Saas Fee 39 Magnetic Fields in the Atmospheres of the Sun and Stars Sami K. Solanki Max Planck Institute for Solar System Research Before starting... Concentrate on observations: only few equations Will use cgs units Many people have contributed tremendously with material, advice etc. Without their help this lecture would never have been possible. Only some are named here: Svetlana Berdyugina, Juan-Manuel Borrero, Paul Charbonneau, Stefan Dreizler, Mark Giampapa, Andreas Lagg, John Landstreet, Theresa Luftinger, Coralie Neiner, Hardi Peter, Ansgar Reiners, Manfred Schüssler, Greg Wade ThankThank you!you! Table of contents 0. Introduction Basics of polarimetry and the measurement of solar magnetic fields The Sun's large-scale magnetic structure Sunspot magnetic fields Faculae and network magnetic fields Magnetic fields in the upper solar atmosphere Manifestations of the magnetic field in the Sun's atmosphere Techniques for stellar magnetic field measurements Magnetic fields in the Herzsprung-Russell diagram Activity in stellar envelopes caused by the magnetic field IntroductionIntroduction The Sun in White Light Gas at 5800 K The Dynamic Sun Prominence Sunspot The Violent Sun Flare Solar wind and coronal mass ejections TheThe sourcesource ofof thethe SunSun’’ss activityactivity isis thethe magneticmagnetic fieldfield ÎÎ InIn orderorder toto understandunderstand thethe dynamicsdynamics andand activityactivity ofof thethe SunSun wewe needneed toto knowknow andand understandunderstand thethe magneticmagnetic fieldfield Wiegelmann 2004 Stellar magnetic fields 40,000 20,000 10,000 7500 5500 4500 3000 (K) 106 Magnetic fields WR are found on ? G AGB 10-3-10 G 4 O-B stars throughout 10 2 10 G the HR-diagram <30% Ae-Be Post-MS 102 (103)G ) ☼ 2 1-10%? RGB 10 1-103 G Often they BpAp 103-104G produce activity T Tau MS 5% 103 on the star or 1 Solar 100%? 3 Luminosity (L 1-10 G influence its ?% WD red −2 6 9 evolution (e.g. of 10 10 -10 G: 10% dwarfs NS 1-106 G: ?% 3 10-10 G Pre-MS stellar rotation) 9 15 10 -10 G 5-40% 100%? 10−4 O B A F G K M Berdyugina 2008 Spectral class BasicsBasics ofof polarimetrypolarimetry andand thethe measurementmeasurement ofof solarsolar magneticmagnetic fieldsfields Methods of solar magnetic field measurement DirectDirect methods:methods: Zeeman effect Î polarized radiation Hanle effect Î polarized radiation Gyroresonance and Bremsstrahlung Î polarized radiation (in radio range) IndirectIndirect methods:methods: ProxiesProxies Bright or dark features in photosphere (sunspots, G- band bright points) Ca II H and K plage Fibrils seen in chromospheric lines, e.g. Hα Coronal loops seen in EUV or X-radiation Atom in magnetic field Consider the Hamiltonian of an atom in a magnetic field (Gaussian cgs units; atom in L-S coupling) ⎛ e e2 ⎞ =−∇+H h 2 V()() r +ξ LS r ⋅+−⎜ BLS( 2 ⋅++ ) (Br sinθ 2 ⎟ ) ⎜ 2 ⎟ 2m ⎝ 2mc 8mc ⎠ First 3 terms are kinetic energy, electronic potential, spin-orbit coupling( )rwith 1ξ /( m= 2 c2 r 2 )( dV / ) dr Last two terms are magnetic energy terms derived from magnetic vector potential For fields up to B~10 MG (1 kT), magnetic terms are small compared to Coulomb potential. Fine structure and field treated by perturbation theory g J. LandstreetinwolFol Magnetic field regimes ⎛ e e2 ⎞ =−∇+H h 2 V()() r +ξ LS r ⋅+−⎜ BLS( 2 ⋅++ ) (Br sinθ 2 ⎟ ) ⎜ 2 ⎟ 2m ⎝ 2mc 8mc ⎠ Perturbation theory regimes: Quadratic magnetic term << linear term << spin-orbit term: (linear) Zeeman effect Quadratic magnetic term << spin-orbit term << linear term: Paschen-Back effect un r S Spin-orbit term << linear termFo << quadratic magnetic term: quadratic Zeeman effect Schiff 1955, Quantum Mechanics, Chapts. 