Breaching the Eddington Limit in the Most Massive, Most Luminous Stars Stan Owocki Bartol Research Institute University of Delaware Collaborators: Nir Shaviv Hebrew U. Ken GayleyU. Iowa Rich TownsendU. Delaware Asif ud-DoulaU. Delaware Luc DessartU. Arizona

Massive Stars in “Pillars of Creation”

Massive Stars in the Whirlpool Galaxy

Wind-Blown Bubbles in ISM Some key scalings: WR wind bubble NGC 2359 Superbubble in the Large Magellanic Cloud Henize 70: LMC SuperBubble

Pistol Nebula

Eta Carinae

Massive Stars are Cosmic Engines Help trigger star formation Power HII regions Explode as SuperNovae GRBs from Rotating core collapse Hypernovae “First Stars” reionized Universe after BB & Cosmic Beacons

Q: So, what limits the mass & luminosity of stars? A: The force of light! –light has momentum, p=E/c –leads to “Radiation Pressure” –radiation force from gradient of P rad –gradient is from opacity of matter –opacity from both Continuum or Lines

Continuum opacity from Free Electron Scattering Thompson Cross Section th e-e-  Th  = 8  /3 r e 2 = 2/3 barn= 0.66 x cm 2

Eddington limit The Eddington limit is when the radiative force on free electrons just balances the gravitational force. SUPER-Eddington: radiative force exceeds the force of gravity Gravitational Force Radiative Force

Radiative force  ~ e.g., compare electron scattering force vs. gravity  g el g grav   e L 4  GMGMc r  L 4  r 2 c Th  e GM 2  For sun,  O ~ 2 x But for hot-stars with L~ 10 6 L O ; M=10-50 M O... if  gray

Mass-Luminosity Relation => Hydrostatic equilibrium (  <<1): Radiative diffusion:

Mass-Luminosity Relation

Key point Stars with M ~ 100 M sun have L ~ 10 6 L sun => near Eddington limit! Provides natural explanation why we don’t see stars much more luminous (& massive) than this.

Line-Driven Stellar Winds Stars near but below the Edd. limit have “stellar winds” Driven by line scattering of light by electrons bound to metal ions This has some key differences from free electron scattering...

Q~  ~ Hz * s ~ 10 7 Q ~ Z Q ~ ~ 10 3 Line Scattering: Bound Electron Resonance  lines ~Q  Th g lines ~10 3  g el L  L thin } if  lines ~10 3  el  1 for high Quality Line Resonance, cross section >> electron scattering

Optically Thick Line-Absorption in an Accelerating Stellar Wind L sob For strong, optically thick lines: << R *

CAK model of steady-state wind inertiagravityCAK line-force Solve for: Mass loss rate Wind-Momentum Luminosity Law Velocity law Equation of motion:  < 1 CAK ensemble of thick & thin lines

Summary: Key CAK Scaling Results e.g., for  1/2 Mass Flux: Wind Speed:

How is such a wind affected by (rapid) stellar rotation?

Vrot (km/s) = Hydrodynamical Simulations of Wind Compressed Disks But caution: These assume purely radial driving of wind

WCD Inhibition Net poleward line-force inhibits WCD Stellar oblateness => poleward tilt in radiative flux r Flux N

Gravity Darkening increasing stellar rotation

Non-radial line-force + gravity dark.:

Effect of gravity darkening on line-driven mass flux e.g., for w/o gravity darkening, if F(  )=const. highest at equator w/ gravity darkening, if F(  )~g eff (  ) highest at pole Recall:

Effect of rotation on flow speed *

Smith et al. 2002

Eta Car’s Extreme Properties Present day: Giant Eruption: => Mass loss is energy or “photon-tiring” limited

But lines can’t explain eta Carinae’s mass loss O O

Super-Eddington Continuum-Driven Winds moderated by “porosity”

Porosity Same amount of material More light gets through Less interaction between matter and light Incident light

Monte Carlo

Monte Carlo results for eff. opacity vs. density in a porous medium Log(average density) ~1/  Log(eff. opacity) blobs opt. thin blobs opt. thick “critical density  c

Pure-abs. model for “blob opacity”

Key Point For optically thick blobs: Blobs become opt. thick for densities above critical density  c, defined by: volume filling factor

G. Dinderman Sky & Tel.

Radiation vs. Gas Pressure Radiative diffusion Hydrostatic equilibrium

Convective Instability Classically expected when dT/dr > dT/dr ad –e.g., hot-star core  ~ T ; cool star env.  increase But  (r) -> 1 => decreases dT/dr ad => convection –e.g., if  e ~1/2 => M(r) < M * /2 convective! For high density interior => convection efficient –L conv > L rad  L Edd =>  rad (r) < 1: hydrostatic equilibrium Near surface, convection inefficient => super-Eddington –but any flow would have M ~ L/a 2 –implies wind energy Mv esc 2 >> L –would“tire” radiation, stagnate outflow –suggests highly structured, chaotic surface..

Initiating Mass Loss from Layer of Inefficient Convection => => flow would stagnate due to “photon tiring”

Stagnation of photon-tired outflow

Shaviv 2001

Power-law porosity

Porous opacity  “porosity length”

Super-Eddington Wind Wind driven by continuum opacity in a porous medium when  * >1 Shaviv At sonic point: “porosity-length ansatz” O

Power-law porosity At sonic point:

Results for Power-law porosity model

Effect of gravity darkening on porosity-moderated mass flux w/ gravity darkening, if F(  )~g eff (  ) highest at pole highest at pole

Eta Carinae

Summary Themes Continuum vs. Line driving Prolate vs. Oblate mass loss Porous vs. Smooth medium

Future Work Radiation hydro simulations of porous driving Cause of L > L Edd ? –Interior vs. envelope; energy source Cause of rapid rotation –Angular momentum loss/gain Implications for: –Collapse of rotating core, Gamma Ray Bursts –Low-metalicity mass loss, First Stars