Stellar magnetic fields of young sun-like stars. Aline Vidotto Swiss National Science Foundation Ambizione Fellow University of Geneva

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1 Swiss National Science Foundation Ambizione Fellow University of Geneva

2 Age-rotation-activity relation Skumanich 72 rotation velocity (km/s) chromospheric activity Young stars = fast rotation & high activity age (Gyr) 2

3 How to measure stellar magnetic fields? Zeeman Broadening Zeeman Doppler imaging

4 Zeeman Broadening Zeeman splitting Reiners 12 Broadening: better sensitivity in the infra-red e = 2 4 mc 2 g lan B 4

5 Zeeman Broadening: example of an accreting star Magnetic field measurements in integrated light (Stokes I) Johns-Krull 2009 Ti I: Zeeman sensitive CO: Zeeman insensitive Best fit: multiple component-field (distribution of f): < BI >= Bi fi Total unsigned magnetic field strength: < BI > 2.1kG 5

6 Zeeman Broadening: example of an accreting star Magnetic field measurements in integrated light (Stokes I) Johns-Krull 2009 Ti I: Zeeman sensitive CO: Zeeman insensitive Best fit: multiple component-field (distribution of f): < BI >= Bi fi Total unsigned magnetic field strength: < BI > 2.1kG How about the field topology? tomographic imaging techniques 5

7 How do we map stellar surface magnetic fields? Doppler Imaging Credit: J.-F. Donati Credit: J.-F. Donati 6

8 How do we map stellar surface magnetic fields? Zeeman Doppler Imaging Radial component Credit: J.-F. Donati 7

9 How do we map stellar surface magnetic fields? Zeeman Doppler Imaging Zeeman effect: magnetic field splits lines Stokes V = - Radial component Credit: J.-F. Donati 7

10 How do we map stellar surface magnetic fields? Zeeman Doppler Imaging Zeeman effect: magnetic field splits lines Stokes V = - Radial Azimuthal component Credit: J.-F. Donati 7

11 How do we map stellar surface magnetic fields? Zeeman Doppler Imaging Zeeman effect: magnetic field splits lines Stokes V = - Track Stokes V get field along observer s direction (Blos) R v V (v) B los = I c g lan c R h 1 dv I(v) I c i dv Radial Azimuthal component Credit: J.-F. Donati 7

12 How do we map stellar surface magnetic fields? From Stokes V profile use inversion techniques to derive Br,Bϕ,Bθ HD (K2V) Fares+(2010) 8

13 How do we map stellar surface magnetic fields? From Stokes V profile use inversion techniques to derive Br,Bϕ,Bθ HD (K2V) Fares+(2010) radial azimuthal meridional 8

14 How do we map stellar surface magnetic fields? From Stokes V profile use inversion techniques to derive Br,Bϕ,Bθ HD (K2V) Fares+(2010) radial azimuthal meridional < BV >~22G 57% of Etoroidal 26% of Eaxisymmetric poloidal 8

15 Comparison between both techniques Reiners & Basri 2009 Zeeman broadening: total field Zeeman Doppler Imaging: vectorial field Morin et al 2010 ZDI reproduces ~ 5-15% of the field observed by ZB 9

16 Comparison between both techniques Reiners & Basri 2009 Zeeman broadening: total field Zeeman Doppler Imaging: vectorial field Morin et al 2010 ZDI reproduces ~ 5-15% of the field observed by ZB What causes this discrepancy? A: flux cancelation of unresolved regions of opposite polarity field (small scale) 9

17 ZDI typical resolution Br,Bϕ,Bθ: described as spherical harmonics. Example: B r (, )= X l,m b lm P l,m (cos )e im where the highest order component is l max ' 2 v sin i FWHM Stellar magnetograms: lmax ~ 5 to 10 Credit: Colin Johnstone 10

