepe cca 7.5 Myr, pp: 10 Myr
% 1001 - nejlepe cca 533 Myr (evolved), pp: 10 Myr
% 1298 - nejlepe cca 0.9 Myr, pp: 10 Myr
% 1407 - nejlepe cca 12 Myr, pp: 10 Myr
% 2186 - nejlepe vice nezli 24 Myr (evolved), pp: 10 Myr
% 2225 - nejlepe mladsi nezli 5 Myr nebo evolved vice nezli 290Myr
% 2251 - nejlepe cca 4 Myr, pp: 10 Myr
% 2524 - nejlepe cca 11 Myr, pp: 10 Myr
% 2534 - nejlepe cca 18 Myr, pp: 10 Myr
% 3594 - nejlepe cca 3.2 Myr, pp: 10 Myr
% 3677 - nejlepe cca 30 Myr, pp: 10 Myr
% 3951 - nejlepe vice nezli 23.9 Myr (evolved), pp: 10 Myr
% 4955 - nejlepe cca do 1 Myr
% 5233 - reseni neexistuje!!!
% 5422 - nejlepe cca 4 Myr, pp: 10 Myr
% 5434 - nejlepe cca 13 Myr, pp: 10 Myr



%\section{Internal structure constant} \label{INT}
%
%Thanks to the analysis of apsidal motion via the period changes and the light curve analysis one is
%able to use the derived quantities for a rough estimation of the internal structure constants. The
%theoretical $\log k_{\mathrm{2,theo}}$ values are taken from Claret (2005) and the comparison with
%the observed ones is presented in Table 4. There are only mean values of $\log k_2$ of both
%components
%which can be derived and these are based on several assumptions. %The errors were only estimated due
%%to the fact that also the input parameters like spectral types are not known with high reliability
%%for most of the systems.
%
%The most speculative is the use of apsidal motion parameters for those systems, where only a short
%time interval (compared with the apsidal motion period) is covered with the data nowadays. For
%systems, where the apsidal period is long (e.g. OGLE-SMC-ECL-2186, OGLE-SMC-ECL-3594, etc.) these
%values are still rather speculative and affected by large errors because of their poor coverage by
%the data points. Therefore, almost the same chi-square value can be reached with slightly different
%values of apsidal motion rate and hence also the estimation of $\log k_2$ is still only preliminary
%yet. Another possible sources of errors for the internal structure estimation are the unknown
%spectral types of the components, hence only rough estimation of both masses. For some systems also
%the interstellar reddening could play a role when the spectral type was only estimated from the
%$B-V$ photometric index. And finally of course the unknown value of the semimajor axis of the
%system (dealing with no radial velocities). Also better the quality of the light curves, better the
%result of the LC fit and the parameters derived from this fit. All of these are the possible
%sources of errors which affect the resulted $\log k_2$ values. Therefore, we have only estimated
%the error of the observed value as 0.20, while the error of the theoretical value was set to 0.05.
%Moreover, the average age was set to 10~Myr (North et al. 2010), after several unsuccessful
%attempts with higher age.
%
%As one can see in Fig. \ref{FigK2} and in Table \ref{logK2}, for most of the systems the observed
%internal structure constants and the theoretical values lie within their respective error bars.
%However, a few comments are necessary to be said for several systems. For the system
%OGLE-SMC-ECL-0720 there resulted a large discrepancy between the observed and predicted value of
%$\log k_2$ assuming the age of 10~Myr. Nevertheless, its spectral type was derived to be of B0IV
%(hence an evolved star), so the values published by Claret (2005) for the evolved star are very
%different, and this value (assuming an age of 14~Myr) is given in Table \ref{logK2} for this star.
%For three other stars (OGLE-SMC-ECL-1001, OGLE-SMC-ECL-2186, and OGLE-SMC-ECL-3951) their ages as
%resulted from comparison between the theoretical and observed $\log k_2$ values indicated that the
%stars are still very close to the ZAMS. On the contrary, the system OGLE-SMC-ECL-2225 only
%satisfies the condition of $\log k_{\mathrm{2,theor}} = \log k_{\mathrm{2,obs}}$ for the star with
%an age more than 100~Myr. And finally, for the system OGLE-SMC-ECL-5233 no reliable solution was
%found because the $\log k_{\mathrm{2,obs}}$ resulted in a very low value, and this point was
%excluded when plotting Fig. \ref{FigK2}. However, we cannot find any reliable explanation for this
%discrepancy.



%\begin{figure}
%  \centering
%  \includegraphics[width=0.48\textwidth]{LogK2.eps}
%  \caption{Plot of internal structure constants - observed versus theoretical.}
%  \label{FigK2}
%\end{figure}


