The ’s

„ The solar atmosphere is generally described as being composed of multiple layers, with the lowest The solar atmosphere layer being the , followed by the , the transition region and the corona. „ In its simplest form it is modelled as a single component plane-parallel atmosphere.

„ drops exponentially: ρ(z) = ρ0 exp(-z/Hρ) (for isothermal atmosphere). T=6000K Î Hρ≈ 100km „ Mass of the solar atmosphere ≈ mass of the Indian (≈ mass of the photosphere) „ Mass of the chromosphere ≈ mass of the ’s atmosphere

1-D stratification How good is the 1-D approximation?

„ 1-D models reproduce extremely well large parts of the spectrum obtained with low spatial resolution (see spectral synthesis slide)

„ However, any high resolution image of the Sun shows that its atmosphere has a complex structure (as seen at almost any wavelength)

„ Therefore: 1-D models may well describe averaged quantities relatively well, although they probably do not describe any part of the real Sun at all.

The photosphere The

„ The photosphere extends between the solar surface Sun in and the minimum, from which most of White the solar arises. „ The visible, UV (λ> 1600Å) and IR (< 100µm) Light radiation comes from the photosphere. „ 4000 K < T(photosphere) < 6000 K (limb darkening „ T decreases outwards Î Bν(T) decreases outward Î absorption spectrum removed) „ LTE is a good approximation „ transport by and radiation MDI on „ Main structures: Granules, and faculae SOHO

1 Sunspots Granulation Penumbra Umbra „ Physics of convection and the properties of granulation and have been discussed earlier, so that we can skip them here.

H. Schleicher, KIS/VTT, Obs. del Teide, Tenerife

Chromosphere Chromospheric structure

„ Layer lying just above the photosphere, at which the temperature appears to be increasing outwards (classically forming a temperature plateau at around 7000 K) „ Assumption of LTE breaks down „ Energy transport mainly by radiation and waves „ Assumption of plane parallel atmosphere is very likely to break down as well. „ Strong evidence for a spatially and temporally inhomogeneous chromosphere ( at T<4000K is present beside gas with T>8000 K) 7000 K gas Ca II K 5 104 K gas (EIT He 304 Å)

Chromospheric structure II

DOT Ca II K core:DOT chromosphere G-band: photosphere „The chromosphere exhibits a very wide variety of structures. E.g., „Sunspots and Plages „Network and internetwork (grains) „Spicules „Prominences and filaments „Flares and eruptions Ca K core, B. Gillespie, NSO

2 Chromospheric structure Chromospheric structure

„The chromosphere „The chromosphere exhibits a very wide exhibits a very wide variety of structures. variety of structures. E.g., E.g., „Sunspots and „Sunspots and Plages Plages „Network and „Network and internetwork internetwork „Spicules „Spicules „Prominences and „Prominences filaments and filaments „Flares and „Flares and eruptions eruptions

Chromospheric dynamics (DOT) Chromospheric dynamics

„ Oscillations, seen in cores of Network strong lines „ Power at 3 Internetwork min in Inter- network „ Power at 5-7 min in Network Lites et al. 2002

Models: the classical chromosphere Need to heat the chromosphere

„ Radiative equilibrium, „ Classical picture: RE: only form of energy plane parallel, transport is radiation & multi-component atmosphere is in thermal equilibrium. Tmin „ VAL-C: empirical model „ Chromosphere is composed of a „ Dashed curves: temp. gentle rise in stratifications for increasing amount of temperature temperature Fontenla et al. 1993 heating (from bottom to between Tmin and top). transition region. ÎMechanical heating needed to reproduce obs. Anderson & Athay 1993

3 Dynamic models Transition Region

„ Start with piston in , consistent with obs. of photospheric oscillations „ Waves with periods of ≤3min propagate into chromosphere „ Energy conservation (ρv2/2 = const.) & strong ρ decrease Î wave amplitudes increase with height: waves steepen and shock „ Temp. at chromospheric heights varies between Semi-empirical 1D-models of solar atmosphere: steep 3000 K and 10000 K Carlsson & Stein increase of T in transition region (TR): < 100 km thick

