Stellar Magnetospheres part deux: Magnetic Hot Stars. Stan Owocki

Transcription

1 Stellar Magnetospheres part deux: Magnetic Hot Stars Stan Owocki

2 Key concepts from lec. 1 MagRe# --> inf => ideal => frozen flux breaks down at small scales: reconnection Lorentz force ~ mag. pressure + tension plasma β ~ P gas /P mag ~ (a/v A ) 2 press. scale ht. H << R (except in corona) wind mag. conf. η ~B 2 R 2 /Mdot*V

3 Wind Magnetic Confinement Ratio of magnetic to kinetic energy density: η(r) B2 /8π = V A ρv 2 /2 v 2 = B2 r 2 = B q * R * (r /R * ) M v M v (1 R * /r) β η * for OB SG, to get η * ~ 1, need B * ~ 100 G Alfven Radius: η( R A ) 1 2 e.g, for dipole field, q=3; η ~ 1/r 4 For dipole (q=3): R A = η * 1/4 R *

4 Hot Stars vs. Sun Luminous Radiative Envelope (not conv.) Radiatively Driven Wind (line scatt.) T wind ~= T eff M dot ~ 10-7 M O /yr >> M dot,sun Detected B-fields often steady, dipole Rotation can be rapid V rot ~< V crit NOT a (direct) solar Coronal analog!

5 Light s Momentum Light transports energy (& information) But it also has momentum, p=e/c Usually neglected, because c is so high But becomes significant for very bright stars, Key question: how big is force vs. gravity?? Γ e =g e /g < 1 (near but below Edd. limit ) CAK wind model: Γ lines = g lines /g > 1

6 Aside: Radiation Pressure vs. Gas Pressure Force depends on gradient of Pressure grad P rad comes from opacity κ Deep interior (τ>>1), P rad nearly isotropic P rad + P gas act together => H ρ =a 2 /g(1-γ) But near surface (τ ~1) radiation beamed wind is not Radiation Pressure Corona H ~< R

7 g = rad Radiative force dν κ n ˆ I /c ν ν 0 e.g., compare electron scattering force vs. gravity L σ Th g el 4 π r 2 c µ e κ e L Γ = = g grav GM 4 π GM c 2 r For sun, Γ O. ~ 2 x 10-5 But for hot-stars with L~ 10 6 L O. ; M=10-50 M O. Γ<1 ~ = κf /c if κ gray

8 Optically Thick Line-Absorption in an Accelerating Stellar Wind For strong, optically thick lines: g thick ~ g thin τ ~ 1 L sob dv ρ dr τ κρ v th dv/dr << R * ~ v th v R *

9 CAK force for power-law line ensemble g ~ g thin lines τ α ~ L 1 dv r 2 ρ dr α

10 CAK wind in zero-gas-pressure limit v dv dr = GM r 2 w r2 vdv/dr GM a2 ρ dρ dr + g lines τ ~ L 1 dv α r 2 ρ dr g thin α w = 1 + C w α C ~ 1 M α

11 Graphical solution M < M CAK M = M > M CAK M CAK

12 Magnetohydrodynamic (MHD) Equations Dρ Dt + ρ v = 0 Mass e t + ev = P v + H M n 2 Λ(T) Energy B t = v B mag Induction ρ Dv Dt = p + 1 4π B ( ) B + ρ(g lines g grav ) Momentum ( ) B = 0 Divergence free B P = ρa 2 = (γ 1)e Ideal Gas E.O.S.

13 Magnetohydrodynamic (MHD) Equations Dρ Dt + ρ v = 0 Mass T = const. Energy ρ Dv Dt = p + 1 4π B ( ) B + ρ(g lines g grav ) Momentum P = ρa 2 Ideal Gas E.O.S. B t = v B ( ) B = 0 mag Induction Divergence free B

14 MHD Simulation of Wind Channeling Isothermal No Rotation Confinement parameter η * =1/3 A. ud Doula PhD thesis 2002

15 MHD Simulation of Wind Channeling Isothermal No Rotation Confinement parameter η * =1 η * =1

16 MHD Simulation of Wind Channeling Isothermal No Rotation Confinement parameter η * = 3

17 MHD Simulation of Wind Channeling Isothermal No Rotation Confinement parameter η * =10

18 MHD Simulation of Wind Channeling Isothermal No Rotation Confinement parameter η =10 η * * =10 R A ~ η * 1/4 R *

19 Isothermal No Rotation Confinement parameter η =10 η * * =1000!! R A ~ η * 1/4 R *

20 Final state of isothermal models 93 G ; η * = G ; η * = G ; η * = G ; η * = G ; η * = G ; η * = 32

21 Θ 1 Ori C

22 MHD simulation for Θ 1 Ori C (O7 V) B obs ~ 1100 G + P rot = 14 days M dot ~ 10-7 M sun /yr η * ~= 14 Magnetic Confined Wind Shock (MCWS) kev X-rays => match Chandra obs.

