NGC7662 (HST) Imagem N

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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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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

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NGC7662 HST F658N (NII) raw image
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NGC7662 HST F658N (NII) wavelet processed
image
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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

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Hubble 4
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Hb4 - Halo

• F656N (Ha)

Mass Halo 1/3 Mass total
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Hen 2-402 F658N NII
raw image
wavelet processed image
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Hen 2-402 F658N NII
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HST Sample Morphological Structures
NP knots fil. halo shell
Hen 2-402 X
Hubble 4 X X X
Hen 2-389 X ?
M1 - 46 X X
M2 - 43 X X X
PC19 X X
NGC6790 X X X
Hen 2-447 X X
NP knots fil. halo shell
BD303639 X X
M3 - 35 X X X
PN G211.2-03.5 X X X
Hen 2-1 X X
Hen 2-104 X
Hen 2-194 X X X
M1 - 30 X X
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NGC 6891
NOT images Guerrero et al. 2000
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NGC 6891
NOT images Guerrero et al. 2000
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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

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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

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NGC6210
Greensignificative TF White no significative TF
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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
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NGC6818
Greensignificative TF White no significative TF
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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.