Stellar Magnetospheres part deux: Magnetic Hot Stars
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Transcript of Stellar Magnetospheres part deux: Magnetic Hot Stars
Stellar Magnetospherespart 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 ~ Pgas/Pmag ~ (a/VA)2
• press. scale ht. H << R (except in corona)
• wind mag. conf. ~B2R2/Mdot*V
Wind Magnetic Confinement
for OB SG, to get*~ 1, need B* ~ 100 G
€
(r) ≡B2 /8π
ρv 2 /2
Ratio of magnetic to kinetic energy density:
e.g, for dipole field, q=3; ~ 1/r 4
€
=B2r2
M•
v=
B*2R*
2
M•
v∞
(r /R*)2−2q
(1− R* /r)β
*
Alfven Radius: ( RA) 1
For dipole (q=3): RA = *1/4 R*
€
=VA
2
v 2
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!
• 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=ge/g < 1 (near but below “Edd. limit”)
• “CAK” wind model: lines = glines/g > 1
Light’s Momentum
• Force depends on gradient of Pressure
• grad Prad comes from opacity
• Deep interior (>>1), Prad nearly isotropic
–Prad + Pgas act together => H=a2/g(1-)
• But near surface ( ~1) radiation “beamed”
• wind is not “Radiation Pressure Corona” H ~< R
Aside: Radiation Pressure vs. Gas Pressure
Radiative force
€
rg rad = dν
0
∞
∫ κ νˆ n Iν /c
~
e.g., compare electron scattering force vs. gravity
gel
ggrav
eL4GMc
r
L4 r2c
Th
e
GM2
• For sun, O ~ 2 x 10-5
• But for hot-stars with L~ 106 LO ; M=10-50 MO
.. .
if gray
€
=F /c
Optically Thick Line-Absorption in an Accelerating Stellar Wind
gthick~gthin
τ~
1ρ
dvdr
€
≡ vth
dv /dr
LsobFor strong,
optically thick
lines:
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~vth
v∞
R*
<< R*
CAK force for power-law line ensemble
€
glines ~gthin
τ α~
L
r2
1
ρ
dv
dr
⎛
⎝ ⎜
⎞
⎠ ⎟
α
CAK wind in zero-gas-pressure limit
€
vdv
dr= −
GM
r2−
a2
ρ
dρ
dr+ glines
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′w = −1+ C ′ w α
€
′w ≡r2vdv/dr
GM
€
C ~1˙ M α
€
gthin
τ α~
L
r2
1
ρ
dv
dr
⎛
⎝ ⎜
⎞
⎠ ⎟
α
Graphical solution
€
˙ M = ˙ M CAK€
˙ M < ˙ M CAK
€
˙ M > ˙ M CAK
Magnetohydrodynamic (MHD) Equations
€
Dρ
Dt+ ρ∇ • v = 0
Mass Momentum
mag Induction Divergence free B€
P = ρa2 = (γ −1)e
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∂e
∂t+∇ ⋅ev = −P∇ ⋅v + HM − n2Λ(T)
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Dv
Dt= −∇p +
1
4π∇ × B( ) × B + ρ (glines − ggrav )
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∂B
∂t=∇ × v × B( )
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∇• B = 0
Energy Ideal Gas E.O.S.
Magnetohydrodynamic (MHD) Equations
€
Dρ
Dt+ ρ∇ • v = 0
Mass Momentum
mag Induction Divergence free B€
P = ρa2
€
T = const.€
Dv
Dt= −∇p +
1
4π∇ × B( ) × B + ρ (glines − ggrav )
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∂B
∂t=∇ × v × B( )
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∇• B = 0
Energy Ideal Gas E.O.S.
MHD Simulation of Wind Channeling
Confinement parameter
A. ud Doula PhD thesis 2002
IsothermalNo Rotation
*=1/3
MHD Simulation of Wind Channeling
Confinement parameter
IsothermalNo Rotation
€
* =1*=1
MHD Simulation of Wind Channeling
Confinement parameter
IsothermalNo Rotation
*= 3
MHD Simulation of Wind Channeling
Confinement parameter
IsothermalNo Rotation
*=10
MHD Simulation of Wind Channeling
Confinement parameter
IsothermalNo Rotation
€
* =10
RA~ *1/4 R*
*=10
Confinement parameter
IsothermalNo Rotation
€
* =10
RA~ *1/4 R*
*=1000 !!