%In fact the only finding which can be stated from these results is the fact that the internal
%structure constants as derived from our analysis are not sufficiently precise for testing the
%evolutionary models. Their errors are too large and scatter around the theoretical values cannot
%allow us to do any definite conclusion. For example there should be a possibility to test the
%theoretical models on very massive stars. Unfortunately, the most massive system is V1082~Sco and
%its resulting fit does not allow us to derive the internal structure with higher precision.
%However, the distribution of resulting $\log k_{2,obs}$ values follow the predicted relation
%(earlier the spectral type - value of $\log k_2$ closer to zero), but all thirteen values are
%randomly distributed around the theoretical ones. Generally we can say that obtaining the precise
%RV curves for all of these systems would be of great benefit.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%  4  Discussion  %%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%
%\section{Discussion}
%
%\begin{table*}
%\caption{Basic physical properties of HV~982, HV~2284, MACHO~78.6097.13,
% MACHO~81.8881.47, and MACHO~79.5377.76 and their internal structure constants}
%\label{t3}
%\begin{minipage}[]{\textwidth}
%\begin{tabular}{lcccccccc}
%\hline\hline\noalign{\smallskip}
%Parameter & Unit                                     &  HV~982       & HV~2274     & MACHO~78.6097.13  & MACHO~81.8881.47 & MACHO~79.5377.76 \\
%\hline\noalign{\smallskip}
%$M_1$     & \ms                                      &  11.28 (0.46) & 12.2 (0.7)  &  11.76 (0.48)     & 5.51 (0.21)     &  11.26 (0.35)  \\
%$M_2$     & \ms                                      &  11.61 (0.47) & 11.4 (0.7)  &  10.51 (0.40)     & 5.40 (0.19)     &  11.27 (0.35)  \\
%$r_1$     &                                          &  0.194 (0.003)&0.255 (0.013)&  0.258 (0.021)    & 0.169 (0.008)   & 0.212 (0.004)\\
%$r_2$     &                                          &  0.214 (0.003)&0.234 (0.012)&  0.206 (0.020)    & 0.192 (0.010)   & 0.190 (0.004)\\
%\hline\noalign{\smallskip}
%Source    &                                          & Clausen et al.& Ribas et al. &Gonz{\'a}lez et al.& This           & This    \\
%          &                                          & (2003)        & (2000)       & (2005)            & paper          & paper   \\
%\hline\noalign{\smallskip}
%$\dot{\omega}_\mathrm{rel}$ & deg $\:\rm{cycle^{-1}}$& 0.0015        & 0.0014       & 0.0020            & 0.0011         & 0.0023  \\
%$\dot{\omega}_\mathrm{rel} / \dot{\omega}$ & \%      & 5.9           & 3.2          & 3.24              & 3.06           & 3.65    \\
%log $k_\mathrm{2, obs}$  &                           & -2.371 (0.10) &-2.470 (0.15) & -2.174 (0.35)     & -2.017 (0.18)  & -1.859 (0.17)\\
%log $k_\mathrm{2, theo}$ &                           & -2.32         & -2.45        & -2.19             & -2.01          & -1.90   \\
%\hline\noalign{\smallskip}
%\end{tabular}
%\end{minipage}
%\end{table*}
%
%
%
%
%
%The detection of apsidal motion in EEB provides the opportunity to test models of stellar internal
%structure. The internal structure constant (ISC), $k_{2,\rm obs}$, which is related to the
%variation in the density inside the star, can be derived using the following expression:
%
%\begin{equation}
%k_\mathrm{2, obs} = \frac{1}{c_{21} + c_{22}} \, \frac{P_a}{U}
%         = \frac{1}{c_{21} + c_{22}} \, \frac{\dot{\omega}}{360} ,
%\end{equation}
%
%\noindent where $c_{21}$ and $c_{22}$ are functions of the orbital eccentricity, fractional radii,
%the masses of the components, and the ratio between rotational velocity of the stars and Keplerian
%velocity (Kopal 1978). We also assume that the component stars rotate pseudosynchronously with the
%same angular velocity as the maximum orbital value at periastron (see e.g. Kopal 1978). Another
%possible approach is to use the value of $v\!\cdot\!\sin i$ as derived from the combined LC+RV
%analysis published before. However, there could be a problem with the inclination of the rotation
%axis (as in the case of DI~Her), and moreover the error of the internal structure constants is by
%far dominated by the term $r_i^5$ in the equations. In addition to the classical Newtonian
%contribution, the observed rate of rotation of the apses includes the contribution from General
%Relativity, $\dot{\omega}_{\rm rel}$ (Gim\'enez 1985):
%
%\begin{equation}
%\dot{\omega}_\mathrm{rel} = \; 5.45 \times 10^{-4} \: \frac{1}{1-e^2}
%          \:\Biggl( \frac{M_1 + M_2}{P} \Biggr) ^{2/3},
%\end{equation}
%\medskip
%
%\noindent where $M_i$ denotes the individual masses of the components in solar units and $P$ is the
%orbital period in days.
%
%
%
%The values of $\dot{\omega}_\mathrm{rel}$ and the resulting mean internal structure constants
%$k_\mathrm{2,obs}$ for the studied systems are given in Table~\ref{t3}. Theoretical values
%$k_\mathrm{2,theo}$ according to available theoretical models for the internal stellar structure
%computed by Claret (2006) for given masses of components are presented in Table \ref{t3}. % The chemical composition of $X = 0.70$ and $Z = 0.002$ was assumed.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%    Conclusions    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section{Discussion and conclusions}

Our study provides the parameters of the apsidal motion for eighteen early-type binary systems
located in the SMC. For most of the binaries, this is the first attempt to estimate the apsidal
motion rates, and the light curve solution. In our own Galaxy there are a few hundreds of apsidal
motion eclipsing binaries known; however, in other galaxies their number is still very limited.
Hence this study still presents an important contribution to the topic. However, for only three
systems from our sample ($\#$1001, $\#$1298, and $\#$5233), the apsidal motion was derived from
adequately large data set covering almost one apsidal period. The relativistic effects for the
selected systems are weak, being up to 10\,\% of the total apsidal motion rate. For the system
$\#$0888, the third body hypothesis was also presented and discussed.

The apsidal motion in EEBs has been used for decades to test evolutionary stellar models. Thus, one
can ask whether our results can be used for deriving the internal structure constants for these
stars in SMC. However, dealing with no radial velocities for most of the systems and with rather
poor data coverage during the apsidal motion period, the parameters are too uncertain and affected
by large errors. For these systems where the apsidal period is well-covered, a detailed
spectroscopic analysis is missing, and vice versa, for systems where the radial velocity study was
performed, the apsidal period has yet to be only poorly covered with data. However, for any testing
of the stellar structure models or for the general relativity tests, the quality of the input data
has to be an order of magnitude better (which implies long-term collection of the observations and
data that covers the whole apsidal period in the following decades). Some of the systems are bright
enough for a spectral monitoring, hence we encourage the observers to obtain new, high-dispersion,
and high-S/N spectroscopic observations. With such data, methods, like spectral disentangling, can
help us construct the radial velocity curves of both components, confirm the apsidal motion
hypothesis, test the stellar structure models, or detect the third bodies, as indicated from our
analysis.

\medskip


\begin{acknowledgements}
We do thank the {\sc MACHO} and {\sc OGLE} teams for making all of the observations easily public
available. This work was supported by the Czech Science Foundation grant no. P209/10/0715, by the
grant UNCE 12 of the Charles University in Prague, and by the grant LG12001 of the Ministry of
Education of the Czech Republic. We are also grateful to the ESO team at the La Silla Observatory
for their help in maintaining and operating the Danish telescope. The following internet-based
resources were used in research for this paper: the SIMBAD database and the VizieR service operated
at the CDS, Strasbourg, France, and the NASA's Astrophysics Data System Bibliographic Services.
\end{acknowledgements}

\bigskip

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ONLINE %%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%\Online

\begin{appendix} %First online appendix
% Table 1 available electronically only
%\scriptsize \onllongtab{1}{

