iaus247

The structure of the lower solar atmosphereRobert Erdlyi

[email protected], Department of Applied Mathematics, The University of Sheffield (UK)

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

Robert Erdlyihttp://robertus.staff.shef.ac.uk

Lower atmosphere Very highly structured and dynamic; challenge for magnetic seismology via inversion

Three outstanding topics: Atmospheric/coronal heating. Influence of magnetic atmosphere, i.e. magnetic carpet, on oscillations. Role of p modes in the dynamics of the lower atmosphere! (Not yet explored.) Photosphere chromosphere TR ( corona are) magnetically coupled.


Lower atmosphere: coupling


Lower atmosphere Photosphere chromosphere TR ( corona are) magnetically coupled.

Very highly structured and dynamic; challenge for magnetic seismology via inversion

Three outstanding topics: Atmospheric/coronal heating. Influence of magnetic atmosphere, i.e. magnetic carpet, on oscillations. Role of p modes in the dynamics of the lower atmosphere! (Not yet explored.)


Lower atmosphere


Lower atmosphere Photosphere chromosphere TR ( corona are) magnetically coupled.

Very highly structured and dynamic; challenge for magnetic seismology via inversion

Three outstanding topics: Atmospheric/coronal heating. Influence of magnetic atmosphere, i.e. magnetic carpet, on oscillations. Role of p modes in the dynamics of the lower atmosphere! (Not yet explored.)


What is the motivation? Understand atmospheric structures (spicules, prominences, loops, plumes, etc.)Source of atmospheric heating; solar wind/particle accelerationLower atmospheric seismologyObservationsspectroscopicimagingWave 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 (Roberts et al. 1984) /Atmospheric seismology (Erdlyi 2006)


Solar interior Global oscillationsp/f/g-modesUnifying feature of variety of solar atmospheric oscillations Waveguide conceptMHD descriptionSolar atmosphereMore local oscillationsSunspot oscillations, prominence oscillations, coronal loop oscillations, plume oscillationsMoreton & EIT waves Oscillations ubiquitous in Sun Objects: atmospheric oscillations


Global oscillations Red curve : l = 75 Yellow curve : l = 25 Green curve : l = 20 Blue curve : l = 2 White curve : l = 0

= 3mHz


Global oscillations n=14 (radial nodes) m=16 (poloidal nodes) l=20 (spherical harmonic degree) The frequency of this mode determined from the MDI data is 2935.88 0.2 Hz.






Sunspot oscillations




Standing kink (transversal) modes TRACE: Loop oscillation excited by M4.6 flare (14 July 1998)Movie in TRACE 171 AOccurrence rate: 17/255 flares with transverse oscillation Schrijver et al. 2002




Moreton waves Seen in H in the chromosphere at 10000 K (Moreton 60) Propagation speeds 450-2000 km/s, away from a flare site Propagate almost isotropically; confined to an arc rarely exceeding 120 Have been identified as the intersection of coronal shock waves (due to a flare) with the chromosphere (Uchida 68; 74) Are not seen to decelerate The generation mechanism has not been made clear yet Moreton and EIT waves


Moreton and EIT waves


Moreton and EIT waves


Moreton waves on difference images after solar eruptionMoreton and EIT waves




Low atmosphere Ph, Ch, possibly TRIsolated flux tubesEffect of stratificationStratification leads to the Klein-Gordon effectHigher atmosphereTR, CoronaMagnetic environmentvAvA(Roberts 1981, Rae & Roberts 1982, Erdlyi(2005)Oscillations ubiquitous in Sun Atmospheric oscillations(Review: Erdlyi, Roberts, Ruderman, Thompson 2006; Erdlyi 2006)


The Klein-Gordon wavesStratified atmosphere (g=const) Webb & Roberts, Sol. Phys, 56, 5 (1978); Ulmschneider and cos, may papers in A&A; Review by Roberts (2003); Erdlyi & Hargreaves (2005)Erdlyi (2006); De Pontieu & Erdlyi (2006)Equilibrium: Scale height: 1D, sound waves: Introduce


The Klein-Gordon wavesDe Pontieu, Erdlyi & James (2004); De Pontieu, Erdlyi & De Moortel (2005); De Pontieu & Erdlyi (2006)Leakage of photospheric motion into LASound, slow, Alfvn waves=5/3 1Non-adiabatic plasmaInclination of magnetic wave guides

Isothermal atmospherePhotosphere: ac= 4.8 mHz P = 210 s(acoustic cut-off frequency)Corona: ac= 0.18 mHz P = 91.7 min


Coupling scales and elements Magnetic fields Flow fieldsManifestations of presence of solar atmosphere:Organised flows (meridional; differential rotation, etc.)Random flows (granulation, convection, etc.)Coherent global fields (e.g. canopy)Random fields (magnetic carpet)


Solar acoustic oscillations Separated ridges of power predicted: Ulrich (1970), Leibacher & Stein (1971) Separated ridges of power observed: Deubner (1975)MDI observations


