Because of poor weather conditions and unexpected instrumental problems the 1998 campaign was finished slightly earlier than planned in August 1998. The final number of observations including both campaigns was less than originally expected: a total of 76 good quality nights with an average of 35 observations per window. Even if the data is good enough for the discovery of variables, this has limited our analysis of the variables found (see below).

When we finished all the analysis with the *Class32*
program, we had finally obtained data from
124976 objects in the 12 databases. The AlarmFlag
of each object was checked and the stars
that presented a significant variation (sufficient
number of observations, reasonable photometric
errors, large magnitude variations, etc.)
selected. The total number of objects per window
and number of variables found are in Table 5.

Among the variables we have found (see the complete listings in Appendix B), a major subset shows hints of periodic variations. However, if we do not have clear evidence to say that the star is periodic, its classification is highly compromised. As stressed before, the main problem is that we do not have as yet chromatic/spectral information about the objects. Since the variable classes are defined mainly by the spectral characteristics (especially in the case of aperiodic variable stars), the study of the individual stars given in the Appendix B is a natural and necessary next step. It should be remarked that the temporal covering of our data is not (generally speaking) broad enough to affirm whether a given star that does not show periodic variations is actually aperiodic.

In the case of the stars with hints of periodic light curves it is important to estimate the period (or periods) for a tentative classification. Several algorithms to perform period calculation exist, of which the Fourier method is the most popular. However, as is well-known, the Fourier method works with equally-spaced points from a temporal series, which is never the case for astronomical measures. Many authors (see, for example, Cuypers 1987) have developed a modified Fourier analysis for non-equally-spaced points. These works have generally resulted in computational time-consuming algorithms. In our analysis we have adopted a new method (the minimum entrophy method), developed by Cincotta et al. (1995).

This method is based on the minimization of the information entropy for the true period(s). The rigorous mathematical formulation can be found in Cincotta et al. (1996), for example. We will briefly describe the method.

Consider a temporal
series (*u*(*t*_{i})) and the set of periods to test *p*_{j} (*j* =
1,...,*n*).
According to
Cincotta et al. (1995)
we have calculated the phase of the
temporal
series and created a unitary
(normalized) plane ,where is the phase.
For each trial period *p*_{j}, the light curve has been constructed and
distributed
in plane, that is divided in an arbitrary number (*N*) of
partitions.
The next step was to calculate the probability () for a point
to fall
in one partition, dividing the number of points in each partition by the
total number of points in the temporal series. Finally we have computed
the
entropy as

(8) |

The method works very well when the light curve is sufficiently sampled
(empirically, points for the period determination
to be strictly independent of the partition
number (*N*)). This is not quite the case of our databases,
although the actual number of points is not too low
in some cases. Thus,
the application of the method remains
feasible, but noisier *S* vs. *p*_{j} diagrams are obtained.
On the other hand, the computing processing time is less
time-consuming than the modified Fourier analysis and, in principle, we
believed
suitable for our extensive databases
(see discussion below). Another well-known
problem is the presence of
the harmonics, which can cause some confusion when we have few points.

Simulations and comparisons between minimum entropy and modified Fourier analysis were performed by Cincotta et al. (1995). Their tests showed that the minimum entropy method is more efficient for the resolution of multiple periods than the Fourier analysis. However, the accuracy of the estimated periods are not known yet and we intend to collaborate with the development of the method with its massive application to our databases. A comparison between several methods to determine periods present in our data will be the subject of a future study.

For simplicity, we consider that
the stars have only one period. We shall present some examples from our
databases to see how this
works and evaluate the results. As we say before, the method is independent of
the partition number when the series is well sampled, this isn't our case and,
for each star, the calculations
were done for several configurations of parameters,
varying the number of partition (*N*) and trial
period interval. We considered a period
as found when the minimum persisted for all tried configuration
(the differences between minima in each configuration
are in the less significative digits).

The star LI471 is a W Virginis previously identified,
and belonging to GCVS (General Catalogue of
Variable Stars,
Khopolov et al. 1988),
with an attributed
11.49 days period. The light
curve of the star (with our data)
can be seen in Fig. 6.
Figure 5 shows the *S* vs. *p*_{j} diagram for that
star which is noisy as expected.
Nevertheless, the minimum we have obtained
by applying the minimum entropy method is 11.50 days, consistent with
the
catalogued
value. This example shows that, in spite of the noise, accurate
determinations are possible in an efficient form.