TR spatial structure TR dynamic phenomena: blinkers

„ Brightness variability in the (quiet) transition region „ Lower transition is larger than in any other layer of solar atmosphere region (T<5 105 K) „ Typical brightening: blinkers shows structure very „ Occur everywhere, all the time. Last for minutes to similar to hours. How much of the brightening is due to chromosphere, with overlapping network, etc. blinkers? „ C IV (105 K) imaged „ 1 time step Si IV by SUMER ≈ 1 minute „ In upper transition region structures are more similar to corona

Explosive events The Solar Corona

„ Broadenings of TR spectral lines at 1-3 105 K While the surface „ Typical “normal” line width 20 km/s, in explosive is about 6,000 K, event: up to 400 km/s. Cover only a few 1000 km the temperature in the corona and last only reaches about 2 Corona a few minutes a few minutes million K. „ Typically a

few 1000 Solar What causes this interior present on rapid increase in Sun at any temperature is still Surface given time one of the big mysteries in .

4 The Hot and Dynamic Corona Solar corona during

1991

1980

1994

Corona at solar EUV Corona: 106 K White corona (EIT/SOHO 195 Å) (LASCO C3 / SOHO, MPAe) 1988

Coronal structure: active region loops Coronal structures TRACE, 1999

„ Active regions (loops)

„ Quiet Sun

„ X-ray bright points

„ Coronal holes

„ Arcades Fe XII 195 Å (1.500.000 K) 17 May - 8 June 1998

Coronal structure: streamers The solar A constant stream of particles flowing from the Sun’s corona, with a temperature of about a million degrees and with a velocity of about 450 km/s. The reaches out beyond 's orbit, with the heliopause located roughly at 100-120 AU

5 Solar wind characteristics at 1AU Comets and the solar wind Fast solar wind Slow solar wind „ speed > 400 km/s <400 km/s -3 -3 „ np ≈ 3 cm ≈ 8 cm „ homogeneous high variability „ B≈ 5 nT = 0.0005G B < 5 nT „ 95% H, 4% He 94% H, 5% He „ Alfvenic fluctuations Density fluctuations „ Origin: coronal holes Origin: in connection with coronal streamers Transient solar wind „ speed from < 300 km/s up to >2000 km/s Comet „ Variable B, with B up to 100 nT (0.01G) NEAT „ Often very low density (C/2002 V1) „ Sometimes up to 30% He „ Often associated with interplanetary shock waves „ Origin: CMEs

3-D structure of the Solar Wind: Coronal Shape & Solar Wind: Variation over the Ulysses Data & 3D- 1st Orbit: 3/1992 - 11/1997 2nd Orbit: 12/1997 - 2/2002 declining / minimum phase rising / maximum phase

Ulysses SWICS data Woch et al. GRL Activity minimum Activity maximum

Parker’s theory of the solar wind Parker’s solar wind solutions

„ Basic idea: dynamic equilibrium between hot corona „ Parker found 4 CHECK WHY ONLY ONE SOLN and interstellar medium. Mass and families of solar wind IS CORRECT!!!!!!!!! solutions balance equations: d (ρr 2v) = 0 „ 2 not supported by dr Obs. (supersonic at solar surface) dv 1 dP GM v = − „ 1 does not give ρ 2 dr dr r sufficient ÎParker’s Eq. for solar wind speed (isothermal against the atmosphere) interstellar medium. 2 1 dv 2 2c GM „ Correct solution (v2 − c ) = S − v dr S r r 2 must be thick line in Fig.