295 G ; * = 1 Final state of isothermal models
1650 G ; * = 32 930 G ; * = 10520 G ; * = 3.2
165 G ; * = 0.3293 G ; * = 0.1
1 Ori C
MHD simulation for 1 Ori C (O7 V)
• Bobs ~ 1100 G + Prot = 14 days
• Mdot~ 10-7 Msun/yr
• *~= 14
• Magnetic Confined Wind Shock (MCWS)
• kev X-rays => match Chandra obs.
Magnetically Confined Wind-ShocksBabel & Montmerle 1997
Magnetic Ap-Bp stars
Magnetically Confined Wind Shock
~ 2 kev X-rays fit Chandra spectrum
for 1 Ori C
log T
but now with RadiativeCooling
still no rotation
-1 Ori C
QuickTime™ and a decompressor
are needed to see this picture.
Gagne et al. 2005, ApJ, 528, 986
Prot = 13 days
1 Ori C
~ 45o
i ~ 45o
X-ray Light Curve for 1Ori C
Magnetically Torqued Disk (MTD)Cassinelli et al. 2002
Alfven vs. Kepler Radius
when RA > RK :Magnetic spin-up => centrifugal support & ejection
Kepler co-rotation Radius, RK:
GM/ RK2 = V
2/RK
RK = w2/3 R*
w=Vrot/Vcrit Vcrit2 = GM/R*
= Vrot2RK/R*
2
Alfven radius: (RA)=1
RA = *1/4 R*
e.g, for dipole field, ~ 1/r 4
Keplerian spin-up vs. escape
w = Vrot/Vcrit0.2 0.4 0.6 0.8 1
2
4
6
8
10
sqrt(*) ~ B
v > v
escv < v
kep
MHD Sims of Field-Aligned Rotation *=10 ; vrot=250 km/s (w=1/2)
DensityV /Vrigid
RKRA RKRA
Field aligned rotation
€
* = 32
RK RA
Vrot=250 km/s = Vcrit/2
againisothermal, but now with
Magnetically Torqued Disk
Owocki & ud-Doula 2003Cassinelli et al. 2002
Ori E
Magnetic Bp Stars
• Ori E (B2p V)– Prot = 1.2 days => vrot/vcrit ~ 1/2
– Bobs ~ 104 G => * ~ 107 !
– => VAlfven very large => Courant time very small
– => Direct MHD impractical
• Instead treat fields lines as “Rigid”
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: VAlfven ->∞ => can’t do MHD
• But can model semi-analytically
– Rigidly Rotating Magnetosphere (RRM)
– gas accumulates at minima in grav+cent. potential
Effective Gravitational+Centrifugal Potential
Rigidly Rotating Magnetosphere
Townsend & Owocki (2005)
Accumulation Surface
Townsend & Owocki (2005)
RRM model
for Ori E
δδδ
B*~104 G
tilt ~ 55o
*~106 !
EM +B-field
δδδδδδ
polarimetry
photometryRRM model for Ori E
δδδ
B*~104 G
tilt ~ 55o
*~106 !
Townsend, Owocki & Groote (2005)
Ori ERRM Model H Observations
Sanz-Forcada et al. (2004)
MHD sim of centrifugal breakout
*= 620 vrot=vcrit/2
log()
*= 620 vrot=vcrit/2
log T
Centrifugally Driven Reconnection Flare
~ 4-5 kevX-rayflares,as seen in Ori E
Model grid for 2-Parameter study: Rotation & Magnetic Confinement
Isothermal, vrot=vcrit/2, *=100
RK RA
Isothermal, vrot=vcrit/2, *=1000
RK
RA~7R*
Radial disk mass: dme/dr
€
dme
dr≡ 2πr2 ρ sinθdθ
π / 2−Λθ / 2
π / 2+Λθ / 2
∫
Equatorial mass distribution dme/dr R
adiu
s (R
*)
Time (Msec)0
*=100
1
5
W=1/2
Equatorial mass distribution dme/dr R
adiu
s (R
*)
Time (Msec)0
*=100
1
5
W=0
Parameter study: rotation & magnetic confinement
Between RRM and full MHD: “Rigid Field Hydro-Dynamics”
RFHD
Solve time-dependent hydro along completely rigid individual field lines
The flow along an individual field line
Rigid Field - Hydro Model
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 >~ 108 K
• can explain hard X-ray flares in Ori E
• “centrifugally driven reconnection”
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!