\section{Tables of minima}

\begin{table}
 \centering
  \begin{minipage}{95mm}
 \fontsize{1.8mm}{2.4mm}\selectfont
 \caption{List of the minima timings used for the analysis.} \label{minima}
\begin{tabular}{ccclcl}
\hline\hline\noalign{\smallskip}
 Star       &    JD Hel.- &  Error & Type   &  Filter  & Source /     \\
            &   2400000   &  [day] &        &          & Observatory  \\
\noalign{\smallskip}\hline
\noalign{\smallskip}
 OGLE-SMC-ECL-0720 & 48701.29443 & 0.00741 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0720 & 48704.29533 & 0.00922 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0720 & 49548.60490 & 0.01197 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0720 & 49551.64897 & 0.01236 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0720 & 49851.19352 & 0.01915 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0720 & 49854.28789 & 0.02131 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0720 & 50202.21473 & 0.00924 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0720 & 50205.32260 & 0.02286 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0720 & 50547.16343 & 0.00657 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0720 & 50550.33647 & 0.01600 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0720 & 50849.76208 & 0.00929 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0720 & 50852.97305 & 0.00908 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0720 & 51497.34320 & 0.01915 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0720 & 51500.59013 & 0.01798 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0720 & 50550.35962 & 0.00592 & Sec  & I   & OGLE II \\
 OGLE-SMC-ECL-0720 & 50553.18661 & 0.00439 & Prim & I   & OGLE II \\
 OGLE-SMC-ECL-0720 & 51101.12700 & 0.00486 & Sec  & I   & OGLE II \\
 OGLE-SMC-ECL-0720 & 51103.92761 & 0.00022 & Prim & I   & OGLE II \\
 OGLE-SMC-ECL-0720 & 51700.32442 & 0.00002 & Sec  & I   & OGLE II \\
 OGLE-SMC-ECL-0720 & 51703.10399 & 0.00089 & Prim & I   & OGLE II \\
 OGLE-SMC-ECL-0720 & 52199.40921 & 0.00391 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 52202.68144 & 0.00649 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 52574.65616 & 0.01128 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 52577.90814 & 0.00526 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 52925.70455 & 0.00698 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 52928.93350 & 0.00340 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 53300.96643 & 0.00535 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 53304.15675 & 0.00206 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 53652.04092 & 0.01013 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 53655.16657 & 0.00666 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 53997.03938 & 0.00490 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 54000.11047 & 0.00739 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 54348.09727 & 0.01183 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 54351.12853 & 0.00173 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 54802.04975 & 0.00811 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0720 & 54805.02717 & 0.00004 & Sec  & I   & OGLE III \\
   \hline
 OGLE-SMC-ECL-0781 & 48650.52017 & 0.00589 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0781 & 48651.61198 & 0.00601 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0781 & 49498.60339 & 0.00758 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0781 & 49499.71447 & 0.00766 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0781 & 49851.67410 & 0.00639 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0781 & 49852.80913 & 0.00995 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0781 & 50201.46365 & 0.00429 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0781 & 50202.62334 & 0.00207 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0781 & 50551.24174 & 0.00636 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0781 & 50552.42087 & 0.00430 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0781 & 50851.52298 & 0.00449 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0781 & 50852.72368 & 0.00320 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0781 & 51501.59099 & 0.00867 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0781 & 51502.82123 & 0.00378 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0781 & 50950.51118 & 0.00632 & Prim & I   & OGLE II \\
 OGLE-SMC-ECL-0781 & 50951.72688 & 0.00346 & Sec  & I   & OGLE II \\
 OGLE-SMC-ECL-0781 & 51650.06399 & 0.00269 & Prim & I   & OGLE II \\
 OGLE-SMC-ECL-0781 & 51651.34170 & 0.00330 & Sec  & I   & OGLE II \\
 OGLE-SMC-ECL-0781 & 52201.12370 & 0.00245 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 52202.45512 & 0.00330 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 52574.00067 & 0.00203 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 52575.35665 & 0.00219 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 52923.77283 & 0.00191 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 52925.16354 & 0.00283 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 53299.94961 & 0.00223 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 53301.36089 & 0.00390 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 53649.71827 & 0.00569 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 53651.16977 & 0.00287 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 53999.48473 & 0.00358 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 54000.98147 & 0.00319 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 54349.25336 & 0.00150 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 54350.78606 & 0.00575 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 54801.32027 & 0.00152 & Prim & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 54802.88593 & 0.00470 & Sec  & I   & OGLE III \\
 OGLE-SMC-ECL-0781 & 56637.71770 & 0.00052 & Sec  & R   & DK154 \\
 OGLE-SMC-ECL-0781 & 56675.55172 & 0.00225 & Prim & R   & DK154 \\
   \hline
 OGLE-SMC-ECL-0888 & 48650.12114 & 0.00495 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0888 & 48651.22335 & 0.00508 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0888 & 49499.94006 & 0.00870 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0888 & 49501.05324 & 0.00649 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0888 & 49849.07573 & 0.01044 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0888 & 49850.20619 & 0.00930 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0888 & 50200.13984 & 0.00504 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0888 & 50201.26861 & 0.00575 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0888 & 50549.27599 & 0.00811 & Prim & B+R & MACHO \\
  \hline
  \noalign{\smallskip}\hline
\end{tabular}
%Note: * {\it mean value of VR or VRI measurements}
\end{minipage}
\end{table}


