Leiden University Student Repository

Pranger, A (4511)

Period determination of variable sources from Gaia DR3 using the nonuniform discrete Fourier transform

Bachelor thesis | Wiskunde (BSc)

There are many different classes of variable astrophysical sources (which have a luminosity that varies over time), all having a certain physical phenomenon causing their variability. This results in different characteristic light curves, often containing periodicities within certain ranges of frequencies. The Gaia satellite telescope has gathered photometric data of variable sources, at semi-random nonuniform observation times, influenced by the Gaia scanning law. This research aims to use the nonuniform fast Fourier transform (NUFFT) to retrieve the main frequency of the brightness variations of the variable source from the photometric Gaia Data Release 3 data, where it is assumed that the underlying signal has one main frequency. The main goals are to investigate whether the frequency with maximal power in the NUFFT periodogram is the main frequency of the underlying signal and whether it is possible to distinguish between in this way correctly and incorrectly determined...Show moreThere are many different classes of variable astrophysical sources (which have a luminosity that varies over time), all having a certain physical phenomenon causing their variability. This results in different characteristic light curves, often containing periodicities within certain ranges of frequencies. The Gaia satellite telescope has gathered photometric data of variable sources, at semi-random nonuniform observation times, influenced by the Gaia scanning law. This research aims to use the nonuniform fast Fourier transform (NUFFT) to retrieve the main frequency of the brightness variations of the variable source from the photometric Gaia Data Release 3 data, where it is assumed that the underlying signal has one main frequency. The main goals are to investigate whether the frequency with maximal power in the NUFFT periodogram is the main frequency of the underlying signal and whether it is possible to distinguish between in this way correctly and incorrectly determined frequencies. To this end a simulation of photometric data is used, where the time series are taken from actual Gaia DR3 data and the signal is simulated as a sine wave with a known frequency and a signal to noise equal to 5. Taking the frequency with maximal power from the corresponding periodograms results in a correct retrieval in about 90% of the simulated cases. A positive correlation between the number of data 4 points or visibility periods and the fraction of correctly determined frequencies is found. The incorrectly determined frequencies are most likely caused by spurious periods or aliasing. Furthermore, a method to compute a false alarm probability (FAP) for the determined frequency was investigated, but turned out to give no useful results as almost all FAPs were equal to zero. Therefore, further research on other methods is necessary to find out how to correctly identify the main frequencyShow less

Author

Pranger, A

Faculty

Faculty of Science

Supervisors

Brown, A.G.A.
Gaans, O.W. van

ECTS Credits

24

Language

en