Mass Loss from (Hot) Massive Luminous Stars
Stan Owocki Bartol Research Institute Department of Physics & Astronomy University of Delaware
Wednesday, January 12, 2011 Massive Stars in the Whirlpool Galaxy
Wednesday, January 12, 2011 Henize 70: LMC SuperBubble Wind-Blown Bubbles in ISM Some key scalings:
Wednesday, January 12, 2011 Henize 70: LMC SuperBubble Wind-Blown Bubbles in ISM Some key scalings:
WR wind bubble NGC 2359
Wednesday, January 12, 2011 Henize 70: LMC SuperBubble Wind-Blown Bubbles in ISM Some key scalings:
WR wind bubble NGC 2359 Superbubble in the Large Magellanic Cloud
Wednesday, January 12, 2011 Pistol Nebula
Wednesday, January 12, 2011 Eta Carinae
Wednesday, January 12, 2011 P-Cygni Line Profile Line-scattering in massive winds
Wednesday, January 12, 2011 Observed wind line profiles
Resonance line-scattering Recombination line O-star P-Cygni profile WR-star emission profile
−v∞ +v −v∞ ∞
Wednesday, January 12, 2011 Basic Mass Loss Properties
i 2 Mass Loss rate M = 4πρvr
Terminal speed Velocity law v(r) v∞
8
Wednesday, January 12, 2011 Massive-Star Mass Loss i M 1. OB Winds M ~ 10−9 − 10−6 yr v∞ 1000 − 3000 km / s – opt. thin τ c < 1
2. Wolf-Rayet Winds i M M ~ 10−6 − 10−5 yr – opt. thick τ c > 1 v 1000 3000 km / s ∞ − 3. Luminous Blue Variable (LBV) Eruptions
i 1 −5 M -very opt. thick τ c M ~ 10 − 1 !! yr v 50 1000 km / s ∞ −
Wednesday, January 12, 2011 Q: What can drive such extreme mass loss??
Wednesday, January 12, 2011 Q: What can drive such extreme mass loss??
A: The force of light!
Wednesday, January 12, 2011 Q: What can drive such extreme mass loss??
A: The force of light! – light has momentum, p=E/c
Wednesday, January 12, 2011 Q: What can drive such extreme mass loss??
A: The force of light! – light has momentum, p=E/c – leads to “Radiation Pressure”
Wednesday, January 12, 2011 Q: What can drive such extreme mass loss??
A: The force of light! – light has momentum, p=E/c – leads to “Radiation Pressure”
– radiation force from gradient of Prad
Wednesday, January 12, 2011 Q: What can drive such extreme mass loss??
A: The force of light! – light has momentum, p=E/c – leads to “Radiation Pressure”
– radiation force from gradient of Prad – gradient is from opacity of matter
Wednesday, January 12, 2011 Q: What can drive such extreme mass loss??
A: The force of light! – light has momentum, p=E/c – leads to “Radiation Pressure”
– radiation force from gradient of Prad – gradient is from opacity of matter – opacity from both Continuum & Lines
Wednesday, January 12, 2011 Continuum opacity from Free Electron Scattering
e-
Thompson Cross Section 2 -24 2 σTh = 8π/3 re = 2/3 barn= 0.66 x 10 cm
2 σ Th cm th κ e = = 0.2(1+ X) = 0.34 µe g
Wednesday, January 12, 2011 Radiative acceleration vs. gravity
Radiative Force ∞ κ F g = dν ν ν GM rad ∫ 2 0 c r
Wednesday, January 12, 2011 Radiative acceleration vs. gravity
Radiative Force ∞ κ F g = dν ν ν GM rad ∫ 2 0 c r
2 ge κ eL / 4πr c κ eL Γe ≡ = 2 = g GM / r 4πGMc
Wednesday, January 12, 2011 Radiative acceleration vs. gravity
Radiative Force ∞ κ F g = dν ν ν GM rad ∫ 2 0 c r
