Mass loss and the Eddington Limit Stan Owocki

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

Eddington limit Radiative Force Gravitational Force

Stellar Luminosity vs. Mass L ~ M 3. 5

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

Mass-Luminosity Relation 1 ~M ~M 3. 5 Pgas > Prad observed upper limit from young, dense clusters Pgas < Prad

Driving by Line-Opacity Optically thin Optically thick

CAK Line-Driven Wind

Mdot increases with e

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

Key points • Stars with M ~ 100 Msun have L ~ 106 Lsun => near Eddington limit! • Suggests natural explanation why we don’t see stars much more luminous (& massive) • Prad >Pgas => 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 Recall: e. g. , for w/o gravity darkening, if F(q)=const. highest at equator w/ gravity darkening, if F(q)~geff(q) highest at pole

Effect of rotation on flow speed *

Eta Carinae

Historical Light Curve ~ LEdd

Smith et al. 2002

3 Key points about h Car’s eruption • Mdot > 103 Mdot(CAK) Þ can NOT be line-driven! • Lobs > LEdd => “super-Eddington” (by factor > 5!) • Lobs ~ Mdot. V 2/2 ÞMdot limited by energy or “photon-tiring”

Stagnation of photon-tired outflow

Photon Tiring & Flow Stagnation

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

G. Dinderman Sky & Tel.

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

Porous envelopes l=0. 05 r h=0. 5 r h l/f h=r h=2 r l=0. 1 r l=0. 2 r

Expanding Porous envelopes h=0. 5 r h l/f h=r h=2 r l=0. 05 r l=0. 1 r l=0. 2 r

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

Power-law porosity At sonic point:

Effect of gravity darkening on porosity-moderated mass flux w/ gravity darkening, if F(q)~geff(q) 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 > LEdd? – 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 h Car

POWR model for opacity

POWR model of radiative flux

POWR model of radiative force

Mdot increases with Edd

Mdot increases with e