The main reason to calculate the completeness of our dataset is to study the possible star formation histories of the dwarf galaxies. In addition we decided to use it for a study of the characteristics of the algorithms used for the period search.
The simulations were carried out for 5 different amplitudes between 0.2 and 1.8 magnitudes peak to peak variation, 1500 periods with a constant spacing and 81 mag- nitudes in the range between 16 and 24 mag. Each variable was created with 10 differ- ent phases and the result were averaged. We decided not to treat the phase as a major parameter like period and magnitude. The phases of the real variables can safely as- sumed to be randomly distributed, so the analysis of their influence on the detection probability yields no scientific value. Using these parameters a large number of artifi- cial variables were distributed over the image area.
Considering the massive amount of time needed to create the artificial sources for each combination of amplitude, period, magnitude and phase in each epochs image and then running the whole difference imaging and variability detection pipeline, using two different period search algorithms, we decided to use a different approach.
We apply three criteria to detect a variable source in our dataset, namely threshold in the variation mask, a positional coincidence with a detected source in the respective DAOPHOT catalog and, finally, the period detection algorithm.
5.2. THE TECHNICAL IMPLEMENTATION 53
To reduce the needed computational time and to avoid unneeded reiteration of iden- tical detection checks on both period detection algorithms, the different criteria were tested independently. This approach allows an autonomous evaluation of the effects the different tests have on the total completeness of the dataset.
5.2.1 Generation of the light-curves
Instead of assembling the light-curves and then creating the artificial sources in all images we deemed it more efficient to first create a sample of stellar sources with varying brightnesses in all the images and later use this data to assemble the light- curves.
To accomplish this copies of the reference PSF star, with its flux scaled to the cor- responding magnitude were placed in the individual images. These artificial sources were arranged on a set of four regular position grids and these grids were shifted with respect to each other. This process was done in several separate steps to avoid overlap between the different artificial sources. Each source was added onto the observed im- age to preserve the noise already present in the image. The difference imaging pipeline was run on the so prepared images and the values and errors extracted. The resulting three dimensional data-cube served as the basis for the different completeness simula- tions.
First the artificial light-curve was calculated assuming a cosine, as this provides a reasonable approximation of an LPV light-curve. Applying the relevant values for mean magnitude, amplitude, period and phase the magnitudes of the source at our dates of observation were derived. These magnitudes were then translated into their corresponding values after the application of the difference imaging pipeline using the artificial data-cube.
This approach allows the generation of arbitrary light-curves without the need to run the time-consuming difference imaging each time.
5.2.2 Variation mask completeness
As laid out in Sec.4.1the candidates for variable sources are selected using a threshold on a variation mask. This mask is created by summing, for each pixel, the number of epochs for which the pixel values in the difference image is larger than its error n- times. This selection criterion adds another possible source of incompleteness in the resulting catalog of variable sources.
To test the completeness of the detection on the variation mask, the different light- curves were assembled and the number of epochs with a value larger the the associated errorn-times counted. This number was compared with the needed threshold and the completeness derived.
5.2.3 DAOPHOT completeness
The completeness of the DAOPHOT detections was determined by adding artificial sources to the reference image used for the actual DAOPHOT photometry, again copy- ing the reference star PSF and rescaling it to the respective magnitude. FIND,PHOT
and ALLSTARwere run on the resulting image and the artificial object searched in
the output sourcelists. To consider an artificial source as recovered by DAOPHOT a positional coincidence within 1.5 pixel radius and a measured magnitude within 0.75 magnitudes of the magnitude of the artificial source were required. This procedure was repeated using the same positions and the same magnitude range as applied during the generation of the data-cube.
5.2.4 Period search completeness
The most critical as well as the most restrictive completeness is the the one of the algo- rithm to identify a periodic light-curve for the candidates. For the tests the difference image values corresponding to the magnitudes of the artificial light-curves were fed into the detection algorithm and the result compared with the respective thresholding parameters.
It should be kept in mind that this result gives only the probability that the detection algorithm flags the candidate as a source with a possible periodic signal. This test excludes the additional step applied in the standard pipeline, where the resulting light- curve is assessed for its credibility by eye. Considering the number of iteration needed for the simulation, applying this test would not be reasonable. It can be argued that this test is not needed, the simulations give a measurement of the percentage that can be recovered from the dataset in an ideal case.