2 ge κ eL / 4πr c κ eL Γe ≡ = 2 = g GM / r 4πGMc L / L κ Γ 2 × 10−5 F M / M κ e Wednesday, January 12, 2011 Stellar Luminosity vs. Mass
L ~ M 3.3
Wednesday, January 12, 2011 Basic Stellar Structure -> L ~ M3 cf. Lecture by Prof. Sugimoto Hydrostatic equilibrium (Γ<<1): dP gas = −ρg dr
Wednesday, January 12, 2011 Basic Stellar Structure -> L ~ M3 cf. Lecture by Prof. Sugimoto Hydrostatic equilibrium (Γ<<1):
dPgas ρT ρM = −ρg => ~ dr R R2
Wednesday, January 12, 2011 Basic Stellar Structure -> L ~ M3 cf. Lecture by Prof. Sugimoto Hydrostatic equilibrium (Γ<<1):
dPgas ρT ρM => M = −ρg ~ 2 T ~ dr R R R
Wednesday, January 12, 2011 Basic Stellar Structure -> L ~ M3 cf. Lecture by Prof. Sugimoto Hydrostatic equilibrium (Γ<<1):
dPgas ρT ρM => M = −ρg ~ 2 T ~ dr R R R
Wednesday, January 12, 2011 Basic Stellar Structure -> L ~ M3 cf. Lecture by Prof. Sugimoto Hydrostatic equilibrium (Γ<<1):
dPgas ρT ρM => M = −ρg ~ 2 T ~ dr R R R Radiative diffusion: dP F rad = dτ c
Wednesday, January 12, 2011 Basic Stellar Structure -> L ~ M3 cf. Lecture by Prof. Sugimoto Hydrostatic equilibrium (Γ<<1):
dPgas ρT ρM => M = −ρg ~ 2 T ~ dr R R R Radiative diffusion: dP F T 4 L rad = => ~ dτ c κM /R2 R2
Wednesday, January 12, 2011 Basic Stellar Structure -> L ~ M3 cf. Lecture by Prof. Sugimoto Hydrostatic equilibrium (Γ<<1):
dPgas ρT ρM => M = −ρg ~ 2 T ~ dr R R R Radiative diffusion: dP F T 4 L R4T 4 rad = => ~ L ~ dτ c κM /R2 R2 κM
Wednesday, January 12, 2011 Basic Stellar Structure -> L ~ M3 cf. Lecture by Prof. Sugimoto Hydrostatic equilibrium (Γ<<1):
dPgas ρT ρM => M = −ρg ~ 2 T ~ dr R R R Radiative diffusion: dP F T 4 L R4T 4 rad = => ~ L ~ dτ c κM /R2 R2 κM
Wednesday, January 12, 2011 Basic Stellar Structure -> L ~ M3 cf. Lecture by Prof. Sugimoto Hydrostatic equilibrium (Γ<<1):
dPgas ρT ρM => M = −ρg ~ 2 T ~ dr R R R Radiative diffusion: dP F T 4 L R4T 4 rad = => ~ L ~ dτ c κM /R2 R2 κM M 3 L ~ κ Wednesday, January 12, 2011
Basic Stellar Structure -> L ~ M3 cf. Lecture by Prof. Sugimoto Hydrostatic equilibrium (Γ<<1):
dPgas ρT ρM => M = −ρg ~ 2 T ~ dr R R R Radiative diffusion: dP F T 4 L R4T 4 rad = => ~ L ~ dτ c κM /R2 R2 κM
3 M 4 L ~ (1− Γ) κ Wednesday, January 12, 2011
Eddington Standard Model (n=3 Polytrope) 1 ~M 1 ~M Γ≡1 observed upper limit
3 from young, dense clusters ~M Γ=1/2
Pgas > Prad Prad > Pgas
Wednesday, January 12, 2011 Humphreys-Davidson Limit
LBVs
16
Wednesday, January 12, 2011 Key points
Wednesday, January 12, 2011 Key points
6 • Stars with M ~ 100 Msun have L ~ 10 Lsun => near Eddington limit!
Wednesday, January 12, 2011 Key points
6 • Stars with M ~ 100 Msun have L ~ 10 Lsun => near Eddington limit!
Wednesday, January 12, 2011 Key points
6 • Stars with M ~ 100 Msun have L ~ 10 Lsun => near Eddington limit!
• Suggests natural explanation why we don’t see stars much more luminous (& massive)
Wednesday, January 12, 2011 Key points
6 • Stars with M ~ 100 Msun have L ~ 10 Lsun => near Eddington limit!
• Suggests natural explanation why we don’t see stars much more luminous (& massive)
Wednesday, January 12, 2011 Key points
6 • Stars with M ~ 100 Msun have L ~ 10 Lsun => near Eddington limit!
