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Radiatively Driven Winds and Aspherical Mass Loss

This work explores the mechanisms of radiatively driven winds and mass loss in hot stars, comparing line-driven and continuum-driven processes. We analyze the effects of stellar rotation, magnetic fields, and envelope convection on mass loss using models like the CAK theory. Key themes include the differences between oblate and prolate shapes in mass loss, the role of smooth versus porous media, and the implications of gravitational darkening. Our results address the complex dynamics and stability of hot stellar winds, providing insights into their structure and behavior.

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Radiatively Driven Winds and Aspherical Mass Loss

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  1. Radiatively Driven Winds and Aspherical Mass Loss Stan Owocki U. of Delaware collaborators: Ken Gayley U. Iowa Nir Shaviv Hebrew U. Rich Townsend U. Delaware Asif ud-Doula NCSU

  2. General Themes • Lines vs. Continuum driving • Oblate vs. Prolate mass loss • Smooth vs. Porous medium • Rotation vs. Magnetic field

  3. if k gray e.g., compare electron scattering force vs. gravity s L Th g 2 k 4 r c L p m e e el G º = = g 4 GM c p GM grav 2 r • For sun, GO ~ 2 x 10-5 • But for hot-stars with L~ 106 LO ; M=10-50 MO . . . G<1 ~ Radiative force

  4. Q~ n t ~ 1015 Hz * 10-8 s ~ 107 Q ~ Z Q ~ 10-4 107 ~ 103 ~ Q s ´ s lines Th g ~ 103 g ´ lines el } 3 if G ´ G >> ~ 10 1 lines el L L = thin Line Scattering: Bound Electron Resonance for high Quality Line Resonance, cross section >> electron scattering

  5. Optically Thick Line-Absorption in an Accelerating Stellar Wind For strong, optically thick lines:

  6. 0 < a < 1 CAK ensembleof thick & thin lines Mass loss rate Velocity law Wind-Momentum Luminosity Law CAK model of steady-state wind Equation of motion: inertia gravity CAK line-force Solve for:

  7. Wind Compressed Disk Model Bjorkman & Cassinelli 1993

  8. Wind Compressed Disk Model Bjorkman & Cassinelli 1993

  9. Vrot (km/s) = 200 250 300 350 400 450 Vrot = 350 km/s with nonradial forces Wind Compressed Disk Simulations radial forces only

  10. dvn/dn Net poleward line force from: (1) Stellar oblateness => poleward tilt in radiative flux (2) Pole-equator aymmetry in velocity gradient r N faster polar wind r Max[dvn/dn] Flux slower equatorial wind Vector Line-Force from Rotating Star

  11. Gravity Darkening increasing stellar rotation

  12. Vector line-force; With gravity dark.

  13. highest at pole highest at pole w/ gravity darkening, if F(q)~geff(q) Effect of gravity darkening on line-driven mass flux

  14. Rotational effect on flow speed *

  15. Smith et al. 2002

  16. Smith et al. 2003

  17. O O But lines can’t explain eta Car mass loss

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

  19. if k gray compare continuum force vs. gravity s L c g 2 k 4 r c L p m c c G º = = g 4 GM c p GM grav 2 r Continuum Eddington parameter constant in radius => no surface modulation

  20. Convective Instability • Joss, Salpeter Ostriker 1973 • Classically expected in energy-generating core • e.g., CNO burning => e ~ T10-20 => dT/dr > dT/drad • But envelope also convective where G(r) -> 1 • e.g., z Pup: G*~1/2 => M(r) < M*/2 convective! • For high density interior => convection efficient • Lconv > Lrad- Lcrit => Grad (r) < 1: hydrostatic equilibrium • Near surface, convection inefficient => super-Eddington • but flow has M ~ L/a2 • implies wind energy Mvesc2 >> L • would“tire” radiation, stagnate outflow • suggests highly structured, chaotic surface . .

  21. Photon tiring

  22. Stagnation of photon-tired outflow

  23. Shaviv 2001

  24. Power-law porosity

  25. Effective Opacity for "Blob"

  26. “porosity length” Porous opacity

  27. O Super-Eddington Wind Shaviv 98-02 Wind driven by continuum opacity in a porous medium when G* >1 At sonic point: “porosity-length ansatz”

  28. Power-law porosity Now at sonic point:

  29. Results for Power-law porosity model

  30. highest at pole highest at pole w/ gravity darkening, if F(q)~geff(q) Effect of gravity darkening on porosity-moderated mass flux

  31. Eta Carina

  32. Summary Themes • Lines vs. Continuum driving • Oblate vs. Prolate mass loss • Smooth vs. Porous medium • Rotation vs. Magnetic field

  33. e.g, for dipole field, q=3; h ~ 1/r4 Wind Magnetic Confinement Ratio of magnetic to kinetic energy density: for Homunclus, need B*~104G=> for present day eta Car wind, need B*~103G

  34. MHD Simulation of Wind Channeling No Rotation Confinement parameter A. ud Doula PhD thesis 2002

  35. Field aligned rotation A. ud-Doula, Phd. Thesis 2002

  36. w=0.95 ; DVamp = a = 25 km/s = DVorb Disk from Prograde NRP

  37. 1.2 Density Azimuthal Velocity r/R* 1.0 0 5 10 5 10 time (days) 1.2 NRP On NRP Off Kepler Number Mass r/R* 0.98 1.0 1.0 Azimuthal Averages vs. r, t

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