\begin{table}
 \centering
  \begin{minipage}{95mm}
 \fontsize{1.8mm}{2.4mm}\selectfont
 \caption{List of the minima timings used for the analysis.}
\begin{tabular}{ccclcl}
\hline\hline\noalign{\smallskip}
 Star       &    JD Hel.- &  Error & Type   &  Filter  & Source /     \\
            &   2400000   &  [day] &        &          & Observatory  \\
\noalign{\smallskip}\hline \noalign{\smallskip}
 OGLE-SMC-ECL-0888 & 50550.40710 & 0.01648 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0888 & 50850.46408 & 0.00330 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0888 & 50851.59112 & 0.01159 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0888 & 51500.78388 & 0.00681 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-0888 & 51501.89603 & 0.00505 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-0888 & 52199.09028 & 0.00528 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 52200.13742 & 0.00884 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 52600.02846 & 0.00631 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 52601.06977 & 0.00736 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 52949.18978 & 0.00333 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 52950.19052 & 0.00191 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 53300.25949 & 0.00116 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 53301.23084 & 0.00399 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 53674.34361 & 0.00409 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 53675.28319 & 0.01150 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 54050.35279 & 0.00313 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 54051.26885 & 0.00038 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 54374.55955 & 0.00380 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 54375.44152 & 0.00309 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 54800.44108 & 0.00414 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 54801.28789 & 0.00905 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-0888 & 56648.59424 & 0.00055 & Sec  &  R  & DK154 \\
 OGLE-SMC-ECL-0888 & 56699.59546 & 0.00175 & Prim &  R  & DK154 \\
  \hline
 OGLE-SMC-ECL-1001 & 48850.21555 & 0.00273 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-1001 & 48850.79998 & 0.00609 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-1001 & 49849.63212 & 0.00151 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-1001 & 49850.23064 & 0.00839 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-1001 & 50199.41863 & 0.00345 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-1001 & 50200.02376 & 0.00438 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-1001 & 50550.36477 & 0.00404 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-1001 & 50550.98731 & 0.00361 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-1001 & 50850.18196 & 0.00182 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-1001 & 50850.81887 & 0.00465 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-1001 & 51499.80461 & 0.00227 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-1001 & 51500.44253 & 0.00341 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-1001 & 52199.40475 & 0.00254 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 52200.02416 & 0.00093 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 52199.40475 & 0.00254 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 52575.37135 & 0.00282 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 52924.58209 & 0.00070 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 52925.16579 & 0.00325 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 53299.95187 & 0.00042 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 53300.52307 & 0.00219 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 53649.74110 & 0.00006 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 53650.30821 & 0.00044 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 53999.55700 & 0.00150 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 54000.08782 & 0.00011 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 54350.51940 & 0.00014 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 54351.05432 & 0.00070 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 54800.26261 & 0.00178 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 54800.78059 & 0.00223 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1001 & 56641.60734 & 0.00122 & Sec  &  R  & DK154    \\
 OGLE-SMC-ECL-1001 & 56673.54658 & 0.00453 & Prim &  R  & DK154    \\
 OGLE-SMC-ECL-1001 & 56702.60206 & 0.00200 & Prim &  R  & DK154    \\
  \hline
 OGLE-SMC-ECL-1298 & 48700.80975 & 0.00568 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-1298 & 48701.85571 & 0.00730 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-1298 & 49549.34310 & 0.00605 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-1298 & 49550.42315 & 0.00753 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-1298 & 49849.13107 & 0.01288 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-1298 & 49850.24535 & 0.00998 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-1298 & 50199.77445 & 0.00300 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-1298 & 50200.89616 & 0.00724 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-1298 & 50550.42479 & 0.00531 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-1298 & 50551.54191 & 0.00447 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-1298 & 50850.23337 & 0.00688 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-1298 & 50851.33824 & 0.01225 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-1298 & 51500.69514 & 0.00657 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-1298 & 51501.76815 & 0.01206 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-1298 & 50749.64318 & 0.00432 & Sec  &  I  & OGLE II  \\
 OGLE-SMC-ECL-1298 & 50750.29216 & 0.00168 & Prim &  I  & OGLE II  \\
 OGLE-SMC-ECL-1298 & 51360.43853 & 0.00065 & Prim &  I  & OGLE II  \\
 OGLE-SMC-ECL-1298 & 51361.49925 & 0.01471 & Sec  &  I  & OGLE II  \\
 OGLE-SMC-ECL-1298 & 52200.28714 & 0.00109 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 52201.22077 & 0.00300 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 52600.04481 & 0.00253 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 52600.88875 & 0.00701 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 52950.72224 & 0.00129 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 52951.52767 & 0.00227 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 53299.62553 & 0.00384 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 53300.37165 & 0.03122 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 53674.84148 & 0.00361 & Prim &  I  & OGLE III \\
  \hline
  \noalign{\smallskip}\hline
\end{tabular}
%Note: * {\it mean value of VR or VRI measurements}
\end{minipage}
\end{table}


\begin{table}
 \centering
  \begin{minipage}{95mm}
 \fontsize{1.8mm}{2.4mm}\selectfont
 \caption{List of the minima timings used for the analysis.}
\begin{tabular}{ccclcl}
\hline\hline\noalign{\smallskip}
 Star       &    JD Hel.- &  Error & Type   &  Filter  & Source /     \\
            &   2400000   &  [day] &        &          & Observatory  \\
\noalign{\smallskip}\hline \noalign{\smallskip}
 OGLE-SMC-ECL-1298 & 53675.54332 & 0.00274 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 54050.04304 & 0.00084 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 54050.71048 & 0.08333 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 54374.40371 & 0.00178 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 54375.05651 & 0.00324 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 54800.44849 & 0.00472 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 54801.08349 & 0.09458 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1298 & 56397.53405 & 0.00545 & Prim &  R  & DK154    \\
 OGLE-SMC-ECL-1298 & 56580.67593 & 0.01310 & Sec  &  R  & DK154    \\
 OGLE-SMC-ECL-1298 & 56608.70669 & 0.00287 & Sec  &  R  & DK154    \\
 OGLE-SMC-ECL-1298 & 56673.62977 & 0.00118 & Sec  &  R  & DK154    \\
 OGLE-SMC-ECL-1298 & 56702.56995 & 0.00786 & Prim &  R  & DK154    \\
   \hline
 OGLE-SMC-ECL-1407 & 48649.17421 & 0.00323 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-1407 & 48650.40889 & 0.00669 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-1407 & 49499.99436 & 0.00697 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-1407 & 49501.21343 & 0.00811 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-1407 & 49850.83227 & 0.00611 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-1407 & 49852.02643 & 0.00710 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-1407 & 50199.56787 & 0.01047 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-1407 & 50200.74580 & 0.00719 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-1407 & 50550.39800 & 0.00301 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-1407 & 50551.56030 & 0.00742 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-1407 & 50850.81538 & 0.00361 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-1407 & 50851.95315 & 0.00580 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-1407 & 51499.96102 & 0.00528 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-1407 & 51501.07678 & 0.01308 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-1407 & 52199.54100 & 0.00251 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 52200.59766 & 0.00496 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 52575.58581 & 0.00118 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 52576.61588 & 0.00614 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 52924.32346 & 0.00232 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 52925.31293 & 0.00140 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 53300.37128 & 0.00145 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 53301.33887 & 0.00320 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 53649.10211 & 0.00177 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 53650.06528 & 0.00404 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 53999.94323 & 0.00416 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 54000.85550 & 0.00555 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 54350.77939 & 0.00263 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 54351.69302 & 0.00463 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 54800.35016 & 0.00327 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 54801.23674 & 0.00381 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-1407 & 56640.64137 & 0.00119 & Prim &  R  & DK154    \\
 OGLE-SMC-ECL-1407 & 56706.62008 & 0.00212 & Sec  &  R  & DK154    \\
  \hline
 OGLE-SMC-ECL-2186 & 48701.09378 & 0.00523 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-2186 & 48702.98665 & 0.01720 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-2186 & 49550.25484 & 0.00192 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-2186 & 49552.13771 & 0.01594 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-2186 & 49849.77123 & 0.00794 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-2186 & 49851.64007 & 0.02195 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-2186 & 50198.66440 & 0.00176 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-2186 & 50200.50302 & 0.00638 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-2186 & 50550.84602 & 0.00851 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-2186 & 50552.66865 & 0.01982 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-2186 & 50850.36453 & 0.01027 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-2186 & 50852.16776 & 0.00809 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-2186 & 51498.76490 & 0.00206 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-2186 & 51500.54160 & 0.00316 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-2186 & 50748.32719 & 0.00435 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 50750.11970 & 0.00500 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 51699.53127 & 0.00179 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 51701.28957 & 0.00242 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 52199.83143 & 0.00657 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 52201.54632 & 0.00741 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 52575.06110 & 0.00450 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 52576.73683 & 0.00513 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 52923.96294 & 0.00808 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 52925.60931 & 0.00509 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 53299.17085 & 0.00203 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 53300.80791 & 0.00373 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 53651.34727 & 0.00639 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 53652.96525 & 0.00485 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 54000.22926 & 0.00325 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 54001.83984 & 0.00567 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 54349.12883 & 0.00566 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 54350.69183 & 0.00641 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 54800.04630 & 0.00450 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 54801.58628 & 0.00743 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2186 & 56669.56854 & 0.00091 & Prim &  R  & DK154    \\
 OGLE-SMC-ECL-2186 & 56677.58220 & 0.00066 & Sec  &  R  & DK154    \\
   \hline
 OGLE-SMC-ECL-2225 & 48699.87030 & 0.00966 & Prim & B+R & MACHO    \\
  \hline
  \noalign{\smallskip}\hline
\end{tabular}
%Note: * {\it mean value of VR or VRI measurements}
\end{minipage}
\end{table}


