Solar Physics & Space Plasma Research Center (SP 2 RC) Solar - - PowerPoint PPT Presentation

Robertus Erdélyi

Robertus@sheffield.ac.uk

SP2RC, School of Mathematics & Statistics, The University of Sheffield (UK)

http://robertus.staff.shef.ac.uk

Viktor Fedun, Gary Verth Richard Morton Chris Nelson, M-A Luna Michael Ruderman David Jess, David Kuridze Gareth Dorrian, Sergiy Shelyag Mihalis Mathioudakis Marcel Goossens

• Measurement of magnetic fields in the solar chromosphere/corona very difficult!
• Worthwhile problem to solve due to the importance of available magnetic energy.
• How accurate are force free magnetic extrapolations? E.g., Metcalf et al. (ApJ, 1995)

estimate chromosphere not force free < 400 km.

• Vector polarimetry technique proposed by Solanki et al. (Nature, 2003) to produce 3D

magnetic maps using He I multiplet (formed near coronal base). Since discredited by Judge (A&A, 2009), found to give spurious results for simple test cases!

• Kontar et al. (A&A, 2008) used

RHESSI hard X-ray data to estimate expansion of magnetic field of flaring loop on solar limb. (> 400 km biggest error bar).

What is the motivation?

• Source of atmospheric heating; solar wind/particle acceleration
• Understand atmospheric structures (spicules, prominences, loops, plumes, etc.)

Observations

spectroscopic imaging

• Wave properties (speed,

amplitude, spectrum)

• Geometric properties of waveguides

(structuring, shape, curvature)

• Atmospheric diagnostic

parameters (temperature, density)

• Atmospheric physical parameters (B,

fine structure, transport coefficients)

Coronal Seismology (Roberts et al. 1984); Solar Magneto-Seismology (SMS) (Erdélyi 2006)

• Original MHD theory by e.g., Edwin & Roberts (1983) modelled a flux tube as a

magnetic cylinder.

• It was found that there are many different types standing waves, e.g., fast/slow

magneto-acoustic modes in magnetically twisted cylinder (Erdélyi & Fedun 2010).

• Original MHD theory by e.g., Edwin & Roberts (1983) modelled a flux tube as a

magnetic cylinder.

• It was found that there are many different types (standing) MHD waves, e.g.,

Alfvén modes (Erdélyi & Fedun, Science 2007)

Relatively “simple” magnetic topology. MPBs appear at the merging points

• f granules (kG field strength). Small scale (100 - 300 km diameters).

Hinode data Wijn et al. (2008)

Buffeted by granules MHD waves generated! Q: What sort of photospheric motions are observed in MBPs?

Photospheric Doppler shift

• D. Jess et al. (in prep)

Photospheric G-band movie Chromospheric Ca II movie

Bonet et al. (ApJ, 2008) Wedemeyer-Bhöm & Rouppe van der Voort (A&A, 2009)

Magnetic bright point group analysed by Jess, Mathioudakis, Erdélyi et al. (Science, 2009) with SST. Torsional Alfvén waves incompressible so can be detected by periodic spectral line broadening. Chromosphere Photosphere

Intensity oscillations were not found!

• SST: Chromospheric bright point oscillations

2.72 mHz 2.49 mHz 2.22 mHz 2.09 mHz

Torsional Alfvén waves generated independently on each magnetic surface, for the first time, we can resolve the frequency as a function of radius in chromospheric flux tube! Q1: Can photospheric vortex driver cause such a distribution? Q2: What plasma structure will support such a frequency distribution? Q3: What about plasma heating?

Simulations show that convection naturally leads to vortex motion at magnetic flux concentrations (see also Vogler et al. 2005; Carlsson et al. 2010). (Shelyag et al. 2010, 2011a,b)

Full nonlinear ideal MHD simulation using Sheffield Advanced Code (SAC). Flux tube embedded in VAL IIIC (quiet sun) atmosphere. (Fedun et al. 2011a,b,c; Erdélyi et al. 2012)

Full nonlinear ideal MHD simulation using Sheffield Advanced Code (SAC). Flux tube embedded in VAL IIIC (quiet sun) atmosphere. (Fedun et al. 2011a,b,c; Erdélyi et al. 2012)

Full nonlinear ideal MHD simulation using Sheffield Advanced Code (SAC). Flux tube embedded in VAL IIIC (quiet sun) atmosphere. (Fedun et al. 2011a,b,c; Erdélyi et al. 2012)

Full nonlinear ideal MHD simulation using Sheffield Advanced Code (SAC). Flux tube embedded in VAL IIIC (quiet sun) atmosphere. (Fedun et al. 2011a,b,c; Erdélyi et al. 2012)

Computed frequency distribution. Detected frequency distribution.

