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Stellar Magnetospheres part deux: Magnetic Hot Stars

Stellar Magnetospheres part deux: Magnetic Hot Stars. Stan Owocki. Key concepts from lec. 1. MagRe# --> inf => “ideal” => frozen flux breaks down at small scales: reconnection Lorentz force ~ mag. pressure + tension plasma b ~ P gas /P mag ~ (a/V A ) 2

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Stellar Magnetospheres part deux: Magnetic Hot Stars

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  1. Stellar Magnetospherespart 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 b ~ Pgas/Pmag ~ (a/VA)2 • press. scale ht. H << R (except in corona) • wind mag. conf. h ~B2R2/Mdot*V¥

  3. e.g, for dipole field, q=3; h ~ 1/r 4 h* for OB SG, to get h*~1, need B* ~ 100 G Wind Magnetic Confinement Ratio of magnetic to kinetic energy density: Alfven Radius: h( RA) º 1 For dipole (q=3): RA = h*1/4 R*

  4. Hot Stars vs. Sun • Luminous Radiative Envelope (not conv.) • Radiatively Driven Wind (line scatt.) • Twind ~= Teff • Mdot ~ 10-7 MO/yr >> Mdot,sun • Detected B-fields often steady, dipole • Rotation can be rapid Vrot ~< Vcrit • 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?? • Ge=ge/g < 1 (near but below “Edd. limit”) • “CAK” wind model: Glines = glines/g > 1

  6. Aside: Radiation Pressure vs. Gas Pressure • Force depends on gradient of Pressure • grad Prad comes from opacityk • Deep interior (t>>1), Prad nearly isotropic • Prad + Pgas act together => Hr=a2/g(1-G) • But near surface (t ~1) radiation “beamed” • wind is not “Radiation Pressure Corona” H ~< R

  7. if k gray e.g., compare electron scattering force vs. gravity s L Th g 2 k 4 r c L p m e e el G º = = g 4 GM c p GM grav 2 r • For sun, GO ~ 2 x 10-5 • But for hot-stars with L~ 106 LO ; M=10-50 MO . . . G<1 ~ Radiative force

  8. Lsob Optically Thick Line-Absorption in an Accelerating Stellar Wind << R* For strong, optically thick lines:

  9. CAK force for power-law line ensemble

  10. CAK wind in zero-gas-pressure limit

  11. Graphical solution

  12. Magnetohydrodynamic (MHD) Equations Mass Momentum Energy Ideal Gas E.O.S. Divergence free B mag Induction

  13. Magnetohydrodynamic (MHD) Equations Mass Momentum Energy Ideal Gas E.O.S. Divergence free B mag Induction

  14. MHD Simulation of Wind Channeling IsothermalNo Rotation Confinement parameter h*=1/3 A. ud Doula PhD thesis 2002

  15. MHD Simulation of Wind Channeling IsothermalNo Rotation Confinement parameter h*=1

  16. MHD Simulation of Wind Channeling IsothermalNo Rotation Confinement parameter h*= 3

  17. MHD Simulation of Wind Channeling IsothermalNo Rotation Confinement parameter h*=10

  18. RA~ h*1/4 R* MHD Simulation of Wind Channeling IsothermalNo Rotation Confinement parameter h*=10

  19. RA~ h*1/4 R* IsothermalNo Rotation Confinement parameter h*=1000 ! !

  20. 295 G ; h* = 1 93 G ; h* = 0.1 165 G ; h* = 0.32 Final state of isothermal models 520 G ; h* = 3.2 930 G ; h* = 10 1650 G ; h* = 32

  21. Q1 Ori C

  22. MHD simulation for Q1 Ori C (O7 V) • Bobs ~ 1100 G + Prot = 14 days • Mdot~ 10-7 Msun/yr • h*~= 14 • Magnetic Confined Wind Shock (MCWS) • kev X-rays => match Chandra obs.

  23. Magnetically Confined Wind-Shocks Babel & Montmerle 1997 Magnetic Ap-Bp stars

  24. Magnetically Confined Wind Shock log T still no rotation but now with Radiative Cooling ~ 2 kev X-rays fit Chandra spectrum for Q1 Ori C

  25. Q-1 Ori C Gagne et al. 2005, ApJ, 528, 986 Prot = 13 days

  26. Q1 Ori C b ~ 45o i ~ 45o

  27. X-ray Light Curve for Q1Ori C

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

  29. Kepler co-rotation Radius, RK: GM/ RK2 =Vf2/RK =Vrot2RK/R*2 RK= w-2/3R* w=Vrot/Vcrit Vcrit2 = GM/R* Alfven radius: h(RA)=1 RA = *1/4 R* e.g, for dipole field,  ~ 1/r 4 Alfven vs. Kepler Radius when RA > RK : Magnetic spin-up => centrifugal support & ejection

  30. Keplerian spin-up vs. escape sqrt(h*) ~B vf > vesc vf< vkep w = Vrot/Vcrit

  31. RK RA RK RA MHD Sims of Field-Aligned Rotation h*=10 ; vrot=250 km/s (w=1/2) Vf/Vrigid Density

  32. Field aligned rotation again isothermal, but now with Vrot=250 km/s = Vcrit/2 RK RA

  33. Owocki & ud-Doula 2003 Magnetically Torqued Disk Cassinelli et al. 2002

  34. s Ori E

  35. Magnetic Bp Stars • s Ori E (B2p V) • Prot = 1.2 days => vrot/vcrit ~ 1/2 • Bobs ~ 104 G => h* ~ 107 ! • => VAlfvenvery large => Courant time very small • => Direct MHD impractical • Instead treat fields lines as “Rigid”

  36. Strong field limit: B*,h* --> ∞ • Field lines act asrigid guides for wind outflow • Torqueup wind outflow • Holddown disk material vs. centrifugal force • Problem: VAlfven ->∞ => 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. RRM model for s Ori E B*~104 G h*~106 ! tilt ~ 55o

  41. RRM model for s Ori E photometry EM +B-field B*~104 G => h*~106 ! tilt ~ 55o Ha polarimetry

  42. Townsend, Owocki & Groote (2005)

  43. Ha Observations s Ori E RRM Model

  44. Sanz-Forcada et al. (2004)

  45. MHD sim of centrifugal breakout log(r) h*= 620 vrot=vcrit/2

  46. Centrifugally Driven Reconnection Flare log T h*= 620 vrot=vcrit/2 ~ 4-5 kev X-ray flares, as seen in s Ori E

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

  48. RK RA Isothermal, vrot=vcrit/2, h*=100

  49. RK Isothermal, vrot=vcrit/2, h*=1000 RA~7R*

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