• Suggests natural explanation why we don’t see stars much more luminous (& massive)
• Prad > Pgas => Instabilities => Extreme mass loss
Wednesday, January 12, 2011 Mass loss and stellar evolution: Luminous Blue Variable (LBV) winds/eruptions
120 M LBV WNH
60 M WR
Wednesday, January 12, 2011 Mass loss and stellar evolution: Luminous Blue Variable (LBV) winds/eruptions
Γ Γ Γ Γ Γ Γ Γ 120 M LBV WNH
60 M WR
Wednesday, January 12, 2011 Mass loss and stellar evolution: Luminous Blue Variable (LBV) winds/eruptions
Γ Γ Γ Γ Γ Γ Γ 120 M LBV WNH
60 M WR
Wednesday, January 12, 2011 Mass loss and stellar evolution: Luminous Blue Variable (LBV) winds/eruptions
Γ Γ Γ Γ Γ Γ Γ 120 M LBV WNH
Possible fates: LBV WR SNIbc LBV WR GRB 60 M BH WR Pair Instability Ib/c Type IIn GRBs?
Wednesday, January 12, 2011
Wednesday, January 12, 2011
• But before trying to understand LBV eruptive mass loss, let’s consider ways to get a steady, radiatively driven wind.
Wednesday, January 12, 2011
• But before trying to understand LBV eruptive mass loss, let’s consider ways to get a steady, radiatively driven wind. • Key requirement is for Gamma to increase above unity near the stellar surface.
Wednesday, January 12, 2011
• But before trying to understand LBV eruptive mass loss, let’s consider ways to get a steady, radiatively driven wind. • Key requirement is for Gamma to increase above unity near the stellar surface. • Two options: – Assume continuum opacity to increase outward – More naturally: Desaturation of line-opacity
Wednesday, January 12, 2011 Steady Wind Acceleration 2 a T4 Sound speed a ≡ P / ρ s = ≈ 0.001 1 v2 M / R esc
Scale by gravity : dw Accel. = Γ − 1 dx
v2 R w x ≡1− ≡ 2 r vesc ______Kin. En. Pot. En. Escape En.
Wednesday, January 12, 2011 Steady Wind Acceleration 2 a T4 Sound speed a ≡ P / ρ s = ≈ 0.001 1 v2 M / R esc If we neglect gas pressure, steady force balance is simply: dv GM v = − + g dr r2 rad Scale by gravity : dw Accel. = Γ − 1 dx
v2 R w x ≡1− ≡ 2 r vesc ______Kin. En. Pot. En. Escape En.
Wednesday, January 12, 2011 Simplest example of radiatively driven wind Zero sound speed limit (a=0) with constant “anti-gravity” Γ > 1 w′ = Γ − 1
Integrate with B.C. w(0) = 0
w(x) = w∞ x
1/2 ⎛ R⎞ v(r) = v 1− v = w v = Γ − 1 v ∞ ⎝⎜ r ⎠⎟ ∞ ∞ e e
Note: Density independence leaves mass loss rate undetermined. And ignores energy requirement (photon “tiring”).
Wednesday, January 12, 2011 The “beta” velocity law
β ⎛ R⎞ Empirical fitting law: v(r) = v 1− ∞ ⎝⎜ r ⎠⎟ 2β w(x) = w∞ x
Dynamically requires a specific radial increase in opacity:
2β −1 Γ(x)= 1+ w′ = 1+ 2β w∞ x
Wednesday, January 12, 2011 w w w 1.0 w∞ 0.8 Β 1 2 0.6 Β 1
0.4 Β 2 Β 3 0.2
x 0.2 0.4 0.6 0.8 1.0 x 5 Β 3 Γ 4 Β 2
3 Β 1
2 Β 1 2
1
x 0.0 0.2 0.4 0.6 0.8 1.0 x r = R r → ∞
Wednesday, January 12, 2011 Line-Driven Stellar Winds
• A more natural model is for wind to be driven by line scattering of light by electrons bound to metal ions • This has some key differences from free electron scattering...