6 „ Heliosphere = region Solar wind speed The Heliosphere of in which the solar wind and solar „ Speed of Bowshock solar wind dominate over the instellar medium and predicted by Heliopause the galactic magnetic Parker’s field. model for „ Bowshock: where the different interstellar medium is slowed relative to the coronal Heliotail Sun. (simple, „ Heliospheric shock: isothermal Interstellar where the solar wind is decelerated relative case; no medium to Sun magnetic Heliospheric shock „ Heliopause: boundary field) of the heliosphere

The source of the Sun’s activity is the magnetic field

Î in order to Magnetic Field understand the dynamics and activity of the Sun we need measurements and theory of its magnetic field

Thomas Wiegelmann

Open and closed magnetic flux Correlation of field with brightness Closed flux: slow solar wind

Most of the solar flux returns to the solar surface within a few R (closed flux) A small part of the total flux through the solar surface connects as open flux to interplanetary space Open flux: fast solar wind

7 Measured Methods of magnetic field Magnetic measurement Field at „ Direct methods: Sun’s „ Zeeman effect Î polarized radiation Surface „ Hanle effect Î polarized radiation „ Gyroresonance Î radio spectra Month long „ Indirect methods: Proxies sequence of „ Bright or dark features in photosphere (sunspots, magnetograms G-band bright points) (approx. one (approx. one „ Ca II H and K plage solar rotation) „ Fibrils seen in chromospheric lines, e.g. Hα MDI/SOHO „ Coronal loops seen in EUV or X-radiation May 1998

Example of proxies: Continuum vs. G- Ca II K as a magnetic field proxy band „ Ca II H and K lines, the strongest lines in the visible solar spectrum, show a strongly increasing brightness with non-spot magnetic flux. „ The increase is slower than linear „ Magnetic regions (except sunspots) appear bright in Ca II: Ca plage and Continuum G-band network regions

Hα and the chromospheric field Zeeman diagnostics

„ Hα images of active regions show a „ Direct detection of magnetic field by structure similar to observation of magnetically induced splitting iron filing around a and polarisation of spectral lines magnet. Do they (roughly) follow the „ Important: Zeeman effect changes not just field lines? the spectral shape of a (often „ Relatively horizontal subtle and difficult to measure), but also field in introduces a unique polarisation signature chromosphere? ÎMeasurement of polarization is central to „ Note spiral structure Measurement of polarization is central to around . measuring solar magnetic fields.

8 Polarized radiation Zeeman splitting of atomic levels

„ „ Polarized „ In the presence of a B- field a level with total radiation is field a level with total angular moment J will described by split into 2J+1 sublevels the 4 Stokes with different M. parameters: I, Q, U and V „ EJ,M = EJ+µ0 gMJB „ I = total intensity = I (0o) + I (90o) = I (45o) + I (135o) = lin lin lin lin „ Transitions are allowed Icirc(right) + Icirc(left) between levels with o o „ Q = Ilin(0 ) - Ilin(90 ) ∆J = 0,±1 & ∆M = 0 (π), o o ±1 (σ , σ ) „ U = Ilin(45 ) - Ilin(135 ) b r „ Splitting is determined „ V = I (right) - I (left) circ circ by Lande factor g : „ Note: Stokes parameters are sums and differences of g(J,L,S) = 1+(J(J+1)+ intensities, i.e. they are directly measurable S(S+1)-L(L+1))/2J(J+1)

Splitting patterns of lines Polarization and Zeeman effect

„ Depending on g of the upper and lower levels, the spectral line shows different splitting patterns „ Positive: π components: ∆M=0 „ Negative: σ components: ∆M=±1 „ Top left: normal Zeeman effect (rare) „ Rest: anomalous Zeeman effect (usual)

Effect of changing field strength Dependence on B, γ, & φ

Formula for Zeeman splitting (for B in G, λ in Å): 2 2 „ I ~ κσ(1+cos γ)/4 + κπ sin γ/2 -13 2 ∆λH = 4.67 10 geffBλ [Å] „ Q ~ B2 sin2γ cos 2φ geff=effective Lande factor of line „ U ~ B2 sin2γ sin 2φ

For large B: ∆λH = ∆λ between σ-component peaks „ V ~ B cos γ

„ Q, U: transverse B=1600 G V component of B „ V: longitudinal component of B I B=200 G Juanma Borrero