\begin{table}
 \centering
  \begin{minipage}{95mm}
 \fontsize{1.8mm}{2.4mm}\selectfont
 \caption{List of the minima timings used for the analysis.}
\begin{tabular}{ccclcl}
\hline\hline\noalign{\smallskip}
 Star       &    JD Hel.- &  Error & Type   &  Filter  & Source /     \\
            &   2400000   &  [day] &        &          & Observatory  \\
\noalign{\smallskip}\hline \noalign{\smallskip}
 OGLE-SMC-ECL-2225 & 48700.45057 & 0.00607 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-2225 & 49550.14572 & 0.00366 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-2225 & 49550.73392 & 0.00506 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-2225 & 49849.97432 & 0.00275 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-2225 & 49850.58771 & 0.00696 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-2225 & 50200.52770 & 0.00631 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-2225 & 50201.12738 & 0.00641 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-2225 & 50549.57873 & 0.01289 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-2225 & 50550.20266 & 0.00979 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-2225 & 50849.39455 & 0.00747 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-2225 & 50850.04827 & 0.00596 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-2225 & 51499.76771 & 0.02076 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-2225 & 51500.44540 & 0.02053 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-2225 & 52199.34712 & 0.00252 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 52200.10630 & 0.01075 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 52575.25680 & 0.00215 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 52576.02555 & 0.00544 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 52924.29983 & 0.00319 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 52925.10071 & 0.00252 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 53300.20601 & 0.00534 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 53301.02592 & 0.00359 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 53649.24349 & 0.00271 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 53650.10421 & 0.00207 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 53999.78851 & 0.00337 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 54000.67118 & 0.00923 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 54350.35287 & 0.00291 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 54351.22518 & 0.00150 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 54799.33928 & 0.00355 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 54800.24310 & 0.00304 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2225 & 56641.62568 & 0.00099 & Prim &  R  & DK154    \\
 OGLE-SMC-ECL-2225 & 56677.43050 & 0.00213 & Prim &  R  & DK154    \\
 OGLE-SMC-ECL-2225 & 56706.66141 & 0.00932 & Sec  &  R  & DK154    \\
 OGLE-SMC-ECL-2225 & 56727.57026 & 0.00856 & Sec  &  R  & DK154    \\
 OGLE-SMC-ECL-2225 & 56739.49729 & 0.00448 & Sec  &  R  & DK154    \\
  \hline
 OGLE-SMC-ECL-2251 & 50750.22871 & 0.01111 & Prim &  I  & OGLE II   \\
 OGLE-SMC-ECL-2251 & 50751.76132 & 0.00909 & Sec  &  I  & OGLE II   \\
 OGLE-SMC-ECL-2251 & 51701.03998 & 0.00534 & Prim &  I  & OGLE II   \\
 OGLE-SMC-ECL-2251 & 51702.49569 & 0.00466 & Sec  &  I  & OGLE II   \\
 OGLE-SMC-ECL-2251 & 52200.98659 & 0.00419 & Prim &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 52202.35316 & 0.00760 & Sec  &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 52574.77804 & 0.00435 & Prim &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 52576.09912 & 0.01312 & Sec  &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 52925.18554 & 0.00564 & Prim &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 52926.45681 & 0.02329 & Sec  &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 53298.99286 & 0.00406 & Prim &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 53300.22628 & 0.02132 & Sec  &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 53649.40932 & 0.00442 & Prim &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 53650.58269 & 0.00382 & Sec  &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 53999.83046 & 0.00299 & Prim &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 54000.94196 & 0.00673 & Sec  &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 54350.26571 & 0.00468 & Prim &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 54351.32752 & 0.03865 & Sec  &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 54801.13489 & 0.00506 & Prim &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 54802.18335 & 0.01739 & Sec  &  I  & OGLE III  \\
 OGLE-SMC-ECL-2251 & 56639.69916 & 0.00113 & Prim &  R  & DK154     \\
 OGLE-SMC-ECL-2251 & 56675.56777 & 0.00287 & Sec  &  R  & DK154     \\
 OGLE-SMC-ECL-2251 & 56689.57815 & 0.00124 & Sec  &  R  & DK154     \\
  \hline
 OGLE-SMC-ECL-2524 & 48749.05117 & 0.00480 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-2524 & 48750.47954 & 0.00177 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-2524 & 49749.07351 & 0.00122 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-2524 & 49750.50676 & 0.00382 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-2524 & 50250.18009 & 0.00171 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-2524 & 50251.61017 & 0.00254 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-2524 & 50749.11909 & 0.00208 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-2524 & 50750.53425 & 0.00654 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-2524 & 51499.69730 & 0.00381 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-2524 & 51501.07663 & 0.00180 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-2524 & 52200.40699 & 0.00311 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 52201.70247 & 0.00847 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 52575.70108 & 0.00258 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 52576.96208 & 0.00417 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 52924.96844 & 0.00138 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 52926.17872 & 0.00242 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 53300.26282 & 0.00111 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 53301.42517 & 0.00349 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 53649.53104 & 0.00122 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 53650.64581 & 0.00225 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 54000.95733 & 0.00455 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 54002.02888 & 0.00174 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 54350.23684 & 0.00791 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 54351.24487 & 0.00204 & Sec  &  I  & OGLE III \\
  \hline
  \noalign{\smallskip}\hline
\end{tabular}
%Note: * {\it mean value of VR or VRI measurements}
\end{minipage}
\end{table}