Figure 7:
S vs. p_{j} diagram for the star LA1552, classified
as
a Mira. The estimated period is 323.2 days |

Besides the problem of the scarcity of the points, our photometric
errors
are quite large, which in turn
provokes more noise in the diagrams. As a result of the analysis we have
checked
that the determination of small periods is
easier and more reliable than the determination of large periods (like
Miras).
This fact is closely related to the definition of the phase
(see
Cincotta et al. 1995)
which is inversely proportional to the period.
To give an example, we discuss the star LA1552, not known before and
preliminary classified as a Mira, which
reflects this difficulty very well (the light curve
can be seen is Fig. 9). Figure 7 shows the *S* vs. *p*_{j}
diagram. We estimate the period in 323.2 days, but in this case the
method is
more dependent on the number the partitions.

As a further example of the capability of the method
to find periods smaller
than 1 day, we show the case of BJ878, a RR Lyrae star already known
and belonging to
GCVS (Fig. 10). The catalogued period is 0.37 days and our best
estimation was
0.33 days. Figure 8 shows the *S* vs. *p*_{j} diagram, with
a well resolved minimum. In fact, it is not impossible that the
catalogued period has to be corrected if further studies confirm
the present value.

Even in cases where periodicity is suggested by the data, we have not been able to determine period for all those candidate stars. Some of them have so few points that it was impossible to draw a reliable conclusion. These stars are indicated with "NC" (not calculated) in the nineth column in the catalogue presented in Appendix B. The stars that we believe to be periodic, but for which a period could not be reliably found, are indicated with "NF" (not found) in the same column.

To perform a preliminary variable star classification, we
have based our judgement on:

- The available periods as calculated with the minimum entropy method;
- The observed amplitude of variations;
- The shape of light curves, which have been compared to the observed for variables already existing in the GCVS;
- The variable classes that we expected a priori among the monitored stars, as described in the Introduction.

All stars positions were compared with the ones of the variable objects belonging to the GCVS and NSV (New Suspected Variables, Kukarkin et al. 1982) catalogues and to those of the SIMBAD database using WWW interface. Among the 479 stars that showed significant light variations found in our database, only 16 were already present in other catalogues (including the IRAS catalog (Beichman et al. 1988), the work of Hazen (1996) on the variables in NGC 6558 (in the center of BE window), the CCDM (Catalog of Double and Multiple stars) by Dommange (1983), besides the quoted GCVS and NSV catalogues). Therefore, 96.7% of the variables in the new databases were unknown until now.

Considering our limitations, we restricted the classification
of our variables to four broad classes *defined* as:

- Mira-type variables: stars with period greater than 80 days, amplitude of the variation greater than 2.5 magnitudes (approximately), and light curves alike BG1159 (Fig. 11, Appendix A), a Mira already present in GCVS;
- Semi-regular-type variables: stars with periods greater than 80 days and light curves alike the Miras, but with amplitude variation smaller than 2.5 magnitudes;
- Cepheid-type variables: stars with periods between 1 and 50 days, (approximately), and mean amplitude variations of 0.9 magnitudes. The differentiation between classical cepheids, that populate the galactic discs, and W Virginis (or type II cepheids), that are present among the older population (halo, bulge), is possible only with the knowledge of morphological differences in their light curves. Since we are not sensitive to these details, we have classified these stars as "cepheids" without attempting a finer discrimination;
- RR Lyrae-type variables: stars with periods between 0.2 and 1 day and light variations of about 1 magnitude. Among the known sub-types RRc stars have periods between 0.2 and 0.5 days and amplitude of 0.5 magnitudes. Their light curves have senoidal shapes. The RRab have periods between 0.4 and 1 day, with amplitudes up to 1 magnitude, and their light curves are asymmetric. Again, we are not sensitive to shape details of the light curves and thus labeled these stars generically as "RR Lyrae".

The result of this analysis can be appreciated in the tenth column of the tables in Appendix B, which constitutes our very preliminary classification of the variable stars and serves as a starting point for more comprehensive studies of these objects.

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