Multiple and changing cycles of active stars: I. Methods of analysis and application to the solar cycles

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Abstract

Context. Long-term observational data have information on the magnetic cycles of active stars and that of the Sun. The changes in the activity of our central star have basic effects on Earth, such as variations in the global climate, so that understanding the nature of these variations is extremely important. Aims. The observed variations related to magnetic activity cannot be treated as stationary periodic variations, therefore methods like Fourier transform or different versions of periodograms only give partial information on the nature of the light variability. We demonstrate that time-frequency distributions provide useful tools for analysing the observations of active stars.Methods. We tested and used different methods, such as short-term Fourier transform, wavelet, and generalised time-frequency distributions, for analysing temporal variations in timescales of observational data.Results. With test data we demonstrate that the observational noise has practically no effect on the determination in the long-term changes of time-series observations of active stars. The rotational signal may modify the determined cycles, therefore it is advisable to remove it from the data. Wavelets are less powerful in recovering complex long-term changes than other distributions that are discussed. By applying our technique to the sunspot data we find a complicated, multi-scale evolution in the solar activity.

Original languageEnglish
Pages (from-to)695-702
Number of pages8
JournalAstronomy and Astrophysics
Volume501
Issue number2
DOIs
Publication statusPublished - Jul 2009

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solar cycles
solar cycle
stars
cycles
frequency distribution
long-term change
wavelet
Fourier transform
calculus of variations
sunspots
solar activity
wavelet analysis
climate
periodic variations
sunspot
global climate
temporal variation
analysis
method
time series

Keywords

  • Methods: Data analysis
  • Sun: Activity

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

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title = "Multiple and changing cycles of active stars: I. Methods of analysis and application to the solar cycles",
abstract = "Context. Long-term observational data have information on the magnetic cycles of active stars and that of the Sun. The changes in the activity of our central star have basic effects on Earth, such as variations in the global climate, so that understanding the nature of these variations is extremely important. Aims. The observed variations related to magnetic activity cannot be treated as stationary periodic variations, therefore methods like Fourier transform or different versions of periodograms only give partial information on the nature of the light variability. We demonstrate that time-frequency distributions provide useful tools for analysing the observations of active stars.Methods. We tested and used different methods, such as short-term Fourier transform, wavelet, and generalised time-frequency distributions, for analysing temporal variations in timescales of observational data.Results. With test data we demonstrate that the observational noise has practically no effect on the determination in the long-term changes of time-series observations of active stars. The rotational signal may modify the determined cycles, therefore it is advisable to remove it from the data. Wavelets are less powerful in recovering complex long-term changes than other distributions that are discussed. By applying our technique to the sunspot data we find a complicated, multi-scale evolution in the solar activity.",
keywords = "Methods: Data analysis, Sun: Activity",
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T2 - I. Methods of analysis and application to the solar cycles

AU - Kolláth, Z.

AU - Oláh, K.

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N2 - Context. Long-term observational data have information on the magnetic cycles of active stars and that of the Sun. The changes in the activity of our central star have basic effects on Earth, such as variations in the global climate, so that understanding the nature of these variations is extremely important. Aims. The observed variations related to magnetic activity cannot be treated as stationary periodic variations, therefore methods like Fourier transform or different versions of periodograms only give partial information on the nature of the light variability. We demonstrate that time-frequency distributions provide useful tools for analysing the observations of active stars.Methods. We tested and used different methods, such as short-term Fourier transform, wavelet, and generalised time-frequency distributions, for analysing temporal variations in timescales of observational data.Results. With test data we demonstrate that the observational noise has practically no effect on the determination in the long-term changes of time-series observations of active stars. The rotational signal may modify the determined cycles, therefore it is advisable to remove it from the data. Wavelets are less powerful in recovering complex long-term changes than other distributions that are discussed. By applying our technique to the sunspot data we find a complicated, multi-scale evolution in the solar activity.

AB - Context. Long-term observational data have information on the magnetic cycles of active stars and that of the Sun. The changes in the activity of our central star have basic effects on Earth, such as variations in the global climate, so that understanding the nature of these variations is extremely important. Aims. The observed variations related to magnetic activity cannot be treated as stationary periodic variations, therefore methods like Fourier transform or different versions of periodograms only give partial information on the nature of the light variability. We demonstrate that time-frequency distributions provide useful tools for analysing the observations of active stars.Methods. We tested and used different methods, such as short-term Fourier transform, wavelet, and generalised time-frequency distributions, for analysing temporal variations in timescales of observational data.Results. With test data we demonstrate that the observational noise has practically no effect on the determination in the long-term changes of time-series observations of active stars. The rotational signal may modify the determined cycles, therefore it is advisable to remove it from the data. Wavelets are less powerful in recovering complex long-term changes than other distributions that are discussed. By applying our technique to the sunspot data we find a complicated, multi-scale evolution in the solar activity.

KW - Methods: Data analysis

KW - Sun: Activity

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