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  ~ P gas /P mag ~ (a/V A ) 2 press. scale ht. H << R (except in corona) wind mag. conf.  ~B 2 R 2 /Mdot*V 

3. Wind Magnetic Confinement for OB SG, to get  * ~ 1, need B * ~ 100 G Ratio of magnetic to kinetic energy density: e.g, for dipole field, q=3;  ~ 1/r 4 ** Alfven Radius:  ( R A )  1 For dipole (q=3): R A =  * 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 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??  e =g e /g < 1 (near but below “Edd. limit”) “CAK” wind model:  lines = g lines /g > 1 Light’s Momentum

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

7. Radiative force  ~ e.g., compare electron scattering force vs. gravity  g el g grav   e L 4  GMGMc r  L 4  r 2 c Th  e GM 2  For sun,  O ~ 2 x 10 -5 But for hot-stars with L~ 10 6 L O ; M=10-50 M O... if  gray

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

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 mag Induction Divergence free B EnergyIdeal Gas E.O.S.

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

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

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

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

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

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

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

20. 295 G ;  * = 1 Final state of isothermal models 1650 G ;  * = 32 930 G ;  * = 10520 G ;  * = 3.2 165 G ;  * = 0.3293 G ;  * = 0.1

21.  1 Ori C

22. MHD simulation for  1 Ori C (O7 V) B obs ~ 1100 G + P rot = 14 days M dot ~ 10 -7 M sun /yr  * ~= 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. Magnetically Confined Wind Shock ~ 2 kev X-rays fit Chandra spectrum for  1 Ori C log T but now with Radiative Cooling still no rotation

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

26.  1 Ori C  ~ 45 o i ~ 45 o

27. X-ray Light Curve for  1Ori C

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

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

30. Keplerian spin-up vs. escape w = V rot /V crit sqrt(  * ) ~ B v  > v esc v   < v kep

31. MHD Sims of Field-Aligned Rotation  * =10 ; v rot =250 km/s (w=1/2) Density V  /V rigid RKRK RARA RKRK RARA

32. Field aligned rotation RKRK RARA V rot =250 km/s = V crit /2 again isothermal, but now with

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

34.  Ori E

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

36. Strong field limit: B *,  * --> ∞ 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. R igidly R otating M agnetosphere Townsend & Owocki (2005)

39. Accumulation Surface Townsend & Owocki (2005)

41. RRM model for  Ori E B * ~10 4 G tilt ~ 55 o  * ~10 6 !

42. EM +B-field polarimetry  photometry RRM model for  Ori E B * ~10 4 G tilt ~ 55 o  * ~10 6 !

43. Townsend, Owocki & Groote (2005)

44.  Ori E RRM Model H  Observations

45. Sanz-Forcada et al. (2004)

46. MHD sim of centrifugal breakout  * = 620 v rot =v crit /2 log(  )

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

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

49. Isothermal, v rot =v crit /2,  * =100 RKRK RARA

50. RKRK RARA

51. Isothermal, v rot =v crit /2,  * =1000 RKRK R A ~7R *

52. Radial disk mass: dm e /dr

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

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

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

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

62. Current & Future Work 3D MHD of MCWS –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!