Hexagonal generalisation of Van Siclen

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Hexagonal generalisation of Van Siclens
information entropy-Application to solar
granulation

• Stefano Russo
• Università di Tor Vergata Dipartimento di Fisica

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Granulation
Set of images obtained trough a fast frame
selection system, at the SVST (La Palma) on the
5-6-1993. Technical data wave lenght 468 5 nm
exposure time 0.014s. The time series covers 35
min. the field of view is 10 ? 10 Mm2.
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Convection
Parameters to describe the convective regime
? thermal expansion coefficient d3 convective
cell volume ? cinematic dissipation coeff. k
thermal diffusivity coeff.

• Lab experiments showed a new convective regime
  at high Rayleigh numbers (Rgt107).

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A new paradigm
Granule as classic convective cell

• Old paradigm (mixing-length model)
• fully developed turbulence with a hierarchy of
  eddies
• quasi-local, diffusion-like transport
• flows driven by local entropy gradient
• New paradigm (lab numerical experiments)
• turbulent downdrafts, laminar isentropic upflows
• flows driven by surface entropy sink (radiative
  cooling)
• larger scales (meso/super granulation) driven by
  compressing and merging
• Spruit, H.C., 1997, MemSAIt, 68, 397

Convection guided by surface instability
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Convection and ordering
It is necessary to determine a objective
criterion in order to individuate a possible
ordering of the granular structures
The resulting pattern after an average operation
resembles that observed in Rayleigh-Bénard
convection experiments.
It seems to be present a kind of
self-organization in the photosphere. (Getling
Brandt, 2002)
Rast (2002) showed as, applying the same average
operation on a random flux field, it is possible
to derive the same geometrical shape.
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Segmentation and statistical methods
Structures individuation
Da Prima lezione di Scienze cognitive P.
Legrenzi, 2002, Editori Laterza
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Power spectrum
The most known method to characterise
regularities in a system is the power spectrum
This method is not usable in the granulation case
Å. Nordlund et al. 1997, AA 328, 229.
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Geometrical properties of an hexagonal and square
lattice

• Adjacency
• Orientation
• Self-similarity

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Hexagonal generalisation

• In order to utilise the isotropy properties of
  the hexagonal lattice, we have to
• represent the images with hexagonal pixels
• modify the shape of the counting sliding boxes.

A more correct individuation of the lattice
constant when the distribution of the structures
follows a non-square disposition higher
intensity of the peaks for structures disposed
randomly or on a hexagonal way.
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Observation The R. B. Dunn Solar Telescope
The DST1996 series
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Results for single granulation images
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Higher scales of clustering
The average of the H(r) shows a small bump near
7.5 Mm.
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Granulation Entropy
The Suns surface is like a newspaper page!!!
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Conclusions

• A more isotropic tool in image analysis has been
  developed.
• The peaks disposition of the H(r) has shown a
  hierarchy of scales of clustering that we have
  interpreted as an ordering of the convective
  structures.
• A lattice constant has been measured (1.5 Mm).
• Granulation images show a typical scale of
  clustering comparable to the mesogranular scale
  (7.5 Mm).