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)

Wavelet Transform: What for?

Wavelet Transform is a mathematical transform that analyzes the spatialfrequencies content of images

Wavelet Transform is invariant to scaling (e.g. particularly fit to put into evidence fractal structures)

The decomposition functions have finite supportno artificial high frequencies (like in Fourier Transform) the frequency information is kept locally, and can easily be visualized Noise can be removed according to the spatial scales

NGC7662 HST F658N ([NII])

raw image

NGC7662 HST F658N ([NII])

wavelet processed image

Our Sample

14 PN selected from HST archiveSelected 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

Hubble 4

Hb4 - Halo

F656N (H)

Mass Halo = 1/3 Mass total

Hen 2-402 F658N [NII]

raw imagewavelet processed image

Hen 2-402 F658N [NII]

HST Sample – Morphological Structures

NP knots fil. halo shell

Hen 2-402 XHubble 4 X X XHen 2-389 X ?M1 - 46 X XM2 - 43 X X XPC19 X XNGC6790 X X XHen 2-447 X X

NP knots fil. halo shell

BD+30°3639 X XM3 - 35 X X XPN G211.2-03.5 X X XHen 2-1 X XHen 2-104 XHen 2-194 X X XM1 - 30 X X

NGC 6891NOT images – Guerrero et al. 2000

NGC 6891NOT images – Guerrero et al. 2000

Application of Wavelet Transform toTemperature 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

How can Wavelets help ?

Can put into evidence faint structures, as TF from [OIII] maps ratios 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

NGC6210

Green:significative TFWhite: no significative TF

Region without significative TF Region with significative TF

NGC6210

Observadas

Simuladas

Observadas

Simuladas

[OIII] 4363/5007 Å

Null information:

Simulation of intrinsic

[OIII] 4363/5007 Å

through

(5007 + noise)/5007 Å

NGC6818

Green:significative TFWhite: no significative TF

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.

Conclusions