18 ZDI typical resolution Br,Bϕ,Bθ: described as spherical harmonics. Example: B r (, )= X l,m b lm P l,m (cos )e im where the highest order component is l max ' 2 v sin i FWHM Stellar magnetograms: lmax ~ 5 to 10 Solar magnetograms: lmax > 192 (?!) Credit: Colin Johnstone 10

19 ZDI typical resolution Br,Bϕ,Bθ: described as spherical harmonics. Example: B r (, )= X l,m b lm P l,m (cos )e im where the highest order component is l max ' 2 v sin i FWHM Stellar magnetograms: lmax ~ 5 to 10 Solar magnetograms: lmax > 192 (?!) ZDI: probes the large-scale field of the star Credit: Colin Johnstone 10

20 What does this mean? Total field measured? Topology studied? (ie, vector B) Ideal targets Zeeman Broadening (Stokes I) Yes: large and small scales No: average over entire surface only slow rotators (no rotational broadening) Zeeman Doppler Imaging (Stokes V) No: limited to large-scale fields (lmax 10) Yes: surface distribution of Br, Bϕ, Bθ moderate/fast rotators 11

21 What does this mean? Total field measured? Topology studied? (ie, vector B) Ideal targets Zeeman Broadening (Stokes I) Yes: large and small scales No: average over entire surface only slow rotators (no rotational broadening) Zeeman Doppler Imaging (Stokes V) No: limited to large-scale fields (lmax 10) Yes: surface distribution of Br, Bϕ, Bθ moderate/fast rotators Complementary techniques 11

22 What have we learned so far? Results from large-scale field measurements

23 Magnetism increases towards more active stars Stokes V (snapshot) survey of 167 solar-type stars with ages up to 9 Gyr Mean value of Blos is 3.9 G (F-stars), 3.4 G (G-stars) and 6.1 G (K-stars) Blos increases with Ca H&K emission Marsden+2014 Marsden+2014 Magnetic field detection rate almost 100% when Index(CaHK)>0.3 13

24 Field topology depends on rotation Petit+08 Solar twins mostly poloidal for low rotation rates, significant large-scale toroidal component for fast rotators slow rotators: Prot~ 20 to 23 days fast rotators: Prot~ 9 to 12 days radial azimuthal meridional 14

25 Field topology depends on rotation Solar twins Petit+08 rotation threshold at 12 days: for the toroidal magnetic energy to dominate over the poloidal component 15

26 Field topology depends on rotation Solar twins Petit+08 rotation threshold at 12 days: for the toroidal magnetic energy to dominate over the poloidal component 15

27 Magnetic Cycles: τ Boo June/06 (Catala+07) June/07 (Donati+08) January/08 (Fares+09) July/08 (Fares+09) Planet-host star: radial 1.34 M Prot=3 days age ~ 2.5 Gyr azimuthal meridional Pcycle = 2 years (Fares+09) Vidotto

28 Magnetic Cycles: τ Boo June/06 (Catala+07) June/07 (Donati+08) January/08 (Fares+09) July/08 (Fares+09) Planet-host star: radial azimuthal meridional Data-driven simulations of stellar winds & exoplanet interaction: Lunch-talk on Wednesday 1.34 M Prot=3 days age ~ 2.5 Gyr Pcycle = 2 years (Fares+09) Vidotto

29 Magnetic cycles: HD M 2 polarity reversals within 3 years Prot=11.4 days age ~ 2.5 Gyr Morgenthaler

30 Magnetic field topology is very diverse... Zeeman Doppler imaging: large-scale magnetic fields Size: magnetic energy Colour: purely toroidal (blue) or poloidal (red) fields. Shape: purely axisymmetric (decagon) or nonaxisymymmetric (star). Donati & Landstreet (2009) 18

31 Magnetic field topology is very diverse... Zeeman Doppler imaging: large-scale magnetic fields Size: magnetic energy Colour: purely toroidal (blue) or poloidal (red) fields. Shape: purely axisymmetric (decagon) or nonaxisymymmetric (star). Donati & Landstreet (2009) Variety of intensities and topologies 18