9 Zeeman polarimetry Effect of wavelength of spectral line Fe I 1564.8630.2 nm nm „ Most used of astrophysical I V (and certainly solar) magnetic fields „ Effective measurement of field strength if Zeeman splitting is comparable to Doppler width or more: B > 200 G … 1000 G (depending on spectral line) Î works best in photosphere Q U „ Splitting scales with λ Î works best in IR „ Sensitive to cancellation of opposite magnetic polarities Î needs high spatial resolution

Cancellation of magnetic polarity Magnetograms

„ Magnetograph: Spatial resolution Instrument that element makes maps of (net circular) polarization in wing of Zeeman sensitive line. „ Example of magnetogram obtained by MDI = positive polarity „ Conversion of magnetic field polarization into magnetic field requires a careful = negative polarity calibration. magnetic field

What does a Synoptic charts magnetogram show?

„ Plotted at left: „ Top: Stokes I, Q and V along a spectrograph slit „ Middle: Sample Stokes Q profile „ Bottom: Sample Stokes V profile „ Red bars: example of a spectral range used to make a magnetogram. Generally only Stokes V is used Synoptic maps approximate the radial magnetic flux observed (simplest to measure), gives near the central meridian over a period of 27.27 days (= 1 longitudinal component of B. Carrington rotation)

10 Polarized radiative transfer Polarized radiative transfer II

„ Complication: RTE required for 4 Stokes The absorption matrix parameters: Written as differential equation for Stokes vector I = (I ,Q ,U ,V ) for Stokes vector Iν= (Iν ,Qν ,Uν ,Vν) 1+η η η η   I Q U V  „ Eq. in plane parallel atmosphere for a η +η − ρ ρ  Q 1 I V U  spectral line (Unno-Rachkowsky equations): Ω = ν  η ρ 1+η ρ  µ dI /dτ = Ω I – S  U V I Q  ν c ν ν ν  η − ρ − ρ +η   V U Q 1 I  „ Ων = absorption matrix (basically ratio of line SAY MORE ABOUT MATRIX ELEMENTS!!!!!! to continuum absorption coefficient), Sν= SAY MORE ABOUT MATRIX ELEMENTS!!!!!! source function vector, τc = continuum optical SHOW HOW ZEEMAN EFFECT ENTERS depth. INTO THEM, ETC.!!!!!

Polarized radiative transfer III LTE

„ The Zeeman effect only enters through Ων „ In LTE the Unno-Rachkowsky equations simplify since „ Ων contains besides absorption due to Zeeman-split line (ηI , ηQ , ηU , ηV ) also Sν= (Bν , 0, 0, 0) magnetooptical effects, such as Faraday Here Bν = Planck function rotation (ρQ , ρU , ρV ) : rotation of plane of polarization when light passes through B. „ Also, Ων is simplified. The ηI , ηQ , ηU , ηV and ρQ , ρU , ρV values only require application of Saha- „ Ων = Ων(γ, φ, B) , i.e. Ων depends on the full Boltzmann equations (similar situation as for LTE in magnetic vector (in addition to the usual case of normal radiative transfer). Each of these quantities that the absorption coefficient quantities is, of course, frequency dependent. depends on)

Solution of Unno Eqs Basics: magnetic pressure

„ General solution best done numerically (even formal „ Magnetic field exerts a pressure. Pressure balance between solution is non-trivial: exponent of matrix Ων) two components of the atmosphere, 1 and 2 (Gauss units): „ Simple analytical solutions exist for a Milne- B2 B2 Eddington atmosphere (i.e. for Ω independent of τ 1 + = + 2 ν ν P1 P2 and Sν depending only linearly on τν). Particularly 8π 8π simple if we neglect magneto-optical effects „ If, e.g. B2 = 0, then P1 < P2 and it follows: „ I(µ) = β µ (1+ηI)/∆ ÎMagnetic features are evacuated compared to surroundings.