Wednesday, January 12, 2011 Driving by Line-Opacity Optically thin
Γthin ~ QΓe ~ 1000Γe
Wednesday, January 12, 2011 Driving by Line-Opacity
Optically thin Optically thick
Γ ~ QΓ ~ 1000Γ QΓe 1 dv thin e e Γ ~ ~ thick τ ρ dr Wednesday, January 12, 2011 Optically Thick Line-Absorption in an Accelerating Stellar Wind
Lsob << R* For strong, gthin 1 dv g ~ ~ vth vth optically thick thick τ ≡ κρ ~ R τ ρ dr dv/dr v * lines: ∞
Wednesday, January 12, 2011
CAK model of steady-state wind
α GM(1− Γ) Q L ⎛ r2vv′ ⎞ Equation of motion: vv′ ≈ − + ⎜ ⎟ r2 r2 ⎝ M˙ Q ⎠ inertia gravity CAK line-force
Wednesday, January 12, 2011 CAK model of steady-state wind 0 < α < 1 ⎛ 2 ⎞α CAK ensemble of GM(1− Γ) Q L r vv′ thick & thin lines Equation of motion: vv′ ≈ − + ⎜ ⎟ r2 r2 ⎝ M˙ Q ⎠ inertia gravity CAK line-force
Wednesday, January 12, 2011 CAK model of steady-state wind 0 < α < 1 ⎛ 2 ⎞α CAK ensemble of GM(1− Γ) Q L r vv′ thick & thin lines Equation of motion: vv′ ≈ − + ⎜ ⎟ r2 r2 ⎝ M˙ Q ⎠ inertia ≈ gravity ≈ CAK line-force
Wednesday, January 12, 2011 CAK model of steady-state wind 0 < α < 1 ⎛ 2 ⎞α CAK ensemble of GM(1− Γ) Q L r vv′ thick & thin lines Equation of motion: vv′ ≈ − + ⎜ ⎟ r2 r2 ⎝ M˙ Q ⎠ inertia ≈ gravity ≈ CAK line-force
gCAK ≈ gravity Mass loss rate 1 −1 L ⎛ Q Γ ⎞ α M˙ ≈ ⎜ ⎟ c2 ⎝ 1− Γ ⎠
Wednesday, January 12, 2011 CAK model of steady-state wind 0 < α < 1 ⎛ 2 ⎞α CAK ensemble of GM(1− Γ) Q L r vv′ thick & thin lines Equation of motion: vv′ ≈ − + ⎜ ⎟ r2 r2 ⎝ M˙ Q ⎠ inertia ≈ gravity ≈ CAK line-force
gCAK ≈ gravity inertia ≈ gravity Mass loss rate Velocity law 1 −1 L ⎛ Q ⎞ α β β ≈ 0.8 ˙ Γ v(r) ≈ v∞ (1− R∗ / r) M ≈ 2 ⎜ ⎟ c ⎝ 1− Γ ⎠ ~ vesc
Wednesday, January 12, 2011 CAK model of steady-state wind 0 < α < 1 ⎛ 2 ⎞α CAK ensemble of GM(1− Γ) Q L r vv′ thick & thin lines Equation of motion: vv′ ≈ − + ⎜ ⎟ r2 r2 ⎝ M˙ Q ⎠ inertia ≈ gravity ≈ CAK line-force
gCAK ≈ gravity inertia ≈ gravity Mass loss rate Velocity law 1 −1 L ⎛ Q ⎞ α β β ≈ 0.8 ˙ Γ v(r) ≈ v∞ (1− R∗ / r) M ≈ 2 ⎜ ⎟ c ⎝ 1− Γ ⎠ ~ vesc
Wind-Momentum −1+1/α 1 α ≈ 0.6 M v ~ Q Lα Luminosity law ∞ ~ Z 0.6 L1.7 Q ~ Z
Wednesday, January 12, 2011 Point-star vs. Finite-disk
Point-star approx. I * α * gr~I*(dv/dr) r
Finite-disk integration In g ~I (dv /dn)α r r n n
Wednesday, January 12, 2011 Finite-disk reduction of CAK mass loss rate
α C ~ 1 / M α w ′ +1= fd C w ′
Wednesday, January 12, 2011 Finite-disk reduction of CAK mass loss rate
α C ~ 1 / M α w ′ +1= fd C w ′
˙ ˙ 1/α ˙ M CAK ˙ M fd = f d * M CAK = 1/ ≈ M CAK /2 (1+ α) α
Wednesday, January 12, 2011 CAK vs. FD velocity law V(r) β ⎛ R* ⎞ V(r) ≈ V∞ ⎜1− ⎟ Vesc ⎝ r ⎠ 3.0 V∞ ≈ 3Vesc
2.5 FD β ≈ 0.8
2.0
1.5
1.0 V ≈ V 1 ∞ esc CAK β = 0.5 2
0.2 0.4 0.6 0.8 1.0
1− R* / r
Wednesday, January 12, 2011 Effect of finite gas-pressure on CAK wind
s fC a2 ⎛ ⎞ c α s 0.001 ⎜1− ⎟ w′ + 1 = α w′ ≡ 2 ≈ ⎝ w⎠ (1+ δm) Vesc