32 .. and topology depends on the internal structure I M-dwarf stars: Morin+(2008, 2010); Donati+(2010) sharp transition at ~0.5 M Multipolar B dipolar B partially fully convective due to lack of tachocline? 19

33 .. and topology depends on the internal structure I M-dwarf stars: Morin+(2008, 2010); Donati+(2010) sharp transition at ~0.5 M Multipolar B dipolar B partially fully convective due to lack of tachocline? very low mass (M*<0.3M ): strong dipolar versus weak multipolar: dynamo bistability? (Morin+2011, Gastine +2013) 19

34 .. and topology depends on the internal structure II Magnetic field evolution of very young Suns (CTTSs): Gregory+2012, Donati Mconv~Mstar: axisymmetric, strong Bdipole 2.Mconv=[0.5,1] Mstar: axisymmetric, Bl>dipole dominates 3.Mconv<0.5 Mstar: complex, nonaxisymmetric, weak Bdipole Teff (K) 20

35 .. and topology depends on the internal structure II Magnetic field evolution of very young Suns (CTTSs): Gregory+2012, Donati Mconv~Mstar: axisymmetric, strong Bdipole Teff (K) 20

36 .. and topology depends on the internal structure II Magnetic field evolution of very young Suns (CTTSs): Gregory+2012, Donati Mconv~Mstar: axisymmetric, strong Bdipole 2.Mconv=[0.5,1] Mstar: axisymmetric, Bl>dipole dominates 2 Teff (K) 20

37 .. and topology depends on the internal structure II Magnetic field evolution of very young Suns (CTTSs): Gregory+2012, Donati Mconv~Mstar: axisymmetric, strong Bdipole 3 2.Mconv=[0.5,1] Mstar: axisymmetric, Bl>dipole dominates 3.Mconv<0.5 Mstar: complex, nonaxisymmetric, weak Bdipole 2 Teff (K) 20

38 .. and topology depends on the internal structure II Magnetic field evolution of very young Suns (CTTSs): Gregory+2012, Donati Mconv~Mstar: axisymmetric, strong Bdipole 3 2.Mconv=[0.5,1] Mstar: axisymmetric, Bl>dipole dominates 3.Mconv<0.5 Mstar: complex, nonaxisymmetric, weak Bdipole 2 Teff (K) Evolution from strong & simple axisymmetric fields weaker, complex non-axisymmetric fields 20

39 And magnetism evolves in time... Global perspective of the sample: average of 104 ZDI maps 90 of which have age estimates BV 21

40 And magnetism evolves in time... Global perspective of the sample: Vidotto+14b average of 104 ZDI maps 90 of which have age estimates accreting stars Large-scale magnetic field correlated with ~age -0.5 : magnetochronology BV Compare to Skumanich s prediction: B age -1/2 21

41 What have we learned so far? Small/Large-scale vs Large-scale fields

42 Total field saturates at low Rossby numbers Zeeman broadening Saturation occurs at Ro 0.1, < BI > 3kG Reiners+09,10; Saar+96,01 Ro=Prot/τconv + G0-M2 dwarfs o M dwarfs very low mass fast rotators slow rotators 23

43 Total field saturates at low Rossby numbers Zeeman broadening Saturation occurs at Ro 0.1, < BI > 3kG Reiners+09,10; Saar+96,01 Ro=Prot/τconv + G0-M2 dwarfs o M dwarfs very low mass fast rotators slow rotators 23

44 Total field saturates at low Rossby numbers Zeeman broadening Saturation occurs at Ro 0.1, < BI > 3kG Reiners+09,10; Saar+96,01 Ro=Prot/τconv BI Ro -1.2 (Saar 01) + G0-M2 dwarfs o M dwarfs very low mass fast rotators slow rotators 23