\begin{table}
 \centering
  \begin{minipage}{95mm}
 \fontsize{1.8mm}{2.4mm}\selectfont
 \caption{List of the minima timings used for the analysis.}
\begin{tabular}{ccclcl}
\hline\hline\noalign{\smallskip}
 Star       &    JD Hel.- &  Error & Type   &  Filter  & Source /     \\
            &   2400000   &  [day] &        &          & Observatory  \\
\noalign{\smallskip}\hline \noalign{\smallskip}
 OGLE-SMC-ECL-2524 & 54799.30059 & 0.00479 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 54800.24413 & 0.00068 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2524 & 56639.65255 & 0.00061 & Sec  &  R  & DK154 \\
 OGLE-SMC-ECL-2524 & 56673.59328 & 0.00059 & Prim &  R  & DK154 \\
 OGLE-SMC-ECL-2524 & 56689.54270 & 0.00350 & Sec  &  R  & DK154 \\
  \hline
 OGLE-SMC-ECL-2534 & 48800.83606 & 0.00410 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-2534 & 48801.88294 & 0.01385 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-2534 & 49799.92570 & 0.00731 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-2534 & 49800.96534 & 0.00873 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-2534 & 50199.53392 & 0.01529 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-2534 & 50200.59122 & 0.00513 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-2534 & 50550.94672 & 0.01128 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-2534 & 50552.00100 & 0.01895 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-2534 & 50849.50052 & 0.00706 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-2534 & 50850.58736 & 0.02162 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-2534 & 51499.48078 & 0.02502 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-2534 & 51500.57635 & 0.01736 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-2534 & 52199.97862 & 0.00262 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 52201.08392 & 0.00473 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 52574.34158 & 0.00194 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 52575.45897 & 0.00952 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 52925.72595 & 0.00185 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 52926.85598 & 0.00211 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 53300.09757 & 0.00093 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 53301.23659 & 0.00496 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 53649.19553 & 0.00172 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 53650.34464 & 0.00781 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 54000.59273 & 0.00031 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 54001.74718 & 0.00343 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 54349.68687 & 0.00154 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 54350.86174 & 0.00322 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 54799.84807 & 0.00475 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-2534 & 54801.03243 & 0.01016 & Sec  &  I  & OGLE III \\
  \hline
 OGLE-SMC-ECL-3594 & 48751.03362 & 0.00612 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-3594 & 48752.73313 & 0.00487 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-3594 & 49651.74109 & 0.00235 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-3594 & 49653.46092 & 0.00449 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-3594 & 49998.15595 & 0.00554 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-3594 & 49999.88282 & 0.00592 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-3594 & 50348.91199 & 0.00310 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-3594 & 50350.65164 & 0.01405 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-3594 & 50652.02791 & 0.00688 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-3594 & 50653.78149 & 0.00711 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-3594 & 50950.81588 & 0.00496 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-3594 & 50952.56833 & 0.00282 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-3594 & 51548.38929 & 0.00442 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-3594 & 51550.18670 & 0.00918 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-3594 & 52202.24613 & 0.00398 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 52204.07478 & 0.00003 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 52574.64781 & 0.00245 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 52576.49461 & 0.00434 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 52925.39286 & 0.00217 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 52927.26649 & 0.00003 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 53302.12389 & 0.00793 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 53304.00261 & 0.00601 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 53648.54075 & 0.00042 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 53650.43839 & 0.00270 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 53999.28473 & 0.00329 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 54001.21997 & 0.00223 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 54350.03062 & 0.00353 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 54351.97934 & 0.00245 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 54800.37520 & 0.00173 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3594 & 54802.34160 & 0.00842 & Sec  &  I  & OGLE III \\
  \hline
 OGLE-SMC-ECL-3677 & 48699.80729 & 0.01272 & Sec  & B+R  & MACHO \\
 OGLE-SMC-ECL-3677 & 48701.90985 & 0.01951 & Prim & B+R  & MACHO \\
 OGLE-SMC-ECL-3677 & 49548.92971 & 0.01937 & Sec  & B+R  & MACHO \\
 OGLE-SMC-ECL-3677 & 49551.04309 & 0.00854 & Prim & B+R  & MACHO \\
 OGLE-SMC-ECL-3677 & 49847.71464 & 0.02852 & Sec  & B+R  & MACHO \\
 OGLE-SMC-ECL-3677 & 49849.81264 & 0.01114 & Prim & B+R  & MACHO \\
 OGLE-SMC-ECL-3677 & 50198.88911 & 0.01522 & Sec  & B+R  & MACHO \\
 OGLE-SMC-ECL-3677 & 50201.00269 & 0.01166 & Prim & B+R  & MACHO \\
 OGLE-SMC-ECL-3677 & 50550.07712 & 0.02286 & Sec  & B+R  & MACHO \\
 OGLE-SMC-ECL-3677 & 50552.19617 & 0.01038 & Prim & B+R  & MACHO \\
 OGLE-SMC-ECL-3677 & 50848.82438 & 0.02664 & Sec  & B+R  & MACHO \\
 OGLE-SMC-ECL-3677 & 50850.97001 & 0.00644 & Prim & B+R  & MACHO \\
 OGLE-SMC-ECL-3677 & 51498.77983 & 0.02237 & Sec  & B+R  & MACHO \\
 OGLE-SMC-ECL-3677 & 51500.92187 & 0.00895 & Prim & B+R  & MACHO \\
 OGLE-SMC-ECL-3677 & 52201.14249 & 0.01502 & Sec  &  I   & OGLE III \\
 OGLE-SMC-ECL-3677 & 52203.31297 & 0.00469 & Prim &  I   & OGLE III \\
 OGLE-SMC-ECL-3677 & 52573.27233 & 0.00763 & Sec  &  I   & OGLE III \\
 OGLE-SMC-ECL-3677 & 52575.46868 & 0.00569 & Prim &  I   & OGLE III \\
  \hline
  \noalign{\smallskip}\hline
\end{tabular}
\end{minipage}
\end{table}