Wednesday, January 12, 2011 Effect of finite gas-pressure on CAK wind
s fC a2 ⎛ ⎞ c α s 0.001 ⎜1− ⎟ w′ + 1 = α w′ ≡ 2 ≈ ⎝ w⎠ (1+ δm) Vesc
Perturbation expansion of FD-CAK soln in s<<1 gives:
4 1− α a δm ≈ + ≈+ 0.1 increases Mdot ~ 10% α Vesc
Wednesday, January 12, 2011 Effect of finite gas-pressure on CAK wind
s fC a2 ⎛ ⎞ c α s 0.001 ⎜1− ⎟ w′ + 1 = α w′ ≡ 2 ≈ ⎝ w⎠ (1+ δm) Vesc
Perturbation expansion of FD-CAK soln in s<<1 gives:
4 1− α a δm ≈ + ≈+ 0.1 increases Mdot ~ 10% α Vesc 2 a δv∞ ≈ − ≈− 0.1 decreases Vinf ~ 10% 1− α Vesc
Wednesday, January 12, 2011 Summary: Key CAK Scaling Results
i L1/α Mass Flux: M g1/α −1 eff
Wind Speed: V∞ ~ Vesc ~ geff
Wednesday, January 12, 2011 How is stellar mass loss affected by (rapid) stellar rotation?
Wednesday, January 12, 2011 Gravity Darkening
increasing stellar rotation
F(θ) ~ geff (θ)
Wednesday, January 12, 2011 Effect of gravity darkening on line-driven mass flux Recall: 1/α F(θ) F 2(θ) e.g., for m˙ (θ) ~ 1/α−1 ~ geff (θ) geff (θ) α =1/2
Wednesday, January 12, 2011 Effect of gravity darkening on line-driven mass flux Recall: 1/α F(θ) F 2(θ) e.g., for m˙ (θ) ~ 1/α−1 ~ geff (θ) geff (θ) α =1/2
1 w/o gravity darkening, m˙ ( ) ~ highest at θ if F(θ)=const. geff (θ) equator
Wednesday, January 12, 2011 Effect of gravity darkening on line-driven mass flux Recall: 1/α F(θ) F 2(θ) e.g., for m˙ (θ) ~ 1/α−1 ~ geff (θ) geff (θ) α =1/2
1 w/o gravity darkening, m˙ ( ) ~ highest at θ if F(θ)=const. geff (θ) equator
w/ gravity darkening, m˙ (θ) ~ F(θ) highest at if F( )~g ( ) pole θ eff θ
Wednesday, January 12, 2011 Effect of rotation on flow speed
V∞(θ) ~ Veff (θ) ~ geff (θ)
2 2 geff (θ) ~ 1−ω Sin θ ω =1 ω = 0.9 ω ≡ Ω/Ω crit *
Wednesday, January 12, 2011 Wednesday, January 12, 2011 Smith et al. 2003
Wind is faster & denser over the poles!
Wednesday, January 12, 2011 Be stars • Hot, bright, & rapidly rotating stars of mass ~ 3-10 Msun • The “ e” stands for emission lines in the star’s spectrum
Hβ Hα Hydrogen spectrum
Wednesday, January 12, 2011 Be stars • Hot, bright, & rapidly rotating stars of mass ~ 3-10 Msun • The “ e” stands for emission lines in the star’s spectrum
Hβ Hα Hydrogen spectrum • Emission intensity split into blue and red peaks
Wednesday, January 12, 2011 Be stars • Hot, bright, & rapidly rotating stars of mass ~ 3-10 Msun • The “ e” stands for emission lines in the star’s spectrum
Hβ Hα Hydrogen spectrum • Emission intensity split into blue and red peaks Intensity
λo Wavelength
Wednesday, January 12, 2011 Be stars • Hot, bright, & rapidly rotating stars of mass ~ 3-10 Msun • The “ e” stands for emission lines in the star’s spectrum
Hβ Hα Hydrogen spectrum • Emission intensity split into blue and red peaks
• From Doppler shift of Intensity gas moving toward and λo Wavelength away from the observer .
