Zeeman Paschen-Back effects ZE: Weak Bfield Magnetic splitting level separation Splitting linear with B Equal total strength of σ b, π, σ r components (Anti-)symmetric Zero net polarization (Incomplete) PBE Strong Bfield Magnetic splitting level separation Splitting non-linear with B Relative strength of σ b, π, σ r components changed Asymmetric Stokes profiles Net polarization of profiles Mixing of levels (same m, different J) Forbidden lines
Outline 1. Description of polarized radiation 2. Zeeman and Paschen-Back effects 3. Solar activity Activity phenomena and role of magnetic field Solar activity cycle 4. Stellar magnetic fields 5. Scattering polarization
Coronal Mass Ejections (CME) (LASCO C3, SOHO)
Coronal Mass Ejections (CME)
Aurorae Saturn Earth Jupiter
Corona: X-ray (YOHKOH)
Magnetic loops and flares (TRACE Satellit)
Active Region Chromosphere, Hα Photosphere, G-band Dutch Open Telescope (DOT)
Photosphere Quiet Sun Convective motions Photosphere, G-band
Height dependence of the temperature
Magnetic fields Extremely high electrical conductivity of solar plasma magnetic field frozen to gas Upper atmosphere: Magnetically controlled Magnetic pressure dominates over gas pressure B field force-free Lower atmosphere: Hydrodynamicallycontrolled Gas pressure dominates Transition or regimes in chromosphere (TRACE Satellit)
Magnetic phenomena
Magnetic fields in sunspots Visible light Magnetogram(Stokes V) (Hinode satellite)
Why molecules? Solar photosphere = G stars Sunspot umbra = M stars McMath / NSO
Why molecules? Sunspot umbra: TiO Stokes V/I Sunspot penumbra: only atomic lines Stokes V/I IRSOL / ZIMPOL Wavelength [Å]
Sunspots: Imaging in molecular bands TiO band filter high contrast in umbra SST, Berger & Berdyugina (2003) Zakharov et al. (2005)
Sunspots: 3D structure Simultaneous inversion of Fe I and OH lines in the IR Bottom of photosphere log τ 0.5 = 0 Middle photosphere log τ 0.5 = 2 Wilson depression at τ 1.6 =1 1000 2000 3000 Mag. Field, G 2000 4 Tempe 4000 6000 erature, K Mathew et al. (2003) Mathew et al. (2004)
Small-scale magnetic fields 3D MHD models vs. observations in CH band Radiativelyheated magnetic flux concentrations Schüssler et al.(2003) Shelyag et al. (2004) SST
Small-scale magnetic fields CN band filter Excellent quantitative agreement with predictions CN contrast CH cont Zakharov et al.(2005)
Quiet Sun: fractal magnetic fields Fractal magnetic field structure Field strength probability distribution (1% by volume has 1 4 kg) Stenflo (2004) 400 000 km 40 000 km
Activity cycle: sunspot number Average monthly sunspot numbers 11-year cycle
Activity cycle: total solar irradiance (TSI) variations In phase with 11-year activity cycle Amplitude: 0.1% Maximum TSI during activity maximum
Surface magnetism Spots Faculae Network
Influence of spots on TSI
Influence of faculae on TSI
Influence of network on TSI
Activity cycle: wavelength variability of TSI Variability of the TSI: Total: 0.1% (dominated by visible) UV: factor of 2 X-ray: factor of 100 X-ray images 1991 1995 (Yohkoh satellite) EUV images (Fe XII 195 Å, EIT, SOHO)
Activity cycle: Prediction of cycle 24
Activity cycle: dynamo theory Dynamo generating the solar activity cycle Oscillation between poloidal (dipole-like) and toroidal B field Polarity reversal every 11-years 22-year period of magnetic cycle Requirements: Turbulence Rotation Seed magnetic field
Activity cycle: dynamo theory Ω-effect: Poloidal toroidal (differential rotation) Location: tachocline Amplification to 10 4 10 5 G Buoyant flux tubes rise to surface bipolar active regions α-effect: Toroidal poloidal Cyclonic convection (Coriolis force)