„ P(µ)= β µ ηP/∆, where P = Q, U, or V „ If B2 = 0 and T1 = T2, then also ρ1 < ρ2 , so that the magnetic 2 2 2 2 features are buoyant compared to the surrounding gas. „ ∆ = (1+ηI) - ηQ - ηU - ηV takes care of line saturation „ In the convection zone this means that rising field bundles (flux tubes) keep rising (unless stopped by other „ „ β is derivative of Planck function with respect to τν . , e.g. curvature forces.

11 Basics: plasma β Supergranules and magnetic field

„ Plasma β describes the ratio of thermal to magnetic „ Magnetogram: black and white patches energy density: π β = 8 P „ Horizontal velocity: B2 arrows „ Divergence: „ β < 1 Î Magnetic field dominates and dictates the blue arrows > 0; dynamics of the gas red arrows: < 0 „ Supergranule boundaries: „ β >1 Î Thermal energy, i.e. gas dominates & forces Supergranule boundaries: the field to follow yellow „ Magnetic field is „ β changes with r/R concentrated at edges of „ β >1 in convection zone supergranules „ β <1 in atmosphere, particularly in corona β <<1 ÎB swept out by flow

Frozen-in magnetic fields Magnetic field in the convection zone

„ Magnetic field is swept to supergranule boundaries „ Magnetic field thought to be produced by a Î magnetic field is “frozen” into the plasma dynamo located near the bottom of the „ This happens if there are a sufficient number of convection zone (e.g. in the overshoot layer ionised particles, or equivalently, if the electric below the convection zone). conductivity is very high, since charged particles cannot cross field lines (gyration) Îtoroidal flux tubes „ This is the case, even in the cool photosphere of sunspots (only 10-4 of all particles are ionized), due „ Once field becomes strong enough, it is to the large number of collisions susceptible to buoyancy (Parker instability)

ÎIf plasma moves perpendicularly to the field, it drags „ A loop-like structure moves towards the solar the field with it (or is stopped by the field) and vice versa. Flows parallel to the field are unaffected. surface and breaks out.

Emergence of a magnetic Emergence and of active region: GET BETTER MOVIE!!!!!!!!!! Magnetic field is believed to be generated mainly in the near bottom of convection zone. Due to its buoyancy (see earlier slide; Parker instability), a magnetic field will rise towards the solar surface. At the solar surface it will produce a bipolar active region.

12 The photospheric field Sunspots

Sunspot Umbra Penumbra Granule umbra

Teff ≈ 4500 K penumbra Teff ≈ 5500 K plage T ≈ 5800 K quiet eff Sun

Sunspots, some properties Why are sunspots dark?

„ Field strength: Peak values „ Basically the strong nearlly vertical magnetic field, not 2000-3500 G allowing motions across the field lines, quenches convection inside the spot. „ Brightness: umbra: 20% of „ Since convection is the main source of energy transport just quiet Sun, penumbra: 75% below the surface, less energy reaches the surface through the spot Î dark „ Sizes: Log-normal size distribution. Overlap with pores (log-normal = Gaussian on a logarithmic scale) „ Lifetimes: T between hours & months: Gnevyshev- Waldmeier rule: Amax ~ T, where Amax = max spot area.

Why are sunspots dark? II Magnetic structure of sunspots „ Where does the energy blocked by sunspots go? „ Peak field strength ≈ 2000 – „ Spruit (1982) showed: both heat capacity and 3500 G (usually in darkest, thermal conductivity of CZ gas is very large central part of umbra)

ÎHigh thermal conductivity: blocked heat is „ B drops steadily towards redistributed throughout CZ (no bright rings around boundary, B(Rspot) ≈ 1000 G sunspots) „ At centre, field is vertical, High heat capacity: the additional heat does not lead becoming almost horizontal to a measurable increase in temperature near Rspot . „ In addition: time scale for thermal relaxation of the „ Regular spots have a field CZ is long, 105 years: excess energy is released structure similar to a buried almost imperceptibly. dipole