Differences in sound speed


Internal structure vs BCs? EVP with proper BCs Surface term = ALL the atmospheric physics included!! Inversion should include (magnetic) solar atmosphere


Problem: solar cycle effectsTime dependent ridges of power observed: systematic frequency decrease (0.42 Hz 0.14 Hz) of low spherical (l) degree p-modes from maximum (1980) to minimum (1984) activity (Woodard & Noyes)

Most obvious theoretical candidate for interpretation: magnetic field (Ledoux & Simon 1957; Goossens et al. 1972, 1976; Biront et al. 1982 in stellar context)(Campbell & Roberts 1989; Evans & Roberts 1990, 1991, 1992; Jain & Roberts 1993, 1994abc; Miles & Roberts 1992; Erdlyi & Taroyan 2000, 2001, 2002a-c, 2005; Erdlyi, Kerekes & Mole 2005; Erdlyi & Pintr 2005; Shelyag, Erdlyi & Thompson 2005; Petrovay, Erdlyi & Thompson 2005 Erdlyi, Taroyan & Barlow 2006, etc. in solar context)


Problem: frequency differenciesStrong dependence of frequency shifts on the frequency and degree of the mode Libbrecht & Woodard 1975


GONG observations of line-width Variation of with magnetic activity for a single multiplet (l = 50, m = 9) Magnetic flux (dashed line) Sunspot number (dotted line)

Komm et al., ApJ, 531, 1094, 2000


BiSON observation of line width variation Changes in LW of low-angular degree p-modes during fall of SC22 Averaged over 2.6 to 3.6 mHz 24 3% mean increase in the modal line width from activity minimum to maximum

Chaplin et al., MNRAS, 313, 32, 2000


An example: line-widths (GONG) Surface gravity(f) modesAcoustic(p) modesDziembowski and Goode, ApJ 2005


Model Concept Magnetic fields Flow fieldsManifestations of coupling scales:Organised flows (meridional; differential rotation, etc.)Random flows (granulation, convection, etc.)Coherent global fields (e.g. canopy)Random fields (magnetic carpet)


Model Concept Global modes interact (e.g. resonantly ) with local MHD modesDissipation Damping of global oscillationsSteady state Global oscillations influenced by atmosphere


Model Concept Manifestations of presence of solar atmosphere:


Simple-minded solar model coronachromospheric transitional layer (L)photospheresolar interior


Eigenmodes


Frequency spectrum (L=0, B=0) Role of atmosphere: cut-off frequencies I and II


Eigenmodes (L=0, B=0)


Frequency spectrum (L0, B=0) Role of chromospheric transitional layer (L0): chromospheric g-modes Modes below Brunt-Visl frequencyUchida 1965, Thomas et al. 1971, Deubner & Gough 1984, Clark & Clark 1989, Braun & Fan 1998, Pintr et al. 1998g1


Eigenmodes (L0, B=0) g-modes are trapped in the transition layer where BV>0


Frequency spectrum (L=0, B 0)






Frequency spectrum (L=0, B 0) Two-layer model Polytrop interior Isothermal atmosphere vA=cst =cst (C&R89) B=cst (E&R90) No Alvn/slow continua




Eigenmodes (L 0, B 0)


Resonant coupling (L 0, B 0)


Driven problem is prescribed Eigenvalue problem is searched forJumps are independent of dissipative coefficientResonant coupling (L 0, B 0)


Inhomogeneous plasmas: natural behaviour Easy wave energy transfer resulting in heating Condition to occur: driver = local Could/may/viable to explain: - local/atmospheric heating - power loss of acoustic waves in sunspots - damping of standing waves coronal loop oscillations - damping of helioseismic (p/f/g) eigenmodes - energisation of MHD waves in magneto/heliosphereResonant coupling (L 0, B 0)


Eigenmodes (L 0, B 0) Three-layer model Polytrop interior Magnetic transitional layer resonances damping Isothermal magnetic upper atmosphere Presence of Alvn/slow continuaTirry et al. 1998, Pintr et al. 1999


Three-layer model Polytrop interior Magnetic transitional layer resonances damping Isothermal magnetic upper atmosphere Presence of Alvn/slow continua Erdlyi and Pintr 2005Eigenmodes (L 0, B 0)


Eigenmodes (L 0, B 0) Three-layer model Polytrop interior Magnetic transitional layer resonances damping Isothermal magnetic upper atmosphere Presence of Alvn/slow continua Non-parallel propagationPintr, Erdlyi & Goossens 2005


Eigenmodes (L 0, B 0) Three-layer model Polytrop interior Magnetic transitional layer resonances damping Isothermal magnetic upper atmosphere Presence of Alvn/slow continua Non-parallel propagationPintr, Erdlyi & Goossens 2005


Eigenmodes (L 0, B 0) Pintr, Erdlyi & Goossens 2005


Eigenmodes (L 0, B 0) Pintr, Erdlyi & Goossens 2005 Poster by Erdlyi & Pintr


Erdlyi, Pintr & Goossens 2005Eigenmodes (L 0, B 0)


Erdlyi, Pintr & Goossens 2005Eigenmodes (L 0, B 0)


Observations of sub-surface flows The order of the observed velocity of a poleward meridional flow is 10 m/s.Values of U for each data set, averaged over both hemispheres. The triangles indicate the SOI-MDI observations and the squares show the GONG observations.Braun & Fan 1998


Observations of sub-surface flows Residual angular velocity as function of time. Each 1-month-wide stripe represents one 3-month dataset, so that adjacent strips are not independent. Howe R., Komm R., Hill R., Sol. Phys. 192, 427, 2000


Physical process Variation of dampingTemporal variation of a sub-photospheric flow?


