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Planetary Nebulae and Wavelet Transform

Planetary Nebulae and Wavelet Transform. Francois Cuisinier GEMAC/OV – UFRJ ( Brazil). Co-workers: A.P. Moises (ON/MCT, IAG/USP) M.L. Ferreira (GEMAC/OV – UFRJ) C.R. Rabaca (GEMAC/OV – UFRJ) D.R. Goncalves (IAG/USP).

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Planetary Nebulae and Wavelet Transform

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  1. Planetary Nebulae and Wavelet Transform Francois Cuisinier GEMAC/OV – UFRJ (Brazil) Co-workers: A.P. Moises (ON/MCT, IAG/USP) M.L. Ferreira (GEMAC/OV – UFRJ) C.R. Rabaca (GEMAC/OV – UFRJ) D.R. Goncalves (IAG/USP)

  2. Wavelet Transform: What for? • Wavelet Transform is a mathematical transform that analyzes the spatial • frequencies content of images • Wavelet Transform is invariant to scaling • (e.g. particularly fit to put into evidence fractal structures) • The decomposition functions have finite support a no artificial high frequencies (like in Fourier Transform) a the frequency information is kept locally, and can easily be visualized • Noise can be removed according to the spatial scales

  3. NGC7662HSTF658N ([NII]) raw image

  4. NGC7662HSTF658N ([NII]) wavelet processed image

  5. Our Sample • 14 PN selected from HST archive • Selected on the basis of their size: Angular diameter between 5 and 30 arcsec, in order (1) to have a sufficient size to present detectable substructures (2) to fit into the planetary camera of the WFPC2

  6. Hubble 4

  7. Hb4 - Halo F656N (Ha) Mass Halo = 1/3 Mass total

  8. Hen 2-402 F658N [NII] wavelet processed image raw image

  9. Hen 2-402 F658N [NII]

  10. HST Sample – Morphological Structures

  11. NGC 6891 NOT images – Guerrero et al. 2000

  12. NGC 6891 NOT images – Guerrero et al. 2000

  13. Application of Wavelet Transform to Temperature Fluctuations • Temperature Fluctuations have historically been put into evidence by the comparison of temperatures derived by different methods, sensitive to different regions (e.g. [OIII] and Bac). • Some direct measurements (e.g. through the mapping of one temperature indicator ([OIII] or Bac) exist (HST imaging or ground based /HST spectroscopy), but generally indicate fairly low Temperature Fluctuations • Temperature fluctuations are however usually described by a unique weighted mean indicator, t2 • t2 does not yield any indication on the location of the Temperature Fluctations

  14. How can Wavelets help ? • Can put into evidence faint structures, as TF from [OIII] maps ratios a Te = f ( TW (I4363) / TW (I5007) ) • The amplitude of the variations is however small, possibily • at the limit of the detection of Wavelet Transform • Need to find some objective argument to segregate artifacts • from true structures

  15. NGC6210 Green:significative TF White: no significative TF

  16. NGC6210 Observadas Observadas [OIII] 4363/5007 Å Simuladas Simuladas Null information: Simulation of intrinsic [OIII] 4363/5007 Å through (5007 + noise)/5007 Å Region without significative TF Region with significative TF

  17. NGC6818 Green:significative TF White: no significative TF

  18. Conclusions • Wavelets allow to put into evidence faint substructures, even in dense areas in planetary nebulae which have not been much explored • before. • Though our HST sample is far from complete, much more planetary • nebulae seem to present substructures than quoted in previous studies. • This needs however to be verified, since many of these substructures have scales of 1-2 pixels. • Wavelet Transform has a potential to assess temperature fluctuations from [OIII] images ratios.

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