45 also Large-scale field saturates at low Rossby numbers 4 Vidotto+14b (a) < B I > Ro 1.2 Ro=Prot/τconv 3 log(< B V > [G]) 2 o mid dm o late dm 1 0 solar like young suns H-J hosts early-dm Sun Bv < B V > Ro -1.38± log(ro) 24

46 also Large-scale field saturates at low Rossby numbers 4 Vidotto+14b (a) < B I > Ro 1.2 Ro=Prot/τconv 3 Different efficiencies at producing small/large-scale fields (Morin+08, Donati+08) log(< B V > [G]) solar like young suns H-J hosts early-dm Sun Bv < B V > Ro -1.38± log(ro) o mid dm o late dm 24

47 also Large-scale field saturates at low Rossby numbers 4 3 Vidotto+14b (a) BI Ro -1.2 < B I > Ro 1.2 (Saar 01) Ro=Prot/τconv Different efficiencies at producing small/large-scale fields (Morin+08, Donati+08) log(< B V > [G]) solar like young suns H-J hosts early-dm Sun Bv < B V > Ro -1.38± log(ro) o mid dm o late dm 24

48 also Large-scale field saturates at low Rossby numbers 4 3 Vidotto+14b (a) BI Ro -1.2 < B I > Ro 1.2 (Saar 01) Ro=Prot/τconv Different efficiencies at producing small/large-scale fields (Morin+08, Donati+08) log(< B V > [G]) solar like young suns H-J hosts early-dm Sun Bv < B V > Ro -1.38± log(ro) o mid dm o late dm Similar slopes 24

49 X-ray correlates with (total) magnetic flux Magnetic Flux: ΦI = BI (4π R* 2 ) Pevtsov+03 x F,G,K dwarfs o accreting stars. quiet Sun X-ray bright points solar active regions + solar disk Lx ΦI 1.13±

50 X-ray correlates with (total) magnetic flux Pevtsov+03: ~ linear correlation between Lx and ΦI across 12 orders of magnitude large scatter Magnetic Flux: ΦI = BI (4π R* 2 ) x F,G,K dwarfs o accreting stars. quiet Sun X-ray bright points solar active regions + solar disk Lx ΦI 1.13±0.05 Pevtsov+03 25

51 X-ray correlates with (total) magnetic flux Pevtsov+03: ~ linear correlation between Lx and ΦI across 12 orders of magnitude large scatter For the stellar sample: Zeeman broadening measurements Magnetic Flux: ΦI = BI (4π R* 2 ) x F,G,K dwarfs o accreting stars. quiet Sun X-ray bright points solar active regions + solar disk Lx ΦI 1.13±0.05 Pevtsov+03 25

52 X-ray correlates with (total) magnetic flux Pevtsov+03: ~ linear correlation between Lx and ΦI across 12 orders of magnitude large scatter For the stellar sample: Zeeman broadening measurements Magnetic Flux: ΦI = BI (4π R* 2 ) x F,G,K dwarfs o accreting stars. quiet Sun X-ray bright points solar active regions + solar disk Lx ΦI 1.13±0.05 Pevtsov+03 25

53 X-ray correlates with (total) magnetic flux Pevtsov+03: ~ linear correlation between Lx and ΦI across 12 orders of magnitude large scatter For the stellar sample: Zeeman broadening measurements Magnetic Flux: ΦI = BI (4π R* 2 ) x F,G,K dwarfs o accreting stars. quiet Sun X-ray bright points solar active regions + solar disk Pevtsov+03 Lx Lx (dwarfs) ΦI 1.13±0.05 ΦI 0.98± objects 25

54 X-ray correlates with (total) magnetic flux Pevtsov+03: ~ linear correlation between Lx and ΦI across 12 orders of magnitude large scatter For the stellar sample: Zeeman broadening measurements Magnetic Flux: ΦI = BI (4π R* 2 ) x F,G,K dwarfs o accreting stars. quiet Sun X-ray bright points solar active regions + solar disk Pevtsov+03 Lx Lx (dwarfs) ΦI 1.13±0.05 ΦI 0.98± objects Do we find similar relation for ΦV = Bv (4πR* 2 )? 25