23 & 39 g J. LandstreetinwolFol (Linear) Zeeman effect In weak-field (Zeeman) limit, atomic energy level is only slightly perturbed by (e/2mc)B⋅( L+2 S) In L-S coupling (light atoms), J and MJ are good quantum numbers. Magnetic moment of atom is aligned with J. Energy shift of level is proportional to B⋅J, so there are 2J+1 different magnetic sublevels Ei=Ei 0 + gi (eℏ/2mc) B MJ = EEi 0++ μμ0 ggi MMJ BB where gi=1+[ J ( J+1)+S (S+1)−L( L+1)]/ [2 J ( J+1) ] is the (dimensionless) Landé factor (L-S coupling) Zeeman splitting of atomic levels & lines Transitions between B = 0 B > 0 M Zeeman split upper J and lower atomic levels J = 1 +1 lead to spectral lines 0 that are split in -1 wavelength Transitions are allowed Energy between levels with ∆J = 0, ±1 & J = 0 0 ∆MJ = 0 (π), ±1 (σb, σr) (for the most common I types of transitions: electric dipole radiation) λλ Splitting patterns of lines G. Mathys DependingDepending onon gg ofof thethe upperupper andand lowerlower levels,levels, thethe spectralspectral lineline showsshows differentdifferent splittingsplitting patternspatterns Positive:Positive: ππ components:components: ΔΔMMJ == 00 Negative:Negative: σσ components:components: ΔΔMMJ == ±±11 TopTop left:left: normalnormal ZeemanZeeman effecteffect (rare)(rare) Rest:Rest: anomalousanomalous ZeemanZeeman effecteffect (usual)(usual) Zeeman effect observed First measurement of a cosmic magnetic field, in a sunspot, was carried out 1908 by G.E. Hale On Sun: Zeeman effect changes spectral shape of a spectral line (subtle in most lines outside sunspots) Zeeman effect also introduces a unique polarisation signature Î Measurement of polarization is central to measuring solar magnetic fields Polarized radiation Polarized radiation is described by the 4 Stokes parameters: I, Q, U and V o o o o I = total intensity = Ilin(0 ) + Ilin(90 ) = Ilin(45 ) + Ilin(135 ) = Icirc(right) + Icirc(left) o o Q = Ilin(0 ) - Ilin(90 ) o o U = Ilin(45 ) - Ilin(135 ) V = Icirc(right) - Icirc(left) Note: Stokes parameters are sums and differences of intensities, i.e. they are directly measurable Polarization and Zeeman effect Zeeman effect: information content Line splitting I/Ic Stokes I ⇒ B Line broadening Stokes I : no info on B Q/I Polarization Stokes V ⇒ <Blong> Stokes Q, U, V ⇒ B U/I Atomic diagnostics (hot gas) Zeeman effect (except V/I some Ap stars & WDs) Molecular diagnostics (cool) Zeeman & Paschen Back (ZIMPOL, J. Stenflo) Effect of changing field strength Formula for Zeeman splitting (for B in G, λ in Å): -13 2 ΔλH = 4.67 10 geff B λ [Å] 1 1 g= g() g +( + g )( g + (+ J 1 J ) − ( J + 1 J )) eff 2 l u 4 l u l l u u geff is the effective Landé factor of line 2 For large geff Bλ : ΔλH = Δλ betw. σ-component peaks B=1600 G V I B=200 G Zeeman splitting ~ λ2 FeFeFe III 1564.81564.8630.2 nm nmnm II VV QQ UU Dependence on B, γ, and φ 2 2 II ~~ κκσ(1+(1+coscos γγ)/4)/4 ++ κκπ sinsin γγ/2/2 QQ ~~ BB2 sinsin2γγ coscos 22φφ UU ~~ BB2 sinsin2γγ sinsin 22φφ VV ~~ BB coscos γγ VV:: longitudinallongitudinal componentcomponent ofof BB J.M. Borrero Q,Q, UU:: transversetransverse componentcomponent ofof BB AboveAbove formulaeformulae forfor Q,U,VQ,U,V referrefer toto relativelyrelatively weakweak fieldsfields (e.g.