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Radiatively Driven Winds and Aspherical Mass Loss. Stan Owocki U. of Delaware. collaborators: Ken GayleyU. Iowa Nir Shaviv Hebrew U. Rich TownsendU. Delaware Asif ud-DoulaNCSU. General Themes. Lines vs. Continuum driving Oblate vs. Prolate mass loss Smooth vs. Porous medium - PowerPoint PPT Presentation
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Radiatively Driven Winds and Aspherical Mass Loss
Stan OwockiU. of Delaware
collaborators:Ken Gayley U. IowaNir Shaviv Hebrew U.Rich Townsend U. DelawareAsif ud-Doula NCSU
General Themes
• Lines vs. Continuum driving
• Oblate vs. Prolate mass loss
• Smooth vs. Porous medium
• Rotation vs. Magnetic field
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
eGM
2
• For sun, O ~ 2 x 10-5
• But for hot-stars with L~ 106 LO ; M=10-50 MO
.. .
if gray
€
=F /c
Q~ ~ 1015 Hz * 10-8 s ~ 107
Q ~ Z Q ~ 10-4 107 ~ 103
Line Scattering: Bound Electron Resonance
lines~QTh
glines~103 g el
LLthin} iflines
~103
el 1
for high Quality Line Resonance,
cross section >> electron scattering
Optically Thick Line-Absorption in an Accelerating Stellar Wind
gthick~gthin
τ~
1ρ
dvdr
For strong,
optically thick
lines:
CAK model of steady-state wind
inertia gravity CAK line-force
Solve for:
˙ M ≈Lc2
Q− ⎛ ⎝ ⎜
⎞ ⎠ ⎟
α−
Mass loss rate
˙ M v∞ ∝ L1
αWind-Momentum
Luminosity Law
α ≈0.6
v(r) ≈v∞(1−R∗/r)Velocity law
~vesc
Equation of motion: v ′ v ≈−GM(1−Γ)
r2 +Q Lr2
r2v ′ v ˙ M Q
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟ α α < 1
CAK ensemble ofthick & thin lines
Wind Compressed Disk ModelBjorkman & Cassinelli 1993
Wind Compressed Disk ModelBjorkman & Cassinelli 1993
Wind Compressed Disk SimulationsVrot (km/s) = 200 250 300 350 400 450
radial forcesonly
Vrot = 350 km/s
withnonradial
forces
Vector Line-Force from Rotating Star
€
rg lines ~ dΩ
Ω*
∫ ˆ n I*ˆ n ⋅∇(
r n ⋅
r v )[ ]
α
dvn/dn
fasterpolarwind
slower equatorial wind
r
Max
[dv n
/dn]
(2) Pole-equator aymmetry in velocity gradient
Net poleward line force from:
r
Flux
(1) Stellar oblateness => poleward tilt in radiative flux
N
Gravity Darkening
increasing stellar rotation
Vector line-force; With gravity dark.
Effect of gravity darkening on line-driven mass flux
€
˙ m ≡˙ M
4πR2
€
~ F(θ)Q F(θ)
geff (θ)
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
−1+1/α
€
˙ m (θ)
€
~ F(θ)w/ gravity darkening, if F()~geff()
€
˙ m (θ) highest at pole
€
v∞(θ) ~ vgeff (θ) ~ geff (θ) highest at pole
Rotational effect on flow speed
€
V∞(θ) ~ Veff (θ) ~ geff (θ)R*(θ)
€
ω ≡Ω /Ωcrit
*€
ω =1
€
ω =0.9
Smith et al. 2002
Smith et al. 2003
But lines can’t explain eta Car mass loss
€
˙ M CAK ≈L
c 2
Q Γ
1− Γ
⎛
⎝ ⎜
⎞
⎠ ⎟
1
α−1
€
L6 ≡ L /106 Lsun
€
Q3 ≡ Q /103
€
α =1/2
€
≈7 ×10−5 M• / yr L6 Q 3 Γ /(1− Γ)O
€
˙ M obs
€
≈10−3 −10−1 M• / yrO
€
V∞ ≈ 600km /s M(1− Γ) /R€
Vobs ≈ 500 − 800 km /s
Super-Eddington Continuum-Driven Winds
moderated by “porosity”
Continuum Eddington parameter
€
rg rad = dν
0
∞
∫ κ νˆ n Iν /c
compare continuum force vs. gravity
gc
ggrav
cL4GMc
r
L4 r2c
c
GM
2
constant in radius => no surface modulation
if gray
€
=F /c
Convective Instability• Classically expected in energy-generating core
– e.g., CNO burning => ~ T10-20 => dT/dr > dT/drad
• But envelope also convective where (r) -> 1
– e.g., Pup: *~1/2 => M(r) < M*/2 convective!