Revised solar model Space & Atmosphere Research Centercoronachromospheric transitional layer (L)photospheresolar interiorcanopy (h)


Flow effects on frequency spectrum


Flow effects on frequency spectrumCan be done analytically in small wavelength limit






Flow effects on frequency spectrumErdlyi & Taroyan 2002a,bCyclic frequency shift =(l,B,V)-(l,B,0) in Hz for the f-modeCyclic frequency shift =(l,B,V)-(l,B,0) in Hz for the n=1 p mode


Flow effects on line widthPintr, Erdlyi & New R., A&A, 2001


Rotational splitting of sectoral modes


Rotational splitting of sectoral modesPintr B., New R. & Erdlyi R., A&A, 378, 1, 2001Relative increase of n,l,l : 0.41%&GONG & MDI - observational error: 0.25%More realistic models are required.


Model improvement


Random field effects: magnetic carpet, granular motion mixed polarity network almost everywhere on the solar surface 95% of the photospheric flux closes low down in the magnetic carpet continuous emergence and disappearance of flux the magnetic concentrations follow the dominant flow patternsMagnetic carpet Full disc magnetogram by SOHO/MDI, 1998 June 13.


The origin of quiet Sun so far unexplained: smaller loops from below the convection zone the product of local field generation due to small-scale shearing processes in the sub-surface layersMean absolute flux density ~2GaussReplacement time ~40 hs10 hsMean total flux / event1016 (obs. limit) - 1019 MxObserved featuresRandom field effects: magnetic carpet, granular motion


Random field effects: magnetic carpet, granular motion


Demo: Random magnetic field & the surface-modezxz=0

B (x, z), 2 (atmosphere) field-free interior, 1

Basic assumptions2D Cartesian geometrytime-independent random fieldincompressible media no coherent background fieldno flowRandom field effects: magnetic carpet, granular motion


Demo: Random magnetic field & the surface-modeBasic assumptionsatmospheric magnetic field:B0=[B1(x, z), 0, B3(x, z)] in z0

Bi(x, z)=0 ensemble average

B0(x, z)=A0(x, z)

A0=[0, A, 0]= zexp( 2z)b(x)

b(x)=0 2 decay factorRandom field effects: magnetic carpet, granular motion


Dimensionless dispersion relation (K

2-D model solar atmosphere based on the VALIIIc temperature profile and the condition of hydrostatic equilibrium

Applied vertical velocity perturbations to this atmosphere under hydrodynamic equations.2D leakage of photospheric acoustic waves into non-magnetic atmosphereErdlyi & Malins (2006)


30 second period. This driver has a frequency well above the acoustic cut-off frequency in the lower solar atmosphere, Waves propagate well through the lower atmosphere and then through the transition region into the corona. Series of images at 25 second intervals showing velocity perturbations propagating into the corona, with a relatively low level of reflection at the transition regionHigh frequency driver


300 second driver

Just above the acoustic cut-off in the lower atmosphere (and slightly below it at the temperature minimum)

Experience strong reflection at the transition region standing wave formation in the vertical direction

Drives the development of the horizontally propagating surface waves Low frequency (5 min) driver


Vertical velocity along the central vertical axis alongside the full 2-D velocity structure Clear (left) stratification driven amplification and clean propagation of the high frequency 30 second wave with height The generation (right) of a standing wave form with a node between the driver and transition region which are anti-nodesPropagation versus cavity modes


Time-distance image of the propagation of vertical velocity signals across a line drawn at a height of 1.3MmStanding waves in the lower atmospheric cavity (5 mins)The power spectrum shows clearly a fundamental mode at the driver frequency, but also a set of higher harmonics


P-mode driven spicules: 2-D


Moss oscillationsLower atmospheric seismology


Numerous examples of waves and oscillations by SOHO and TRACE in lower solar atmosphere structures Lower atmosphere has back-reaction of global oscillations (M)HD theory seems to be a satisfactory description Atmospheric seismology provides us information about: magnetic field, transport coefficients, fine structures, etc. Coupling of photospheric motions (p-modes, granular, etc.) to lower atmosphere (and above) Stratification has significant effectSummary


Further challenges: What are the details of p mode coupling to LA (2/3D)? What are the exact consequencies of stratification?? Atmospheric magnetic field effects on time-distance analysis? Role of global oscillations (coupling)? Role of Transition Region (spicules)? Effect of non-uniform temperature Effect of radiation (hot loops!); include proper chromosphere (leakage) Work out inverse problem for coronal structures (fine scale)Summary


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