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Breaching the Eddington Limit in the Most Massive, Most Luminous Stars

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Breaching the Eddington Limit in the Most Massive, Most Luminous Stars 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..
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