\begin{table}
 \centering
  \begin{minipage}{95mm}
 \fontsize{1.8mm}{2.4mm}\selectfont
 \caption{List of the minima timings used for the analysis.}
\begin{tabular}{ccclcl}
\hline\hline\noalign{\smallskip}
 Star       &    JD Hel.- &  Error & Type   &  Filter  & Source /     \\
            &   2400000   &  [day] &        &          & Observatory  \\
\noalign{\smallskip}\hline \noalign{\smallskip}
 OGLE-SMC-ECL-3677 & 52924.45135 & 0.00696 & Sec  &  I   & OGLE III \\
 OGLE-SMC-ECL-3677 & 52926.65837 & 0.00648 & Prim &  I   & OGLE III \\
 OGLE-SMC-ECL-3677 & 53301.81466 & 0.01272 & Sec  &  I   & OGLE III \\
 OGLE-SMC-ECL-3677 & 53304.07030 & 0.00956 & Prim &  I   & OGLE III \\
 OGLE-SMC-ECL-3677 & 53647.75372 & 0.01490 & Sec  &  I   & OGLE III \\
 OGLE-SMC-ECL-3677 & 53650.01979 & 0.00356 & Prim &  I   & OGLE III \\
 OGLE-SMC-ECL-3677 & 53998.92989 & 0.01257 & Sec  &  I   & OGLE III \\
 OGLE-SMC-ECL-3677 & 54001.21811 & 0.00470 & Prim &  I   & OGLE III \\
 OGLE-SMC-ECL-3677 & 54350.11175 & 0.01169 & Sec  &  I   & OGLE III \\
 OGLE-SMC-ECL-3677 & 54352.39886 & 0.00198 & Prim &  I   & OGLE III \\
 OGLE-SMC-ECL-3677 & 54800.87834 & 0.00487 & Sec  &  I   & OGLE III \\
 OGLE-SMC-ECL-3677 & 54803.18740 & 0.00587 & Prim &  I   & OGLE III \\
  \hline
 OGLE-SMC-ECL-3951 & 50548.54640 & 0.00520 & Prim &  I  & OGLE II \\
 OGLE-SMC-ECL-3951 & 50550.20977 & 0.00469 & Sec  &  I  & OGLE II \\
 OGLE-SMC-ECL-3951 & 51101.11593 & 0.00465 & Prim &  I  & OGLE II \\
 OGLE-SMC-ECL-3951 & 51102.74425 & 0.00397 & Sec  &  I  & OGLE II \\
 OGLE-SMC-ECL-3951 & 51700.25361 & 0.00386 & Prim &  I  & OGLE II \\
 OGLE-SMC-ECL-3951 & 51701.88334 & 0.00627 & Sec  &  I  & OGLE II \\
 OGLE-SMC-ECL-3951 & 52200.06093 & 0.00382 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 52201.66655 & 0.00436 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 52575.68577 & 0.00775 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 52577.27291 & 0.00530 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 52926.47673 & 0.00762 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 52928.03171 & 0.00860 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 53298.99469 & 0.00262 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 53300.53536 & 0.00247 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 53649.79107 & 0.00178 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 53651.30663 & 0.00770 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 54000.58489 & 0.00707 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 54002.10747 & 0.00979 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 54351.38258 & 0.00162 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 54352.86482 & 0.00654 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 54801.52124 & 0.00479 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-3951 & 54802.98917 & 0.01250 & Sec  &  I  & OGLE III \\
  \hline
 OGLE-SMC-ECL-4955 & 48750.12518 & 0.00631 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-4955 & 48751.38801 & 0.02229 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-4955 & 49651.08861 & 0.00532 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-4955 & 49652.33413 & 0.03385 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-4955 & 50000.39638 & 0.00395 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-4955 & 50001.62993 & 0.02874 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-4955 & 50349.71256 & 0.00389 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-4955 & 50350.87651 & 0.01422 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-4955 & 50649.11491 & 0.00313 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-4955 & 50650.25954 & 0.01288 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-4955 & 50951.29501 & 0.00429 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-4955 & 50952.44016 & 0.01871 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-4955 & 51550.09921 & 0.00687 & Prim & B+R & MACHO \\
 OGLE-SMC-ECL-4955 & 51551.18926 & 0.01608 & Sec  & B+R & MACHO \\
 OGLE-SMC-ECL-4955 & 52198.83073 & 0.00972 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 52199.82288 & 0.00238 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 52575.85660 & 0.00253 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 52576.84703 & 0.00743 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 52925.15650 & 0.00209 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 52926.11742 & 0.00000 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 53299.40496 & 0.00020 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 53300.35027 & 0.00720 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 53651.48950 & 0.00772 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 53652.42259 & 0.00203 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 54000.79736 & 0.00435 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 54001.70010 & 0.00418 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 54350.10388 & 0.00792 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 54350.99198 & 0.00293 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 54799.20041 & 0.00141 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-4955 & 54800.08989 & 0.00558 & Sec  &  I  & OGLE III \\
  \hline
 OGLE-SMC-ECL-5233 & 52198.73233 & 0.00798 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 52201.92612 & 0.00000 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 52573.81356 & 0.00377 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 52576.99968 & 0.00250 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 52923.55994 & 0.01665 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 52926.74636 & 0.00955 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 53298.63156 & 0.00478 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 53301.76315 & 0.00548 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 53648.41252 & 0.03105 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 53651.42894 & 0.00478 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 53998.17633 & 0.01331 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 54001.10599 & 0.00849 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 54347.97205 & 0.00515 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 54350.74730 & 0.01452 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 54799.11105 & 0.02745 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 54801.71854 & 0.00803 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5233 & 48747.75771 & 0.02284 & Prim & B+R & MACHO    \\
  \hline
  \noalign{\smallskip}\hline
\end{tabular}
\end{minipage}
\end{table}

