MagneticMagnetic fieldsfields inin thethe HerzsprungHerzsprung--RussellRussell diagramdiagram
57-19 = 38 slides Stellar magnetic fields
40,000 20,000 10,000 7500 5500 4500 3000 (K) 106 Magnetic fields are WR ? G AGB found on stars 10-3-10 G 4 O-B 10 102 G throughout the HR- <30% Ae-Be diagram Post-MS 102 (103)G )
☼ 2 1-10%? RGB 10 1-103 G PN BpAp Often they produce 103 G 103-104G T Tau MS 5% activity on the star 103 1 Solar 100%? or influence its 3 Luminosity (L 1-10 G ?% evolution (e.g. of WD red −2 6 9 10 10 -10 G: 10% dwarfs stellar rotation). NS 1-106 G: ?% 3 10-10 G Pre-MS 9 15 See next lecture 10 -10 G 5-40% 100%? 10−4 O B A F G K M Berdyugina 2009 Spectral class Stellar magnetic fields
40,000 20,000 10,000 7500 5500 4500 3000 (K) 106 Magnetic fields in WR ? G AGB green shaded part 10-3-10 G 4 O-B 10 102 G of HR diagram are <30% Ae-Be likely produced by Post-MS 102 (103)G ) a dynamo and ☼ 2 1-10%? RGB 10 1-103 G PN BpAp have a complex 103 G 103-104G T Tau MS 5% structure 103 1 Solar 100%? 3 Luminosity (L 1-10 G ?% WD red −2 6 9 10 10 -10 G: 10% dwarfs NS 1-106 G: ?% 3 10-10 G Pre-MS 9 15 10 -10 G 5-40% 100%? 10−4 O B A F G K M Berdyugina 2009 Spectral class Stellar magnetic fields
40,000 20,000 10,000 7500 5500 4500 3000 (K) 106 Magnetic fields in WR ? G AGB degenerate stars 10-3-10 G 4 O-B 10 102 G and those on the <30% Ae-Be path to degeneracy Post-MS 102 (103)G ) are not discussed ☼ 2 1-10%? RGB 10 1-103 G PN BpAp here 103 G 103-104G T Tau MS 5% 103 Randomly discuss 1 Solar 100%? 3 Luminosity (L 1-10 G a few other parts of ?% WD red HR diagram −2 6 9 10 10 -10 G: 10% dwarfs NS 1-106 G: ?% 3 10-10 G Pre-MS 9 15 10 -10 G 5-40% 100%? 10−4 O B A F G K M Berdyugina 2009 Spectral class Cool stars
BfBf ≤≤ 10G10G –– 10103GG ||BB|| ~~ 10103 GG
MagneticMagnetic fieldfield complexcomplex onon smallsmall scalesscales Sun, etc 1-103 G ?% ProducedProduced byby red dwarfs dynamodynamo inin oror 10-103 G 5-40% belowbelow convectionconvection zonezone Dependence of measured cool star fields on rotation rate
Saar 1996
RotationRotation raterate hashas aa dominantdominant influence,influence, justjust asas itit doesdoes forfor XX--rays.rays.
ff ~~ fBfB ~~ PP -1.8,, withwith saturationsaturation forfor PP << 33 daysdays (?)(?) (not(not allall datadata showshow saturation)saturation) Polar spots on active stars Solar spot latitudes RapidRapid rotators:rotators: E.g.E.g. ABAB Dor:Dor: MajorMajor spotspot atat polespoles
RSRS CVnCVn stars:stars: LargeLarge spotsspots atat oror nearnear polespoles Solar spot latitudes ÎSituationSituation forfor rapidrapid rotatorsrotators isis quitequite differentdifferent thanthan forfor sunsun
Solar spot latitudes DonatiDonati etet al.al. The effect of rotation on buoyant flux tube
FCoriolis = ρΩ u )0,(2 φ, −uR Î restoring force u = −2 Ω u &φ R u 2 Ω= u &R φ → uu Ω∝ t)2sin(, R φ
Îinertial oscillations perpendicular to rotation axis Î amplitude depends on Buoyantly expanding flux ring the strength of the buoyancy force Polar spots
Whether tube travels radially in the CZ or is deflected to poles depends on ratio of Coriolis frorce, FC , to Buoyancy, FB
FC || 2 ρ υ Ω 2ΩH = rise ∝ p 2 FB || π HB p)8(/ υA
ρ = density in tube, Hp= pressure scale height, Ω = rotation rate
For Ω = Ω~ : FC For Ω = 3Ω~ : FC >FB For Ω = 10Ω~ : FC >>FB Schüssler & Solanki 1992 A sources of high latitude spots Rising flux tube in rapidly rotating star Schüssler & Solanki 1992; Schüssler et al. 1996; Granzer et al. Truly polar spots only for stars with very deep convection zones Assumption:Assumption: PMS star dynamodynamo residesresides atat interfaceinterface toto radiativeradiative zonezone alsoalso forfor deepdeep convectiveconvective envelopesenvelopes FluxFlux tubestubes risingrising |||| toto rotationrotation axisaxis appearappear veryvery closeclose toto polepole Schüssler et al. 1996 What determines the emergence latitude? MultiplicityMultiplicity Rotation Î Coriolis force AgeAge CoreCore sizesize && BB Î curvature force Mass GravityGravity Î buoyancy force Pre-main-sequence stars (Granzer, 2000) Alternative sources of high latitude spots Schrijver & Title 2001 Meridional flow Latitudinal spot drift on HR1099 (Strassmeier & Bartus, 2000) Eruption vs. trapping: buoyancy vs. curvature Main-sequence star Giant Sufficiently small