Wednesday, January 12, 2011 Be stars • Hot, bright, & rapidly rotating stars of mass ~ 3-10 Msun • The “ e” stands for emission lines in the star’s spectrum
Hβ Hα Hydrogen spectrum • Emission intensity split into blue and red peaks
• From Doppler shift of Intensity gas moving toward and λo Wavelength away from the observer .
Wednesday, January 12, 2011 Be stars • Hot, bright, & rapidly rotating stars of mass ~ 3-10 Msun • The “ e” stands for emission lines in the star’s spectrum
Hβ Hα Hydrogen spectrum • Emission intensity split into blue and red peaks
• From Doppler shift of Intensity gas moving toward and λo Wavelength away from the observer .
• Indicates a disk of gas orbits the star. Wednesday, January 12, 2011 3 components of Be star circumstellar gas
Wednesday, January 12, 2011 3 components of Be star circumstellar gas gravity brightened poles drive denser polar wind
Wednesday, January 12, 2011 3 components of Be star circumstellar gas gravity brightened poles drive denser polar wind
equatorial Viscous Decretion Disk (VDD)
Wednesday, January 12, 2011 3 components of Be star circumstellar gas gravity brightened poles drive denser polar wind
equatorial Viscous Decretion Disk (VDD)
eq. disk ablation flow
Wednesday, January 12, 2011 Wolf-Rayet winds i M V > L / c • WR winds have ∞ i L • Requires multiple scattering prad = τ c
for lines separated by ΔV < V∞ V τ = ∞ ΔV Wednesday, January 12, 2011 Wolf-Rayet winds i M V > L / c • WR winds have ∞ i L • Requires multiple scattering prad = τ c
for lines separated by ΔV < V∞ V τ = ∞ ΔV Wednesday, January 12, 2011 Wolf-Rayet winds i M V > L / c • WR winds have ∞ i L • Requires multiple scattering prad = τ c
for lines separated by ΔV < V∞ V τ = ∞ ΔV Wednesday, January 12, 2011 Wolf-Rayet winds i M V > L / c • WR winds have ∞ i L • Requires multiple scattering prad = τ c
for lines separated by ΔV < V∞ V τ = ∞ ΔV Wednesday, January 12, 2011 courtesy Wolf-Rayet Wind Driving G. Graefener Radiative acceleration
radius = Opacity log Density X
Flux
2 3 4 UV log Wavelength IR Wednesday, January 12, 2011 Mdot increases with Γe
Graefener & Hamman 2005 Wednesday, January 12, 2011 Monte-Carlo models • Abbott & Lucy 1985; LA 93; Vink et al. 2001 • Assume beta velocity law, use MC transfer through line list to compute global radiative work Wrad and momentum prad
Wednesday, January 12, 2011 Monte-Carlo modelsi • Then compute mass loss rate from: i 2W rad M ≈ V 2 + V 2 esc ∞
i W rad i log i p Text NOTE: M ≈ rad Ewind Global Vesc + V∞ not local soln of EOM
i log M Wednesday, January 12, 2011 Line-Deshadowing Instability
Wednesday, January 12, 2011 Line-Deshadowing Instability
for λ < Lsob: iω = δg/δv
= +go/vth= Ω
Wednesday, January 12, 2011 Line-Deshadowing Instability
for λ < Lsob: Instability with growth rate
iω = δg/δv Ω ~ go/vth ~vv’/vth~ v/Lsob ~100 v/R = +g /v = Ω o th => e100 growth!