\begin{table}
 \centering
  \begin{minipage}{95mm}
 \fontsize{1.8mm}{2.4mm}\selectfont
 \caption{List of the minima timings used for the analysis.}
\begin{tabular}{ccclcl}
\hline\hline\noalign{\smallskip}
 Star       &    JD Hel.- &  Error & Type   &  Filter  & Source /     \\
            &   2400000   &  [day] &        &          & Observatory  \\
\noalign{\smallskip}\hline \noalign{\smallskip}
 OGLE-SMC-ECL-5233 & 48749.89493 & 0.01255 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-5233 & 49751.21107 & 0.01683 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-5233 & 49753.48924 & 0.01297 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-5233 & 50247.75172 & 0.03015 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-5233 & 50250.30258 & 0.00997 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-5233 & 50749.41555 & 0.00521 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-5233 & 50752.16203 & 0.01977 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-5233 & 51499.37910 & 0.01377 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-5233 & 51502.33500 & 0.00936 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-5233 & 56669.66164 & 0.00089 & Prim &  R  & DK154    \\
 OGLE-SMC-ECL-5233 & 56676.65528 & 0.00095 & Sec  &  R  & DK154    \\
  \hline
 OGLE-SMC-ECL-5422 & 48701.27481 & 0.00746 & Prim & B+R & MACHO1+2 \\
 OGLE-SMC-ECL-5422 & 48702.82150 & 0.02491 & Sec  & B+R & MACHO1+2 \\
 OGLE-SMC-ECL-5422 & 49549.49972 & 0.01280 & Prim & B+R & MACHO1+2 \\
 OGLE-SMC-ECL-5422 & 49551.05868 & 0.00682 & Sec  & B+R & MACHO1+2 \\
 OGLE-SMC-ECL-5422 & 49850.48551 & 0.00818 & Prim & B+R & MACHO1+2 \\
 OGLE-SMC-ECL-5422 & 49852.05883 & 0.00491 & Sec  & B+R & MACHO1+2 \\
 OGLE-SMC-ECL-5422 & 50200.10518 & 0.00840 & Prim & B+R & MACHO1+2 \\
 OGLE-SMC-ECL-5422 & 50201.70786 & 0.01002 & Sec  & B+R & MACHO1+2 \\
 OGLE-SMC-ECL-5422 & 50549.72721 & 0.00918 & Prim & B+R & MACHO1+2 \\
 OGLE-SMC-ECL-5422 & 50551.35470 & 0.00736 & Sec  & B+R & MACHO1+2 \\
 OGLE-SMC-ECL-5422 & 50850.70503 & 0.00509 & Prim & B+R & MACHO1+2 \\
 OGLE-SMC-ECL-5422 & 50852.35616 & 0.00474 & Sec  & B+R & MACHO1+2 \\
 OGLE-SMC-ECL-5422 & 51501.30424 & 0.01298 & Prim & B+R & MACHO1+2 \\
 OGLE-SMC-ECL-5422 & 51502.98810 & 0.00716 & Sec  & B+R & MACHO1+2 \\
 OGLE-SMC-ECL-5422 & 50549.70892 & 0.00210 & Prim &  I  & OGLE II  \\
 OGLE-SMC-ECL-5422 & 50551.35676 & 0.00230 & Sec  &  I  & OGLE II  \\
 OGLE-SMC-ECL-5422 & 51099.98977 & 0.00336 & Prim &  I  & OGLE II  \\
 OGLE-SMC-ECL-5422 & 51101.66027 & 0.00092 & Sec  &  I  & OGLE II  \\
 OGLE-SMC-ECL-5422 & 51698.90939 & 0.00154 & Prim &  I  & OGLE II  \\
 OGLE-SMC-ECL-5422 & 51700.61184 & 0.00215 & Sec  &  I  & OGLE II  \\
 OGLE-SMC-ECL-5422 & 52200.54217 & 0.00385 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 52202.27954 & 0.00557 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 52574.48865 & 0.00266 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 52576.25467 & 0.00306 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 52924.11355 & 0.00205 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 52925.89530 & 0.00320 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 53301.10369 & 0.00275 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 53302.89816 & 0.00329 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 53650.71277 & 0.00982 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 53652.53418 & 0.00438 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 54000.35282 & 0.00120 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 54002.17710 & 0.00006 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 54349.98870 & 0.00116 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 54351.81853 & 0.00001 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 54799.94233 & 0.00889 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5422 & 54801.77785 & 0.00402 & Sec  &  I  & OGLE III \\
  \hline
 OGLE-SMC-ECL-5434 & 48798.94606 & 0.01483 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-5434 & 48800.47699 & 0.00603 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-5434 & 49800.72760 & 0.00678 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-5434 & 49802.25181 & 0.01099 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-5434 & 50199.12527 & 0.01339 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-5434 & 50200.65017 & 0.00750 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-5434 & 50551.33912 & 0.00586 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-5434 & 50552.84222 & 0.01509 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-5434 & 50848.71070 & 0.00518 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-5434 & 50850.18788 & 0.01259 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-5434 & 51501.15782 & 0.00807 & Prim & B+R & MACHO    \\
 OGLE-SMC-ECL-5434 & 51502.62719 & 0.02513 & Sec  & B+R & MACHO    \\
 OGLE-SMC-ECL-5434 & 50551.33644 & 0.00503 & Prim &  I  & OGLE II  \\
 OGLE-SMC-ECL-5434 & 50552.82479 & 0.00705 & Sec  &  I  & OGLE II  \\
 OGLE-SMC-ECL-5434 & 51099.85925 & 0.02141 & Prim &  I  & OGLE II  \\
 OGLE-SMC-ECL-5434 & 51101.33185 & 0.01155 & Sec  &  I  & OGLE II  \\
 OGLE-SMC-ECL-5434 & 51700.34958 & 0.00445 & Prim &  I  & OGLE II  \\
 OGLE-SMC-ECL-5434 & 51701.82145 & 0.00903 & Sec  &  I  & OGLE II  \\
 OGLE-SMC-ECL-5434 & 52199.81176 & 0.00436 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 52201.23825 & 0.00482 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 52575.12842 & 0.00442 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 52576.53465 & 0.00466 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 52924.44326 & 0.00311 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 52925.84853 & 0.00567 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 53299.75304 & 0.00310 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 53301.15126 & 0.00369 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 53649.08118 & 0.00282 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 53650.46107 & 0.00647 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 54001.28546 & 0.00260 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 54002.65242 & 0.00208 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 54350.61859 & 0.00245 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 54351.97724 & 0.00573 & Sec  &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 54800.98529 & 0.00261 & Prim &  I  & OGLE III \\
 OGLE-SMC-ECL-5434 & 54802.33139 & 0.00413 & Sec  &  I  & OGLE III \\
 \hline
\noalign{\smallskip}\hline
\end{tabular}
\end{minipage}
\end{table}


\end{appendix}
\end{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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