initial radius: Î curvature force increases more rapidly than buoyancy force Î new equilibrium within the convection zone Trapping for Rtube / Rstar ~< 0.2 Radial vs. toroidal magnetic field Radial Toroidal AB Dor: toroidal field > radial and meridional field Typical of ZDI images of rapid rotators. BUT: Solar field is dominantly radial. Lower MS stars The Sun displays mainly a radial field (due to evacuation, FTs are buoyant and vertical). Are the large toroidal fields found in ZD Images of cool stars real or an artifact? Poloidal (P~20d) Toroidal (P~10d) Radial Toroidal Meridional (Petit et al. 2008) Lower MS stars: M,L,T dwarfs ZeemanZeeman effecteffect FeFe II (IV)(IV) FeH,FeH, TiO,TiO, CaH,CaH, etc.etc. (IV)(IV) Sun, etc OnsetOnset ofof distributeddistributed 1-103 G ?% dynamodynamo red dwarfs 10-103 G M4 (expected), M8 5-40% (observed?) M dwarfs: topology Main question: what changes when going to a fully convective star? Can’t have an overshoot layer dynamo! ZDI with LSD IV (Donati et al. 2008; Morin et al. 2008) M1: toroidal (+non-axi-symm-poloidal) M1: Teff=3950K bipolar region with Br in cool spots M4: axisymmetric poloidal M4: Teff=3750K bipolar region with Br in cool spots How much flux does ZDI miss? B(I) B(I) B(V) B(V) Stars: fully convective stars A. Reiners ForFor G,G, KK andand earlyearly MM starsstars ZDIZDI missedmissed upup toto 95%95% ofof magneticmagnetic fluxflux ForFor fullyfully convectiveconvective MM dwarfsdwarfs thisthis fractionfraction dropsdrops toto 85%:85%: signssigns ofof aa structuringstructuring onon largerlarger scales?scales? Pre-MS stars: T Tauri stars DynamoDynamo actionaction (distributed?)(distributed?) activityactivity && kGkG BB-- Ae-Be 102 (103) G fieldsfields withwith fillingfilling 1-10%? factorfactor ofof almostalmost T Tau unity.unity. Diff.Diff. fromfrom 103 100%? sunsun--likelike starsstars (C.Johns(C.Johns--Krull)Krull) topologytopology ofof fieldfield fromfrom ZDIZDI withwith LSDLSD Imaging a cTTS Clear bipolar signature (1.2 kG) with an additional 1.6 kG octupole. Explains large filling factors deduced from Stokes I spectra Accretion takes place over the pole Low mass cTTS BP Tau (Donati et al. 2008) M=0.7M~ Upper MS stars: Ap and Bp stars Bf~|Bf~|BB|~10|~103––10104 GG O-B 102 G DipolesDipoles (some(some <30% multipoles)multipoles) BpAp FossilFossil fields?fields? 103-104G 5% ProgenitorsProgenitors ofof magneticmagnetic WDs?WDs? Ap and Bp stars A few % of stars with 2-3 M~ show (static) magnetic fields ranging from 60 G to 30,000 G in different stars (lower limit is detection limit) These “magnetic Ap stars” show very unusual atmospheric chemistry – underabundant He, O; overabundant Si, Cr, Sr, rare earths.... Surface abundances vary over surface and with height in atmosphere! Ap stars rotate unusually slowly for these spectral types, with periods of 0.5d to many years Oblique rotator model Arrows show field Rotation axis vectors of roughly axi-symmetric field Coloured bands indicate field strength variations over surface Star rotates about axis not aligned with dipole axis Zeeman Doppler map of 53 Cam ZDIZDI basedbased onon IQUV.IQUV. AlsoAlso determinedetermine abundanceabundance mapmap BB Direction of B Fe I abund. (Kochukhov et al. 2004) Evolution of field strength in Ap stars Sample of magnetic stars in associations and clusters spanning the full main sequence lifetime from ZAMS to TAMS At right, field strengths in 3-4M~ Ap stars seem to decline after an age of about 40 Myr Landstreet et al. Upper MS stars: O - B stars 2 Asymmetric For all observed stars: Maximum CIV wind Symmetric absorption occurs in magnetic equator Magnetically confined wind of β Cep This andpreviousslidekindly provided byHuibHenrichts Pulsating B-star with magnetic field of ~100 G In all magnetic stars: Maximum CIV wind absorption in magnetic equator (predicted: also minimum X-ray flux) Stellar magnetic fields 40,000 20,000 10,000 7500 5500 4500 3000 (K) 106 WR ? G AGB 10-3-10 G 4 O-B 10 102 G <30% Ae-Be Post-MS 102 (103)G So many stars ) ☼ 2 1-10%? RGB 10 1-103 G PN BpAp 103 G 103-104G so little time... T Tau MS 5% 103 1 Solar 100%? 3 Luminosity (L 1-10 G ?% WD red −2 6 9 10 10 -10 G: 10% dwarfs NS 1-106 G: ?% 3 10-10 G Pre-MS 9 15 10 -10 G 5-40% 100%? 10−4 O B A F G K M Berdyugina 2009 Spectral class