55 also X-ray correlates with (large-scale) magnetic flux Lx(ΦV) and Lx(ΦI) ~agree Vidotto+14b 26

56 also X-ray correlates with (large-scale) magnetic flux Lx(ΦV) and Lx(ΦI) ~agree Vidotto+14b 26

57 also X-ray correlates with (large-scale) magnetic flux Lx(ΦV) and Lx(ΦI) ~agree Vidotto+14b For non-accreting stars: Lx(ΦV) is steeper than Lx(ΦI) 61 objects 26

58 also X-ray correlates with (large-scale) magnetic flux Lx(ΦV) and Lx(ΦI) ~agree Vidotto+14b For non-accreting stars: Lx(ΦV) is steeper than Lx(ΦI) Further investigation: finding a different power law for ΦV and ΦI may shed light on how the small- and largescale field structures contribute to LX 61 objects 26

59 Small+large-scale vs large-scale fields Only a few objects that have measurements of Bv & BI Comparison made from statistics of 2 samples 27

60 Small+large-scale vs large-scale fields Only a few objects that have measurements of Bv & BI Comparison made from statistics of 2 samples Large-scale field Bv Ro -1.38±0.14 (Vidotto+14b) Bv Prot -1.32±0.14 (Vidotto+14b) Lx ΦV 1.80±0.20 (Vidotto+14b) Large+small scale field BI Ro -1.2 (Saar 01) BI Prot -1.7 (Saar 96) Lx ΦI 0.98±0.19 (Pevtsov+03) 27

61 Small+large-scale vs large-scale fields Only a few objects that have measurements of Bv & BI Comparison made from statistics of 2 samples Large-scale field Bv Ro -1.38±0.14 (Vidotto+14b) Bv Prot -1.32±0.14 (Vidotto+14b) Lx ΦV 1.80±0.20 (Vidotto+14b) Large+small scale field BI Ro -1.2 (Saar 01) BI Prot -1.7 (Saar 96) Lx ΦI 0.98±0.19 (Pevtsov+03) Agreement between 2 techniques: possible coupling between Bv & BI only one dynamo process that generates both fields? 27

62 One-slide summary: unified interpretation Vidotto+14b 28

63 One-slide summary: unified interpretation log(l X /L bol ) ±0.15 L X /L bol < B V > Vidotto+14b Wright L x /L bol < B I > 2.25 solar like young suns H-J hosts early-dm Sun log(< B V > [G]) 4 (a) < B I > Ro log(< B V > [G]) solar like young suns H-J hosts early-dm Sun solar like young suns H J host early dm Sun T Tauri 1.38 ±0.14 < B V > Ro log(t [yr]) log(ro) 8 28

64 One-slide summary: unified interpretation log(l X /L bol ) ±0.15 L X /L bol < B V > Vidotto+14b Wright L x /L bol < B I > 2.25 solar like young suns H-J hosts early-dm Sun log(< B V > [G]) 4 (a) < B I > Ro log(< B V > [G]) solar like young suns H-J hosts early-dm Sun solar like young suns H J host early dm Sun T Tauri 1.38 ±0.14 < B V > Ro Stellar magnetism is a complex function of many variables: age, mass, rotation, activity, internal structure... log(t [yr]) log(ro) 8 28

65 One-slide summary: unified interpretation log(l X /L bol ) ±0.15 L X /L bol < B V > Vidotto+14b Wright L x /L bol < B I > 2.25 solar like young suns H-J hosts early-dm Sun log(< B V > [G]) Thank you! 4 (a) < B I > Ro log(< B V > [G]) solar like young suns H-J hosts early-dm Sun solar like young suns H J host early dm Sun T Tauri 1.38 ±0.14 < B V > Ro Stellar magnetism is a complex function of many variables: age, mass, rotation, activity, internal structure... log(t [yr]) log(ro) 8 28