• For high density interior => convection efficient
– Lconv > Lrad Lcrit => rad (r) < 1: hydrostatic equilibrium
• Near surface, convection inefficient => super-Eddington– but flow has M ~ L/a2
– implies wind energy Mvesc2 >> L
– would“tire” radiation, stagnate outflow
– suggests highly structured, chaotic surface
.
Joss, Salpeter Ostriker 1973
.
Photon tiring
Stagnation of photon-tired outflow
€
V 2
Vesc2
€
x =1− R* /r
€
m ≡M•
Vesc2
2L*
€
*(x) =1+ x
Shaviv 2001
Power-law porosity
Effective Opacity for "Blob"
€
eff ≈ l 2 [1− e−τ b ]
€
l
€
b ≡ κρ bl
€
eff ≡σ eff
mb
=l 2 [1− e−τ b ]
ρ bl3
= κ1− e−τ b
τ b
€
≈ /τ b = l 2 /mb ; τ b >>1
€
≈
€
; τ b <<1
€
l
€
l
€
=ρ L3
l2
€
≡ρh
Porous opacity
€
b >>1; κ eff =l2
mb
=κ
τ b
= κρ*
ρ€
b = κρ b l€
l
€
L
“porosity length”
€
ρ* =1/κ h
Super-Eddington Wind
Wind driven by continuum opacity in a porous medium when * >1
€
M•
= 4πR*2ρ Sa
Shaviv 98-02
At sonic point:
€
eff (rS ) = Γ*
ρ c
ρ S
≡1
€
ρS = Γ* ρ c = Γ* /κh
€
≈L*
ac
€
h ≈H
€
≡a2 /g*
“porosity-length ansatz”
€
≈0.001M•
yr
L6
a20O
Power-law porosity
€
M•
= 4πR*2ρ Sa
Now at sonic point:
€
≈L*
acΓ*( )
−1+1/α
€
eff (rS ) = Γ*
ρ c
ρ S
⎛
⎝ ⎜
⎞
⎠ ⎟
α
≡1
€
M•
CAK ≈L*
c 2QΓe( )
−1+1/α
Results for Power-law porosity model
Effect of gravity darkening on porosity-moderated mass flux
€
˙ m ≡˙ M
4πR2
€
~ F(θ)F(θ)
geff (θ)
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
−1+1/α
€
˙ m (θ)
€
~ F(θ)w/ gravity darkening, if F()~geff()
€
˙ m (θ) highest at pole
€
v∞(θ) ~ vgeff (θ) ~ geff (θ) highest at pole
Eta Carina
Summary Themes
• Lines vs. Continuum driving
• Oblate vs. Prolate mass loss
• Smooth vs. Porous medium
• Rotation vs. Magnetic field
Wind Magnetic Confinement
€
η(r) ≡B2 /8π
ρv 2 /2
€
η∗≡Beq
2 R*2
˙ M v∞
= 4 ×B3
2R132
˙ M −3v8
Ratio of magnetic to kinetic energy density:
e.g, for dipole field, q=3; η ~ 1/r4
€
=B2r2
˙ M v=
Beq2R*
2
˙ M v∞
(r /R)2−2q
(1− R /r)β
for present day eta Car wind, need G
for Homunclus, need G
MHD Simulation of Wind Channeling
€
η* =10
Confinement parameter
A. ud Doula PhD thesis 2002
No Rotation
Field aligned rotationA. ud-Doula, Phd. Thesis
2002
€
η* = 32
€
vrot = 250 km /s
QuickTime™ and aBMP decompressor
are needed to see this picture.
Disk from Prograde NRPw=0.95 ; Vamp = a = 25 km/s = Vorb
Azimuthal Averages vs. r, t
Azimuthal Velocity
5 10
Mass
1.0
1.2
r/R*
Kepler Number
0.98 1.0
5 101.0
1.2
r/R*
time (days)
Density
0
NRP Off
NRP On
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