1 Magnetic Magnetic structure of sunspots structure of sunspots II

Azimuthal averages of the various magnetic field components in a sample of regular (near-

circular) medium-sized Schlichenmaier et al. sunspots. 1998, 1999, 2002

„ Regular on large scales (≈ dipole, Bmax ≈ 2500 G, for simple spots) „ Extremely complex on small scales (penumbra, subsurface)

Highest resolution Sunspot fine structure Scharmer et al. 2002

Penumbral filaments (bright and dark)

Penumbral grain (seen to move inward)

Light bridge

Umbral dot

Sunspots Umbral dots seen in TiO

TiO Zakharov 2004 V. Zakharov

2 Magnetic structure of sunspots In photospheric layers penumbra shows nearly horizontal outward motion, visible as oppositely directed Doppler shifts (umbra remains at rest). In chromosphere: inward directed flow Brightness Doppler shift

X?

Sunspots span too many spatial and temporal scales to be successfully simulated from first principles.

Evershed effect: illustration Siphon flow model of Evershed effect

„ Proposed by Meyer & Schmidt (1968). „ Horizontal „ If there is an imbalance in the field strength of the outflow of two footpoints of a loop, then gas will flow from the matter. footpoint with „ Thought to be lower B to that driven by a with higher B. siphon flow „ Supersonic mechanism flows are „ NEED NEW possible. SLIDE !!!!!!!

B1 < B2

The Wilson effect Sunspot Wilson depression

„ Near the solar Map of Wilson depression limb the umbra (determined from T & B measurements and assumption and centre-side that sunspot magnetic field is close to potential) penumbra disappear ÎWe see 400-800 km deeper into sunspots than in photosphere „ Correct interpretation Other interpretation by e.g. W. Herschell: by Wilson (18th photosphere is a layer of hot century). through which we see deeper, cool layers: the true, populated surface of the Sun. Shibu Mathew

3 What causes the Wilson depression? Magnetic elements „ Most of the magnetic flux on the solar surface „ B square/8 pi means gas pressure lower in occurs outside sunspots and pores (=smaller spot than outside i.e. density also lower, i.e. dark magnetic structures). fewer atoms to absorb, i.e. opacity also lower „ These most common magnetic features, „ we see deeper into spot called magnetic elements, are small (diameters partly below spatial resolution of 100 km), bright and concentrated in network and facular regions. „ Magnetic elements are usually described by thin magnetic flux tubes (i.e. bundles of nearly parallel field lines).

Temperature contrast vs. size Surprisingly constant field strength

Magn. elements Pores Sunspots Magn. elements Pores Sunspots

Temperature stratifications of quiet Increased Sun, sunspot, plage contrast of

„ Dashed line: Quiet Sun magnetic atmosphere elements in „ line: sunspot atmosphere higher layers „ Dot-dashed line: active region plage atmosphere „ Plage is hottest everywhere in atmosphere „ Sunspot coldest in photosphere, but gets hotter in chromosphere

4 Why are Why are magnetic elements bright? faculae •Quenching of convection `Hot wall´ radiation best •Partial evacuation seen → enhanced transparency → heating by `hot walls´ near → local flux excess limb? •Inflow of radiation wins because the flux tubes are narrow (diameter ~ Wilson The Sun in depression). White Light, with limb •High heat conductivity darkening → flux disturbance partly propagates into the removed deep convection zone → Kelvin-Helmholtz time MDI on SOHO

Flux tube brightening near limb Bz vz (Z=0) (Z=0) >500G 6 >1000G Mm >1500G

3-D compressible radiation-MHD Ic simulations (Z=0) Plage: BZ(t=0) = 200 G

Grid Size: 288 x 288 x 100 „ The flux tubes expand with height (pressure balance Vertical extent: 1.4 Mm „ They appear brightest when hot walls are well seen, i.e. near limb (closer Horizontal extent: 6 Mm to limb for larger tubes Alexander Vögler et al.

