Multiscale magnetic pattern in the quiet photosphere

1. Multiscalemagnetic pattern in the quietphotosphere Francesco Berrilli(1) Dario Del Moro (1), Silvia Giordano (2), Stefano Scardigli(1) Department of Physics, University of Rome Tor Vergata, Italy (berrilli@roma2.inf.it) ALTRAN ITALIA, Italy 14th European Solar Physics Meeting (ESPM-14) Trinity College Dublin | Ireland| 8th – 12th Sep 2014

2. TURBULENT CONVECTION In a Rayleigh–Bénardconvectionexperiment the distance between adjacent rising and falling regions is about the depth of the experimental box. The Rayleigh number Ra( 2103 R.B.) can be estimated for solar convecting plasma and turns out to have the value of 1012represents a very strongly driven nonequilibrium system. The resulting turbulent convection creates temperature and velocity structures that evolve over a range of spatial and temporal multiple scales. Rayleigh–Bénardconvection

3. The nature of the multiscale convective pattern observed on the solar surface remains a long-standing puzzle in solar physics. MHD simulation The convective plasma flows govern the motion of the single magnetic Features. The analysis of magnetic pattern provides a way to investigate all the organization scales of convection, from granulation to the global circulation HR MDI Mag

4. Three different spatial and temporal scales are traditionally identified on the solar surface: • granulation (∼1 Mm wide, lifetimes of a few minutes), • meso-granulation (5–10 Mm, lifetimes of a few hours), • supergranulation (30–50 Mm, lifetimes of about one day). • A division defined like this is probably of historical and not physical origin (Nordlund et al., 2009) • Different image sampling and identification techniques, using different windows in space and time domains, may be responsible for the perceived different spatial patterns and different dominant scales.

5. If we observe the Universe we see that the galaxies do not fill space uniformly but instead are clustered in sheets and walls with large voids (relatively empty regions) between them. The Sloan Great Wall in a DTFE reconstruction

6. If we observe the Sun we see that the magnetic fields do not fill photosphere uniformly but instead are clustered in a network with large voids (relatively empty regions) between them. The inspection of photosphericmagnetograms that were taken at the limits of the available resolution, (Sánchez Almeida 2003; Lites et al. 2008; Martìnez González et al. 2012; Orozco Suárez & Bellot Rubio 2012) reveals regions where magnetic fields are weak and very inclined (commonly named voids).

7. we study the void size distribution (VSD) to determine whether it reveals distinct flow scales (e.g., supergranular) or it is smoothly distributed. The automatic identification of voids is performed using an improved version of the void-detection algorithm introduced in Aikio & Maehoenen (1998) and Berrilli et al. (2013).

8. The analysis was performed on a series of SOHO/MDI magneto-grams acquired during the solar activity minimum between cycles 23 and 24. We have analyzed a dataset of 511 high-resolution quiet Sun magnetograms selected to cover a period of 18 months from 1/1/2008. The images have a field of view (FOV) of 11 × 11  with a resolution of 1.25". The void-detection algorithm singled out 252 488 voids.

9. The VSD agrees with an exponential decay (constant 12.2 ± 0.2 Mm)in the range 10–60 Mm. • No feature is observed at supergranularscale 30–50 Mm.

10. A similar analysis was performed on a Hinode/SOT/SP line-of-sight magnetogram 302" × 162“ portion of the quiet solar photosphere observed at disk center on 10 March 2007. 1951 magnetic voids were identified.

11. VSD of void length scales present in the Hinode/SOT/SP line-of-sight magnetogram. The inset shows the linear plot of the void length scale distribution and the exponential fit (continuous curve) between 2 and 10 Mm with a decay constant equal to 2.2 ±0.2 Mm. • The VSD agrees with an exponential decay (constant 2.2 ± 0.2 Mm)in the range 2-10 Mm. • No feature is observed at mesogranularscale 4-8 Mm.

12. On the Sun the pattern is not a geometric structure (e.g. a regular R.B. convection) but a statistical deviation from randomly and uniformly distributed points that is difficult for the human visual system to quantify. What is the true solar SOHO/MDI magnetogram?

13. Blue symbols with error bars represent the VSD of 252488 voids. • Red crosses show the mean VSD computed by shuffling the magnetic structures in each magnetogram. • T he gree Gaussian fit is represented by the continuous curve.

14. Conclusions VSD shows a quasi-exponential decay in the observed ranges. The lack of features in the 10–60 Mm range supports the multiscale hypothesis of convective motion flows at the solar surface (e.g., Nordlundet al. 2009; YellesChaouche et al. 2011; Berrilli et al. 2013). The absence of features in the 2–10 Mm supports the findings of Rieutordet al. (2010) that no specific scale exists in the mesoscale range. Berrilli F., Scardigli S., Giordano S., MultiscaleMagneticUnderdenseRegions on the SolarSurface: Granular and MesogranularScales, SolarPhysics, 282, 2013 Berrilli F., Scardigli S., Del Moro D., Magnetic pattern at super-granulation scale: the void size distribution, A&A 568, 2014

15. Go raibh maith agat as do aird Thank you for your attention