Outline 1. Description of polarized radiation 2. Zeeman and Paschen-Back effects 3. Solar activity 4. Stellar magnetic fields Overview Diagnostics Stellar activity Application: Gravity Probe B 5. Scattering polarization
Magnetic fields across the H-R diagram (L ) 10 6 10 4 10 2 Luminosity 10 1 10 2 10 4 40,000 20,000 10,000 7500 5500 4500 3000 (K) WR? G O-B 10 2 G <30% Ae-Be 10 2 (10 3 ) G 1 10%? BpAp 10 3 10 4 G 5% WD 10 6 10 9 G: 10% NS 1 10 6 G:?% 10 9 10 15 G 100%? AGB 10 3 10 G RGB 1 10 3 G T Tau 10 3 100%? Solar 1 10 3 G?% red dwarfs 10 10 3 G 5 40% O B A F G K M Spectral class Post-MS Pre-MS MS
Magnetic fields across the H-R diagram Idealized picture: Hot stars (outer radiation zone): Fossil fields Static Simple topology: dipole or low order multipole Cool stars (outer convection zone): Dynamo generated fields Stellar activity: starspots, plages, chromospheric emission, enhanced UV, X-ray, and radio emission, CMEs
Spectral class dependence: cool dwarfs Solar analogs: Convection envelope Deepens towards cooler dwarfs Red dwarfs: Become fully convective near M4 (expectation) Transition in dynamo: from solar type (in tachocline) to distributed, turbulent dynamo Sun, etc 1-10 3 G?% red dwarfs 10-10 3 G 5-40%
Magnetic fields in red dwarfs Drop near M7 (expected at M4) Consider spots and impact of B fields on internal structure
Magnetic field on White Dwarf G99-37 B = 7.5 ± 0.5 MG, molecules, Paschen-Back regime (net polarization!)
Magnetic field on White Dwarf G99-37 Paschen-Back effect
Magnetic field diagnostics Line splitting (broadening) Stokes I magnetic field strength B Polarization Stokes V B z Stokes Q, U, V Magnetic field vector B Atomic diagnostics: Hot stars Zeeman effect (except Ap stars and White Dwarfs) Molecular diagnostics: Cool stars Zeeman and Paschen-Back effects
Rotation Activity Faster rotation more active Single stars: slowing down with age
Evidence of cool spots Periodic brightness and color variations Brightness variations up to 0.6 mag When darker redder (i.e. cooler)
Doppler Imaging: atoms Unresolved star Spot on rotating star Bump in line profile Doppler shift bump moves across profile from blue to red side Doppler Imaging technique: Time-series of line profiles (Stokes I) surface image (temperature)
Doppler Imaging: molecules Molecules: Only in cool spots Lines visible simultaneously with spot Doppler shifts High temperature sensitivity Doppler Imaging with molecular spectra: Internal structure of spots
Doppler Imaging: starspots Properties of starspots (high activity stars): Area: 5 20% of surface Temperature difference to photosphere: 500 2000 K Latitude: >30 Lifetime: months IM Peg (RS CVnbinary; primary K2 III; P =24.6 d)
Doppler Imaging: starspots Time evolution activity cycle II Peg (RS CVn; K2 IV; rotation period 6.7 d)
Zeeman-Doppler Imaging Extension of Doppler Imaging: Inversion of all 4 Stokes parameters temperature map Bfield map (vector!) In practice: often only Stokes Iand V
Zeeman-Doppler Imaging Molecular bands additional constraints TiO band
Starspots: molecular bands in Stokes V EV Lac (M3.5e V; P = 4.38 d), TiOA 3 Φ X 3 system, telescope: CFHT
3D structure of starspots AU Mic(M1 V; P = 4.85 d) Observations: Stokes Iand V 4 phases Initial guess: Circular spots Background mixed field Radial component Inversions: ZDI TiO, CaH, Ti I, Fe I, FeH separately Results: T, B(ϕ,λ,h) 3D structure TiO: 210 km CaH: 190 km Coordinate grid Ti I: 160 km FeI: 120 km FeH: 60 km
3D structure of starspots: temperature 210 km AU Mic 130 km 60 km T 3650 K 3400 K 3150 K 2900 K 2650 K 2400 K
3D structure of starspots: magnetic field 210 km AU Mic 130 km 60 km B r +4000 G +2000 G 0 2000 G 4000 G
Stellar activity cycles: brightness variation (RS CVn) (Young solar analog)
