1 / 14

Hexagonal generalisation of Van Siclen’s information entropy - Application to solar granulation

Hexagonal generalisation of Van Siclen’s information entropy - Application to solar granulation. Stefano Russo Università di Tor Vergata – Dipartimento di Fisica.

mbarnard
Download Presentation

Hexagonal generalisation of Van Siclen’s information entropy - Application to solar granulation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Hexagonal generalisation of Van Siclen’s information entropy-Application to solar granulation Stefano Russo Università di Tor Vergata – Dipartimento di Fisica

  2. Evolution of an “exploding granule”. the dimension of each box are approximately of 5’’5’’, the whole sequence is of 13.5 min. Hirzberger et al. (1999) 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.

  3. F. Heslot et al.: 1987, Phys. Rev. A 36, 12. 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 (R>107).

  4. 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

  5. Granular pattern averaged for 2 hours. The intensity rms contrast is of 2.9% 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.

  6. Segmentation based on a dynamical threshold Segmentation based on the borders slope It is necessary to individuate a statistical method to correctly characterise the structures distribution Segmentation and statistical methods Structures individuation: Da Prima lezione di Scienze cognitive – P. Legrenzi, 2002, Editori Laterza

  7. 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, A&A 328, 229.

  8. Geometrical properties of an hexagonal and square lattice • Adjacency • Orientation • Self-similarity

  9. Sliding box area: 3m(m-1)+1 with m equal to the side of the rosette. Total area: with Lh horizontal dimension of the rosette. 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.

  10. 512 images exposure time: 8 ms t = 9.4 s 200 x 200 pixels Observation period: ~80 min. Wave lenght: 550 nm FWHM10 nm Pixel scale: 0.123 arcsec/pixel Field of view: 18 Mm x 18 Mm Observation: The R. B. Dunn Solar Telescope The DST1996 series:

  11. (b) (a) (c) (d) a b c d Results for single granulation images

  12. Higher scales of clustering The average of the H’(r) shows a small bump near 7.5 Mm.

  13. Granulation Entropy The Sun’s surface is like a newspaper page!!!

  14. 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).

More Related