Oscillations in hot coronal plasma

1
Oscillations in hot coronal plasma

• The search has been driven by wave-based coronal
  heating theories.
• Few consistent observations in hot material prior
  to 1998.
• EIT and TRACE imaging - 1998, 1999, 2000 - new
  oscillations found.
• SUMER spectroscopy 2002 - MHD wave mode
  conclusively identified.

2
Other methods (1)

• Lomb-Scargle periodogram (Lomb 1976 Scargle
  1982) - good for unevenly sampled data. Well
  understood confidence level properties. Large
  literature of application and theory.
• Empirical mode decomposition (EMD Huang et al
  1998, 1999). The method gives a decomposition of
  the signal into essentially band-limited
  components by using information from the signal
  itself instead of prescribing basis functions
  with fixed frequency, such as in Fourier
  analysis, or imposing a particular set of basis
  functions, as is the case with wavelet analysis.
  Handles nonstationary data, good for filtering -
  but many empirical aspects. See Terradas et al.
  (2004)

3
Other Methods (2)

• Multi-fractals - used to look at bursty type
  behaviour in time series looking for evidence of
  statistical processes (for example, financial
  time series, heart rhythms, or solar flares -
  MacAteer et al, in preparation). Active area of
  research in many disciplines, but problems in
  implementation and interpretation.
• Complex empirical orthogonal eigenfunctions.
  Observed oscillations occur in space and time -
  the signal is decomposed into spatial components
  (eigenfunctions) that have a time varying
  amplitude. The eigenvalues describe how strong
  each component is. See Terradas et al. (2004).
  Noise properties not well understood - unless you
  know better!

4
Randomization test (Linnell Nemec and Nemec 1985)

• Originally developed to test significance of
  periods detected in variable star light curves
• Null hypothesis no periodicity
• Alternative hypothesis the light curve contains
  a periodic function with a given period P.
• Also tests hypotheses that the period is equal to
  a specified value, or not.
• Be careful with light curves containing multiple
  periodicities.

5
Many, many other methods exist - for example.

• The correct period of the time series orders the
  data in the best possible way - this leads to the
  information (Shannon) entropy approach to
  identifying periods - (Cincotta et al., 1995,
  ApJ)
• Expand time series into orthogonal polynomials
  (better for non-sinusoidal signals
  Schwarzenberg-Czerny 1996)
• Phase Dispersion Minimization (Stellingwerf 1976)
• Fractal dimension (Watari 1996)
• Singular spectrum analysis (Watari 1996) -
  separates periodic, chaotic, and random
  components.