Comparison solar stellar activity Outer convection zone required cool stars The faster rotation the more active Highly active stars: Darker at activity maximum Spot dominated (huge spots, high latitude) Low activity stars (including Sun): Brighter at activity maximum Faculae dominated With increasing age (single stars): high low activity
Gravity Probe B Satellite mission to test general relativity theory Polar Earth orbit Science data collection: August 2004 August 2005
Gravity Probe B Test of geodetic effect and frame-dragging effect, both acting on a orbiting gyroscope
Gravity Probe B Geodetic effect: Caused by parallel transport of vector in curved space Precession of orbiting vector (gyroscope): axis of gyroscope slowly drifting within orbital plane Frame-dragging effect (Lense-Thirringeffect): Caused by spinning Earth: drags local spacetime along Precession of vector: gyroscope axis drifting parallel to equator plane Much smaller effect Perpendicular drifts of the two effects
Gravity Probe B Measure drift of the four gyroscopes relative to a distant star with onboard telescope Selected guide star IM Peg Planned accuracy: Geodetic effect: 10 4 Frame-dragging : 10 2 0.5 mas (Note: 0.7 mas 1 R = 13 R ) 300 light years IM Pegasi
Gravity Probe B How much is 0.5 mas? Width of human hair seen from 40 km Diameter 5 Rappen coin seen from 6000 km (Zurich-New York) Astronaut on moon seen from Earth
Gravity Probe B IM Peg: RS CVnbinary Optical centroid shifts Due to binary orbit (detection of secondary as side result) Due to large spots possible errors! daily monitoring; Doppler Imaging Result: Offset due to spots: 0.07 mas( 0.1 R )
Outline 1. Description of polarized radiation 2. Zeeman and Paschen-Back effects 3. Solar activity 4. Stellar magnetic fields 5. Scattering polarization Sun Extrasolar planets
Scattering Polarization Classical description: damped harmonic oscillators as antennas Scattered radiation linearly polarized perpendicular to scattering plane Requires spatial symmetry breaking anisotropy of incident radiation
Second solar spectrum Linearly polarized spectrum arising from coherent scattering Looks completely different than intensity spectrum second solar spectrum Complementary information Different physical mechanisms Continuum (Thomson & Rayleigh scattering, Lyα wings) Resonant line scattering Source of anisotropy: Temperature gradient ( limb darkening)
Second solar spectrum: examples Na ID 2 Na ID 1 Triplet peak Quantum interference
Second solar spectrum: examples Conspicuous molecular lines onlyin Q/I
Hanle effect Modification of scattering polarization due to magnetic field Signatures: Rotation of plane of polarization signature cancels in turbulent fields Depolarization (few exceptions: forward scattering) visible in turbulent fields
Hanle effect: examples Second solar spectrum: Ca II K Turbulent magnetic field depolarization 0 G 6 G 8 G 10 G 100 G
Hanle effect: examples C 2 lines with different Hanle sensitivities (different effective Landé factor) B= 0 G B= 15 G g 0.12-0.12 eff = 0.01 g eff = 0.05 0.001-0.05
Hanle effect Zeeman effect Hanle effect: Weak fields 1 100 G Directed and turbulent fields Turbulent fields: 99% of photospheric volume Zeeman effect: > 100 G Net magnetic flux Strong flux tubes: 1% of photospheric volume
Extrasolar planets Scattered light linearly polarized, perpendicular to scattering plane Periodically varying polarization Idea: Unresolved planet Planets light diluted by star Q/(I star + I planet ) Q/I star Periodic polarization signal (expected signal at most 10 4 ) Diagnostic potential: Orbital parameters Composition of planet s atmosphere Surface structure
Extrasolar planets First polarimetric detection of an extrasolar planet: HD 189733b: Hot Jupiter Period 2.2 d Semi-major axis: 0.0312 AU Needs confirmation!