(e.g. BB andand BB2 dependencedependence ofof field)field) ZeemanZeeman splittingsplitting etc.etc. isis hiddenhidden inin κκσ andand κκπ.. ForFor Q,Q, U,U, VV thesethese dependencesdependences havehave notnot beenbeen givengiven forfor simplicity.simplicity. Dependence on B, γ, and φ 2 2 II ~~ κκσ(1+(1+coscos γγ)/4)/4 ++ κκπ sinsin γγ/2/2 J.M. Borrero QQ ~~ BB2 sinsin2γγ coscos 22φφ UU ~~ BB2 sinsin2γγ sinsin 22φφ VV ~~ BB coscos γγ Q, U: transverse component of B V: longitudinal component of B Formulae for Q,U,V refer to weak fields κσ and κπ (splitting etc.) not given for Q,U,V for simplicity Magnetograph: Magnetograms Instrument to make maps of (net circular) polarization in wing of Zeeman sensitive line Useful when star can be resolved, e.g. Sun Image: Example of magnetogram obtained by MDI Conversion of polarization into magnetic field requires a careful calibration. positive negative polarity polarity What does a magnetogram show? PlottedPlotted atat left: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. Often only Stokes V is used (simplest to measure), gives longitudinal component of B. SynopticSynoptic chartscharts Synoptic maps approximate the radial magnetic flux observed near the central meridian over a period of 27.27 days (= 1 Carrington rotation) Dependence on B, γ, and φ 2 2 II ~~ κκσ(1+(1+coscos γγ)/4)/4 ++ κκπ sinsin γγ/2/2 J.M. Borrero QQ ~~ BB2 sinsin2γγ coscos 22φφ UU ~~ BB2 sinsin2γγ sinsin 22φφ VV ~~ BB coscos γγ Q, U: transverse component of B V: longitudinal component of B Formulae for Q,U,V refer to weak fields κσ and κπ (splitting etc.) not given for Q,U,V for simplicity Measured Magnetic Field at Sun’s Surface MonthMonth longlong sequencesequence ofof magnetogramsmagnetograms (approx.(approx. oneone solarsolar rotation)rotation) MDI/SOHOMDI/SOHO MayMay 19981998 Cancellation of magnetic polarity SpatialSpatial resolutionresolution elementelement Unresolved magnetic features with field strength B and filling factor f= A/ A Stokes ∑ i tot V i == positivepositive polaritypolarity magneticmagnetic fieldfield == negativenegative polaritypolarity magneticmagnetic fieldfield Stokes V signal cancellation Stokes V signal only samples the net magnetic flux. Extreme case: negativenegative polaritypolarity positivepositive polaritypolarity magneticmagnetic fluxflux = magneticmagnetic fluxflux ++ == Scattering polarisation at Sun’s limb IfIf collisionscollisions areare rare,rare, Linearly polarized lightlight isis scatteredscattered scattered photon IlluminationIllumination ofof atomsatoms isis anisotropicanisotropic duedue to:to: Limb darkening (dT/dz < 0, where T = temp.) atom high in atmosph. ScatteringScattering ++ anisotropyanisotropy ÎÎ linearlinear polarisationpolarisation parallelparallel toto limblimb HanleHanle effect:effect: ModificationModification Hanle effect ofof scatteringscattering polarisationpolarisation byby magneticmagnetic field.field. 22 effects:effects: DepolarisationDepolarisation depends on field orientation depends on B (it is complete if ΔλH >> natural line width, i.e.