Bz vz 3-D Radiation-MHD Simulations Alexander Vögler, Robert Cameron, Manfred Schüssler

. Mixed polarity simulations: diffusion & cancellation of opposite Details of polarities (20 km resolution): =200G. thin . Bz Bz < 200 G magnetic flux sheet 6000 km

I Steiner et al.T 1994 C Horizontal cuts near surface level Vögler et al. 2005

1 G-band Spectrum Synthesis Simulations require computers... G-Band (Fraunhofer): spectral range: 4295-4315 Å contains many temperature-sensitive molecular lines (CH)

For comparison with observations, we define as G-band intensity the integral of the spectrum obtained from the

simulation data: 4315 A I = I (l )dl Shelyag et al. 2004 G ò 4295 A

G-band: Simulation vs. Observation Stokes V asymmetry

n Stokes V profiles observed in quiet Sun and in active region plage are asymmetric: typically blue wing has larger area ‘A’ and amplitude ‘a’ Simulation (20 km resolution) Observation (100 km resol.) than red wing Schüssler et al. 2003 (SST, La Palma) Shelyag et al. 2004 Scharmer et al. 2002

Producing Stokes d Flux Tubes, Canopies, Loops and V asymmetry Funnels n Consider 2-layered atmosphere: n Bottom layer a: v but c no B n Top layer b: B but no v n Note the importance b of line saturation for producing asymmetric V profile. a

1 Measurement of B at coronal base Structure of Magnetic Loops „ Previously: Magnetic Magnetic loops vector only known at solar deduced from surface. However, magnetic measurements field has main effect in corona. Exception: radio observations of He I 10830 Å give |B| but low resolution. Stokes profiles „ Now: Direct measurement of in an emerging full magnetic vector at base of flux region. corona & in cool loops possible Left projection: Field strength „ Measurement using He I 10830 Å (TIP, VTT, Tenerife) & simple inversion code Right projection: Vertical velocity Andreas Lagg Solanki et al. 2003, Lagg et al. 2004

Magnetic field extrapolations: Testing Magnetic Extrapolations free and potential fields „ Non-linear force-free fields reproduce the loops „ General problem in solar physics: Magnetic field is reconstructed from observations better than the linear force- free ones and far better than potential field extrapolations. measured mainly in the photosphere, but it makes free ones and far better than potential field extrapolations. the music mainly in the corona. „ Loops harbour strong currents while still emerging. ÎEither improve coronal field measurements or extrapolate from photospheric measurements into the corona. „ If β <<1 then we can neglect the influence of the gas Observed Potential linear force free non-linear ff on the field: the field is force-free. Considerable simplification of the computations „ If we further assume that there are no currents, the Wiegelmann et al. 2004 computations become even simpler (potential field).

Prominences Kippenhahn’s magnetic circus

„ What if we were like plasma, frozen into the field?Problem: prominence material is dense and cool and high in the Î It must be supported „ Trapezeagainst artist . as aObvious model supporting structure: formagnetic a prominence field. However, magnetic field must be curved upwards to keep the material from flowing „ In lower picture, she is downhanging along quite the stably, field lines. Different solutions have although much denserbeen proposed. than the surrounding air.

1 Prominence Large scale magnetic structure of the models quiet Sun Kippenhahn-Schlüter Kippenhahn-Schlüter „ At large scales (below), Kuperus-Raadu dipolar (below right) and flux tube component of the (right) magnetic field survives, since multipoles Î B~r-n-1, where n=2 for dipole, n=3 for quadrupole, etc. „ Closer to sun ever higher order multipoles are important

Solar current sheet at activity minimum Heliospheric current sheet and Parker spiral „ At activity minimum solar magnetic field „ Since solar wind expands radially beyond the Alfven radius is like a dipole, (where the energy density in the wind exceeds that in the whose field lines are magnetic field) and the Sun rotates (i.e. the footpoints of the stretched out by the field), the structure of the field (carried out by the wind, but solar wind. anchored on rotating surface) shows a spiral structure. „ Field lines with opposite polarity lie close to each other near equator: euatorial current sheet. „ If dipole axis inclined to ecliptic: magnetic polarity at Earth changes over solar rotation.

2