Frequency distribution (black) outlines magnetic structure (orange)! Construct magnetic field in lower solar atmosphere!!!

Torsional Alfvén waves  one can reconstruct magnetic topology in chromosphere (or elsewhere)! Q1: Do I miss a key point? Q2: Is the MHD approximation affecting the constructed frequency distribution? Q3: Estimate error…?

Even “simpler” magnetic topology. Pores appear at emerging ARs of with kG field strength and often simple geometry. Small scale (500 - 1000 km diameters).

ROSA data Morton et al. (2011)

Waves generated by

• Global acoustic modes
• Granular buffeting
• Vortex motion

ROSA data Morton et al. (2011)

Two movies: pore_1.mov of pore and pore2.mov shows intensity profile across pore with intensity threshold (straight line)

Empirical Mode Decomposition used to derive IMFs from time series of pore size (red) and intensity (black). EMD separates out distinct timescales in time series. Direct comparison between pore size and intensity IMFs with similar timescales to find out of phase behaviour.

1) Mode identification: Slow magneto-acoustic sausage body mode

1) Mode identification: Slow magneto-acoustic sausage surface mode Wave energy:

• E=108 ergs cm2
• ~10% transmission coeff needed!

Slow MA sausage waves  one can even heat the chromosphere! Q1: Do I miss a key point? Q2: Is the MHD mode interpretation affecting the energy budget? Q3: Estimate error…?

Another “simple” magnetic topology. They appear everywhere with ~few 100 to a kG field strength. Small scale (few 100 km diameters).

ROSA data Kuridze et al. (2011), Jess et al. (2012)

Another “simple” magnetic topology. They appear everywhere with ~few 100 to a kG field strength. Small scale (few 100 km diameters). Waves generated by

• Global acoustic modes
• Granular buffeting
• Vortex motion

ROSA data Kuridze et al. (2012)

1) Ubiquitous in chromosphere

ROSA data Morton et al. (subm., 2012)

2) Concurrent transverse and sausage oscillations

ROSA data Morton et al. (subm., 2012)

• Intensity (solid) and FWHM width (dashed)
• Normalised amplitudes
• Time-distance from cross-cut across mottle

3) Statistics (dark and bright mottles)….

ROSA data Morton et al. (subm.)

Wave energy:

• Ek=1600-6100 Wm-2
• Es=7910-15500 Wm-2
• f~4-5% 10-25% transmission coeff needed!

A brightening in the Hα line wings. Ellerman (1917) described them as: ‘a very brilliant and very narrow band extending four or five angstroms on either side of the line, but not crossing it.’

ROSA data Nelson et al. (2012a-c)

Other important factors which describe an Ellerman bomb are:

ROSA data Nelson et al. (2012a-c)

• Flaring.
• Small-scale (approximately 1 arc-second although high-resolution data

decreases this).

• Short-lived (Estimates range from 1-15 minutes on average).

Top left: RBE in a blue wing image. Top Right: Temporally co-aligned Doppler

• image. Bottom left: Line profile. Bottom right: Line profile through time.

ROSA data Nelson et al. (2012a-c)

Mottles, spicules, EBs  chromospheric (and possibly coronal?) dynamics Q1: Do I miss a key point? Q2: Is the MHD approximation screwing the dynamic coupling and energy budget of the atmosphere? Q3: Estimate error… I don’t even know where to start!

(Courtesy of Unknown Solar Solder)

MDI/SXT potential nonlinear FF Q: Force-free or non-force-free fields

From the same photospheric field distributions, one can extrapolate the magnetic field (by solving ∇.B=0 and ∇×B=αB, with appropriate upper boundary conditions)

Geometrical:

• Non-circular cross-section (elliptical cross-section, cold plasma - Ruderman, 2003

• Loop shape (Andries et al, 2005a,b; Dymova & Ruderman, 2006)
• Curvature (Van Doorsselaere et al, 2004; Diaz, 2006; Diaz et al, 2006;

Physical 2nd order effects :

• Stratification due to gravity (Roberts & Webb, 1978; Diaz & Roberts, 2006)
• Radial density inhomogeneities (Ruderman & Roberts, 2002; Erdélyi & Carter, 2006)
• Longitudinal density inhomogeneities (Erdélyi & Verth, 2007; Verth et al, 2007)
• Magnetic twist (Bennett et al., 1999; Erdélyi & Carter, 2006; Ruderman, 2007)
• Wave leakage (Cally, 1986; De Pontieu et al. 2001; Ruderman & Roberts, 2006; )
• Radiative dissipation (Erdélyi, Luna-Cardozo, Mendoza-Briceño, 2008)
• Resonant absorption (Sakurai et al, 1991a,b; Goossens et al 1992; Goossens &

Non-equilibrium ionisation?

• Resonant absorption (Soler, Ballester, etc…)

The end