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