Mass loss and the Eddington Limit Stan Owocki Bartol Research Institute University of Delaware Collaborators: Nir Shaviv Hebrew U., Israel Ken GayleyU. Iowa A-J van MarleU. Delaware Rich TownsendU. Delaware Nathan SmithU.C. Berkley

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 Gravitational Force Radiative Force

Stellar Luminosity vs. Mass L ~ M 3.5

Basic Stellar Structure -> L ~ M 3+ => Hydrostatic equilibrium (  <<1): Radiative diffusion:

Basic Stellar Structure -> L ~ M 3+ => Hydrostatic equilibrium (  <<1): Radiative diffusion: =>

Basic Stellar Structure -> L ~ M 3+ => Hydrostatic equilibrium (  <<1): Radiative diffusion: =>

Basic Stellar Structure -> L ~ M 3+ => Hydrostatic equilibrium (  <<1): Radiative diffusion: =>

Mass-Luminosity Relation ~M 3.5 ~M 1  observed upper limit from young, dense clusters P gas > P rad P gas < P rad

Interior: Radiation Pressure Radiative diffusion Hydrostatic equilibrium

Interior: Radiation Pressure Radiative diffusion Hydrostatic equilibrium

Key points Stars with M ~ 100 M sun have L ~ 10 6 L sun => near Eddington limit! Suggests natural explanation why we don’t see stars much more luminous (& massive) P rad > P gas => Instabilities => Extreme mass loss

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

Driving by Line-Opacity Optically thin Optically thick

CAK Line-Driven Wind

Mdot increases with  e

Optically Thick Line-Absorption in an Accelerating Stellar Wind l sob For strong, optically thick line: For ensemble of lines: Solve: => &

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

CAK model of steady-state wind Solve equation of motion for: Mass loss rate Wind-Momentum Luminosity Law Terminal velocity

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

Key points Stars with M ~ 100 M sun have L ~ 10 6 L sun => near Eddington limit! Suggests natural explanation why we don’t see stars much more luminous (& massive) P rad >P gas => Instabilities => Extreme mass loss Can not be line-driven? But continuum driving needs to be regulated.

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

Gravity Darkening increasing stellar rotation

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 *

Eta Carinae

Historical Light Curve ~ L Edd

Smith et al. 2002

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

Line-driving can’t explain  Car’s mass loss Must be continuum driven with L > L Edd But how is this regulated when G ~ L/M = const.? Perhaps by “porosity” of structured medium? Structure could arise from instabilities, or “fallback” from stagnation in photon tiring limited wind.

Lines can’t drive  Carinae’s mass loss

3 Key points about  Car’s eruption M dot > 10 3 M dot (CAK)  can NOT be line-driven! L obs > L Edd => “super-Eddington” (by factor > 5!) L obs ~ M dot V 2 /2  M dot limited by energy or “photon-tiring”

Stagnation of photon-tired outflow

V2V2 1-R/r Max mass loss:

Stagnation of photon-tired outflow

Lines can’t drive  Carinae’s mass loss O O

O

Flow Stagnation

Photon Tiring & Flow Stagnation

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

Radiation vs. Gas Pressure Radiative diffusion Hydrostatic equilibrium

Shaviv 2001

Line-driving can’t explain  Car’s mass loss Must be continuum driven with L > L Edd But how is this regulated when G ~ L/M = const.? Perhaps by “porosity” of structured medium? Structure could arise from instabilities, or “fallback” from stagnation in photon tiring limited wind.

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

G. Dinderman Sky & Tel.

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”

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

Porous Envelope Porosity length = size/filling factor h  l/f = h'r

Porous envelopes h=0.5r h=r h=2r l=0.05rl=0.1rl=0.2r h  l/f

Expanding Porous envelopes h=0.5r h=r h=2r l=0.05rl=0.1rl=0.2r h  l/f

Pure-abs. model for “blob opacity”

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

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

X-ray lightcurve for  Car

POWR model for opacity

POWR model of radiative flux

POWR model of radiative force

Mdot increases with  Edd

Mdot increases with  e