Wednesday, January 12, 2011 Non-linear structure for pure-absorption model
Direct force OCR 1988
gthin gdir α t(x,r) r t(x,r) = ∫ dr κρφ(x − u(r ')) R Integral optical depth r t(x,r) = ∫ dr κρφ(x − u(r ')) R
Wednesday, January 12, 2011 Line-Scattering in an Expanding Wind
Wednesday, January 12, 2011 Diffuse Line-Drag
Wednesday, January 12, 2011 Time snapshot of wind structure vs. radius
CAK Velocity
log(Density)
Wednesday, January 12, 2011 Clumping vs. radius
2 Clumping ρ factor fcl ≡ 2 ρ
2 i ρ diagnostics M ~ f overestimate cl
2 Radial velocity v ≡ v2 − v dispersion disp
2 Tx ~ vdisp
Wednesday, January 12, 2011 Turbulence- seeded clump collisions
Enhances Vdisp and thus X-ray emission
Feldmeier et al. 1997
Wednesday, January 12, 2011 Chandra X-ray line-profile for ZPup
Fe Fe XVII XVII
Wednesday, January 12, 2011 observer on left τ = 3
τ = 1 optical depth contours
τ = 0.3
Wednesday, January 12, 2011 isovelocity contours
-0.2vinf +0.2vinf
-0.6vinf +0.6vinf
-0.8vinf +0.8vinf
observer on left τ = 3
τ = 1 optical depth contours
τ = 0.3
Wednesday, January 12, 2011 X-ray emission line-profile
Wednesday, January 12, 2011 Inferring ZPup Mdot from X-ray lines
Traditional mass-loss rate: -6 8.3 X 10 Msun/yr
Cohen et al. 2010 best fit: -6 3.5 X 10 Msun/yr
Wednesday, January 12, 2011 Extension to 3D: the “Patch Method”
Wednesday, January 12, 2011 WR Star Emission Profile Variability WR 140 Lepine & Moffat 1999
Wednesday, January 12, 2011 WR Star Emission Profile Variability WR 140 3D Lepine & “patch” Moffat 1999 model Dessart & Owocki 2002
patch size ~3 deg
Wednesday, January 12, 2011 2D-H + 1D-R nr=1000 nφ=60 Δφ=12deg
Dessart & Owocki 2003
Wednesday, January 12, 2011 Dessart & Owocki 2005
Wednesday, January 12, 2011 Porosity
Wednesday, January 12, 2011 Porosity
Incident light
Wednesday, January 12, 2011 Porosity
Incident light
Wednesday, January 12, 2011 Porosity
• Same amount of material
• More light gets through Incident light • Less interaction between matter and light
Wednesday, January 12, 2011 Porous opacity from optically thick clumps
σ ≈ 2 [1− e−τ b ] eff τ b ≡ κρb = κρ / f “porosity length” h σ −τ b eff 1− e κ κ eff ≡ = κ ≈ ; τ b >>1 mb τ b τ b
Wednesday, January 12, 2011 clump size ℓ=0.05r ℓ=0.1r ℓ=0.2r Porous envelopes h=0.5r
Porosity length h=r h≡ ℓ/fvol vol. fill factor fvol≡(ℓ/L)3 = 1/fcl h=2r
Wednesday, January 12, 2011 clump size ℓ=0.05r ℓ=0.1r ℓ=0.2r Porous envelopes h=0.5r
Porosity length h=r h≡ ℓ/fvol vol. fill factor fvol≡(ℓ/L)3 = 1/fcl h=2r
Wednesday, January 12, 2011 Super-Eddington Continuum-Driven Winds mediated by “porosity”
Wednesday, January 12, 2011 VY CMa IRC+10420 Massive, Luminous stars:
Several M of circumstellar matter resulting from brief eruptions, expanding at about 50-600 km/s. P Cygni
Pistol Star (Figer et al. 1999)
SN1987A HD 168625 Sher 25 (Brandner et al. 1997) (courtesy P. Challis) (Smith 2007) Eta Car
Wednesday, January 12, 2011 Eta Carinae
Wednesday, January 12, 2011 Eta Car’s Extreme Properties Present day:
Wednesday, January 12, 2011 Eta Car’s Extreme Properties Present day:
1840-60 Giant Eruption:
Wednesday, January 12, 2011 Eta Car’s Extreme Properties Present day:
1840-60 Giant Eruption:
=> Mass loss is energy or “photon-tiring” limited
