5 Searching for variable stars

To organize and analyze such an amount of data is not a trivial work, especially if the final goal is to investigate the presence of variable objects in the monitored regions in real time.

A program called Class32 was developed by us to handle the huge volume of data. Basically the program constructs a database for each investigated window, where a main table contains mean information about all objects already detected, and an individual record for each object as well. In the main table we record

• A sequential numerical identification;
• The mean value of the right ascension;
• The mean value of the declination;
• The standard deviations corresponding to right ascension and declination;
• The mean differential magnitude;
• Standard deviation of the mean differential magnitude;
• The number of times that the object was detected;
• A Flag that indicates the confidence of the identification;
• Gregorian date of the last observation;
• A second flag (hereafter, AlarmFlag) that warns if the object suffered light variations and in how many days.

The individual table for each object contains (for each night):

• Gregorian observation date;
• The calculated right ascension;
• The calculated declination;
• Differential magnitude with respect to the reference set;
• The magnitude error;
• The AlarmFlag;
• Apparent magnitude;
• Julian Date of the observation.

Now, we will describe in more detail the contents of the tables. The inputs of this program are the positions values (right ascension in hours, declination in degrees), differential magnitude, magnitude, the respective errors and the Julian Date. For a given night, the input positions of the detected stars are compared with the mean values available in the main table. The first criterion for identification is that the centroid falls within the same pixel.

The second criterion, useful for the confirmation of the identification is

$$\bar{x} + {\rm d}\bar{x} \gt x - {\rm d}x$$ (2)

$$\bar{x} - {\rm d}\bar{x} \gt x + {\rm d}x$$ (3)

for the right ascension and declination, where $\bar{x}$ and ${\rm d}\bar{x}$indicate the mean value and its error and x and ${\rm d}x$ are the night values. The criterion of Eqs. (2, 3) verifies if the last measurement, allowing for the error, is inside the region delimited by the mean value, calculated from the previous nights, plus one standard deviation.

After the identification, the program makes a series of hierarchical tests to verify if the object presents light variations. The first test is somewhat arbitrary and connected with the variations that we consider easily measurable by our project

$$\left\vert{\bar{m} - m}\right\vert \gt 0.3$$ (4)

where $\bar{m}$ is the mean differential magnitude.

The next test, which is applied only if the star satisfies Eq. (4), is more refined and compares the night measurement with the mean value, taking into account the standard deviation of the mean differential magnitude (${\rm d}\bar{m}$)

$$m \gt \bar{m} + n{\rm d}\bar{m}$$ (5)

$$m < \bar{m} - n{\rm d}\bar{m}$$ (6)

where n = 3 was adopted after extensive testing of the method.

The last test, which is applied only if the star passed through the tests of Eqs. (5, 6), takes into account the "instantaneous" error of that particular night and reads

$$\left\vert{m - \bar{m}}\right\vert < \left\vert{{\rm d}m}\right\vert + \left\vert{{\rm d}\bar{m}}\right\vert .$$ (7)

Even if the star satisfies the criterion of Eq. (4) only, the program registers an alarm (the AlarmFlag). Our experience shows that stars passing only in the first criteria are those near the detection limit and have large photometric errors. Most of the stars that show a real (and reliable) variable behavior have passed through all criteria.

As a test of the performance of the Class32 program and with the aim of verifying our actual observational capabilities, we have observed the microlensing event 97-BLG-56, detected by the MACHO group, as a target-of-opportunity. Since the star was known to vary and other groups were monitoring it, a comparison and evaluation of the actual behavior of the devised variability criteria was possible in a quite accurate form. We obtained 16 good quality frames of the event. The reduction was made of the standard way but, since the field does not belong to any of the monitored fields, we had to calculate the differential magnitude with respect to the available Tycho stars in the same field, subtracting the stars brighter than $m_{\rm Val}=8.5$ and those having a Tycho quality index worse than 5 (see Paper I).

The identification of the ongoing event in the database was successful and the program gave the expected alarm in 11 consecutive nights. The light curve of the event can be seen in Fig. 4, where our data was superimposed to the OGLE I filter measurements (Udalski et al. 1997). Our data, and the subsequent analysis of the 97-BLG-56 will be the subject of a future paper.

  

Figure 4: Comparison between our observations (in $V_{\rm Val}$ filter) and OGLE data (I filter, taken from Udalski et al. 1997). The axes indicate the difference between the stationary value of the magnitude (m) and the night measure during the amplification (m(t)), versus the Julian Date

Real time processing of the data, though being the ultimate goal of the programme, was not indeed possible in this first stage of the project. The Class32 is still under development and presently the time it takes for a full processing of one night is greater than expected. We will discuss the future modifications in our analysis methods in the last section.