23 Magnetically Confined Wind-Shocks Babel & Montmerle 1997 Magnetic A p -B p stars

24 log T still no rotation but now with Radiative Cooling ~ 2 kev X-rays fit Chandra spectrum for Θ 1 Ori C Magnetically Confined Wind Shock

25 Θ-1 Ori C Gagne et al. 2005, ApJ, 528, 986 P rot = 13 days

26 Θ1 Ori C β ~ 45 o i ~ 45 o

27 X-ray Light Curve for Θ1Ori C

28 Magnetically Torqued Disk (MTD) Cassinelli et al. 2002

29 Alfven vs. Kepler Radius Kepler co-rotation Radius, R K : GM/ R K 2 = V φ 2 /R K = V rot 2 R K /R * 2 R K = w 2/3 R * w=v rot /V crit V crit 2 = GM/R * Alfven radius: η(r A )=1 R A = η * 1/4 R * e.g, for dipole field, η ~ 1/r 4 when R A > R K : Magnetic spin-up => centrifugal support & ejection

30 Keplerian spin-up vs. escape 10 sqrt(η * ) ~ B w = V rot /V crit

31 MHD Sims of Field-Aligned Rotation V φ /V rigid η * =10 ; v rot =250 km/s (w=1/2) Density R K R A R K R A

32 Field aligned rotation again isothermal, but now with V rot =250 km/s = V crit /2 η * = 32 R K R A

33 Magnetically Torqued Disk Cassinelli et al Owocki & ud-doula 2003

34 σ Ori E

35 Magnetic Bp Stars σ Ori E (B2p V) P rot = 1.2 days => v rot /v crit ~ 1/2 B obs ~ 10 4 G => η * ~ 10 7! => V Alfven very large => Courant time very small => Direct MHD impractical Instead treat fields lines as Rigid

36 Strong field limit: B *,η * --> Field lines act as rigid guides for wind outflow Torque up wind outflow Hold down disk material vs. centrifugal force Problem: V Alfven -> => can t do MHD But can model semi-analytically Rigidly Rotating Magnetosphere (RRM) gas accumulates at minima in grav+cent. potential

37 Effective Gravitational+Centrifugal Potential

38 Rigidly Rotating Magnetosphere Townsend & Owocki (2005)

39 Accumulation Surface Townsend & Owocki (2005)

40

41 RRM model for σ Ori E B * ~10 4 G η * ~10 6! δδδ tilt ~ 55 o

42 RRM model for σ Ori E EM +B-field photometry B * ~10 4 G => η * ~10 6! tilt ~ 55 o δδδ δδδ δδδ Ηα polarimetry

43 Townsend, Owocki & Groote (2005)

44 RRM Model σ Ori E Hα Observations

45 Sanz-Forcada et al. (2004)

46 MHD sim of centrifugal breakout log(ρ) η * = 620 v rot =v crit /2

47 Centrifugally Driven Reconnection Flare log T η * = 620 v rot =v crit /2 ~ 4-5 kev X-ray flares, as seen in σ Ori E

48 Model grid for 2-Parameter study: Rotation & Magnetic Confinement

49 Isothermal, v rot =v crit /2, η * =100 R K R A

50 Isothermal, v rot =v crit /2, η * =100 R K R A

51 Isothermal, v rot =v crit /2, η * =1000 R K R A ~7R *

52 Radial disk mass: dm e /dr dm e dr 2πr2 π / 2 +Λθ / 2 π / 2 Λθ / 2 ρ sinθdθ

53 Equatorial mass distribution dm e /dr 5 η * =100 Radius (R * ) W=1/2 1 0 Time (Msec)

54 Equatorial mass distribution dm e /dr 5 η * =100 Radius (R * ) W=0 1 0 Time (Msec)

55 Parameter study: rotation & magnetic confinement

56 Between RRM and full MHD: Rigid Field Hydro-Dynamics RFHD Solve time-dependent hydro along completely rigid individual field lines

57 The flow along an individual field line

58 Rigid Field - Hydro Model

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61 Summary Magnetic field + hot star wind: η * >10: channel wind into shock (MCWS) explains X-rays from Θ 1 Ori C spin up wind past Kepler co-rotation radius confine material against centrifugal Rigidly Rotating Magnetosphere (RRM) explains H-α vs. rot. phase in σ Ori E mass build up => centrifugal breakout reconnection => T >~ 10 8 K can explain hard X-ray flares in σ Ori E centrifugally driven reconnection

62 3D MHD of MCWS Current & Future Work lateral structure scale, tilted field case Comparison with observations Chandra & XMM X-rays from shocks and flares Optical photometry, spectroscopy, polarimetry Rotation Spin-Down?? VLTI to resolve disk Application to other types of magnetospheres? RRM shock as site for Fermi acceleration?? Could produce up to TeV Gamma Rays!