Wednesday, January 12, 2011 Stagnation of photon-tired outflow κ ⎡V 2 GM GM⎤ 1 x ˙ = + L(r) = L* − M ⎢ + − ⎥ κ Edd ⎣ 2 R r ⎦
• 2 MVesc m ≡ 2L V 2 * 2 Vesc
x =1− R* /r Wednesday, January 12, 2011
Wednesday, January 12, 2011 Wednesday, January 12, 2011 Photon Tiring & Flow Stagnation
Wednesday, January 12, 2011 Fluidized Bed
Spiegel 2006
71
Wednesday, January 12, 2011 Wednesday, January 12, 2011 Monte Carlo results for eff. opacity vs. density in a porous medium
Log(eff. opacity)
Log(average density)
Wednesday, January 12, 2011 Monte Carlo results for eff. opacity vs. density in a porous medium
Log(eff. opacity)
Log(average density)
Wednesday, January 12, 2011 Monte Carlo results for eff. opacity vs. density in a porous medium
Log(eff. opacity)
blobs opt. thin
Log(average density)
Wednesday, January 12, 2011 Monte Carlo results for eff. opacity vs. density in a porous medium
Log(eff. opacity)
blobs blobs opt. thin opt. thick
Log(average density)
Wednesday, January 12, 2011 Monte Carlo results for eff. opacity vs. density in a porous medium
~1/ρ Log(eff. opacity)
blobs blobs opt. thin opt. thick
Log(average density)
Wednesday, January 12, 2011 Monte Carlo results for eff. opacity vs. density in a porous medium “critical density ρc
~1/ρ Log(eff. opacity)
blobs blobs opt. thin opt. thick
Log(average density)
Wednesday, January 12, 2011 Power-law porosity ⎛ ⎞α ρc At sonic point: Γeff (rS ) = Γ⎜ ⎟ ≡1 ⎝ ρS ⎠
Wednesday, January 12, 2011 Power-law porosity ⎛ ⎞α ρc At sonic point: Γeff (rS ) = Γ⎜ ⎟ ≡1 ⎝ ρS ⎠
Wednesday, January 12, 2011 Power-law porosity ⎛ ⎞α ρc At sonic point: Γeff (rS ) = Γ⎜ ⎟ ≡1 ⎝ ρS ⎠
• 2 M = 4πR* ρS a
Wednesday, January 12, 2011 Power-law porosity ⎛ ⎞α ρc At sonic point: Γeff (rS ) = Γ⎜ ⎟ ≡1 ⎝ ρS ⎠
• L M = 4πR2ρ a ≈ * Γ−1+1/α * S ac
Wednesday, January 12, 2011 Power-law porosity ⎛ ⎞α ρc At sonic point: Γeff (rS ) = Γ⎜ ⎟ ≡1 ⎝ ρS ⎠
• L M = 4πR2ρ a ≈ * Γ−1+1/α * S ac
Wednesday, January 12, 2011 Power-law porosity ⎛ ⎞α ρc At sonic point: Γeff (rS ) = Γ⎜ ⎟ ≡1 ⎝ ρS ⎠
• L M = 4πR2ρ a ≈ * Γ−1+1/α * S ac
• −1+1/α L* M CAK Q ≈ 2 ( Γ) c
Wednesday, January 12, 2011
Effect of gravity darkening on porosity-mediated mass flux M˙ ⎛ ⎞− 1+1/α ˙ F(θ) m ≡ 2 m˙ ( ) ~ F(θ) 4πR θ ⎜ ⎟ ⎝ geff (θ)⎠
Wednesday, January 12, 2011 Effect of gravity darkening on porosity-mediated mass flux M˙ ⎛ ⎞− 1+1/α ˙ F(θ) m ≡ 2 m˙ ( ) ~ F(θ) 4πR θ ⎜ ⎟ ⎝ geff (θ)⎠
w/ gravity darkening, m˙ (θ) ~ F(θ) highest at pole if F(θ)~geff(θ)
Wednesday, January 12, 2011 Effect of gravity darkening on porosity-mediated mass flux M˙ ⎛ ⎞− 1+1/α ˙ F(θ) m ≡ 2 m˙ ( ) ~ F(θ) 4πR θ ⎜ ⎟ ⎝ geff (θ)⎠
w/ gravity darkening, m˙ (θ) ~ F(θ) highest at pole if F(θ)~geff(θ)
v (θ) ~ v (θ) ~ g (θ) highest at ∞ geff eff pole
Wednesday, January 12, 2011 Eta Carinae
Wednesday, January 12, 2011 Summary Themes
Wednesday, January 12, 2011 Summary Themes
• Continuum vs. Line driving
Wednesday, January 12, 2011 Summary Themes
• Continuum vs. Line driving
• Prolate vs. Oblate mass loss
Wednesday, January 12, 2011 Summary Themes
• Continuum vs. Line driving
• Prolate vs. Oblate mass loss
• Porous vs. Smooth medium
Wednesday, January 12, 2011 End Lecture 1
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