1. Theory of Stellar Winds from Hot, Luminous Massive Stars Stan Owocki Bartol Research Institute University of Delaware with thanks to numerous collaborators, ex-postdocs, students, etc.... David Cohen, Ken Gayley, Rich Townsend, Asif ud Doula, Jo Puls, Achim Feldmeier, Luc Dessart, Mark Runacres and many more...

2. Acknowledgements Mentors Tom Holzer George Rybicki John Castor Larry Auer Dimitri Mihalas Collaborators Jo Puls Achim Feldmeier Luc Dessart Nir Shaviv Marc Runacres John Hillier Wolf-Rainer Hamman ExPostdocs/Students Ken Gayley Steve Cranmer David Cohen Rich Townsend Asif ud-Doula

3. Outline Basic physics of (CAK) line-driven wind –Monte Carlo models for optically thick winds Line-driven instability –scattering line-drag –Smooth Source Function (SSF) method –X-rays, clumping, “porosity” Effects of pulsation, rotation, & B-field

4. Radiative acceleration vs. gravity Gravitational Force Radiative Force

5. 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...

6. Q~  ~ 10 15 Hz * 10 -8 s ~ 10 7 Q ~ Z Q ~ 10 -4 10 7 ~ 10 3 Line Scattering: Bound Electron Resonance  lines ~Q  Th g lines ~ 10 3  g el L  L thin } if Γ lines ~ 10 3  Γ el  1 for high Quality Line Resonance, cross section >> electron scattering

7. Driving by Line-Opacity Optically thin Optically thick

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

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

10. Sobolev approximation for radial acceleration from single line purely local!

11. Direct force line-frequency integration

12. CAK power-law ensemble line-force

13. Line-ensemble force CAK point-star: only integral no integral Vector force:

14. CAK wind in zero-gas-pressure limit

15. inertiaeff. gravityline-acceleration

16. Graphical solution 2 Solns 1 Soln No solns

17. Critical solution

18. Wind Momentum Luminosity Relation

19. Point-star vs. Finite-disk I*I* r g r ~I * (dv/dr)  Point-star approx. * g r ~I n (dv n /dn)  InIn Finite-disk integration r

20. Point-star vs. Finite-disk I*I* r g r ~I * (dv/dr)  Point-star approx. * g r ~I n (dv n /dn)  InIn Finite-disk integration r

21. Vector line force In spherical wind: finite-disk correction factor

22. Finite-disk reduction of CAK mass loss rate

23. FDCF for  velocity law

24. Finite-disk reduction of CAK mass loss rate

25. Enhanced acceleration

26. High-speed of finite-disk-corrected wind

27. CAK vs. FD velocity law

28. FD CAK

29. Finite Disk Correction FD CAK

30. Effect of finite gas-pressure on CAK wind increases M dot ~ 10-20% decreases Vinf ~ 10% increases M dot ~ 10% Perturbation expansion of FD-CAK soln in s<<1 gives: s <<1

31. Effect of finite gas-pressure on FD-CAK wind increases M dot ~ 10-20% decreases Vinf ~ 10% increases M dot ~ 10% Perturbation expansion of FD-CAK soln in s<<1 gives:

32. finite gas-pressure, cont. increases M dot ~ 10-20%

33. Summary: Key CAK Scaling Results Mass Flux: Wind Speed:

34. Summary: Key CAK Scaling Results Mass Flux: Wind Speed:

35. Monte-Carlo models Abbott & Lucy 1985; LA 93; Vink et al. 2001 Assume beta velocity law, use MC transfer through line list to compute global radiative work W rad and momentum p rad

36. Monte-Carlo models Then compute mass loss rate from: Text NOTE: Global not local soln of EOM

37. WR wind momentum WR winds have Requires multiple scattering for lines separated by

38. Multi-line scattering

39. “Bunched” line-distribution photon “leakage” “Effectively gray” line-distribution Friend & Castor 1982; Gayley et al. 1995 Onifer &Gayley 2006

40. Wolf-Rayet Wind Driving log Density log Wavelength Flux Opacity Radiative acceleration X = courtesy G. Graefener radius IRUV

41. POWR Code for WR Winds log Density Flux Opacity Radiative acceleration X = courtesy G. Graefener radius UVlog WavelengthIR 4 3 2

42. Mdot increases with Γ Edd Graefner & Hamman

43. Mdot increases with Γ e Graefener & Hamman 2005

44. Line-Deshadowing Instability Good overview in Feldmeier 2000 (habilitation thesis) Early work: Milne 1924; Lucy & Solomon 1971 Linear analyses: Macgregor et. al. 1979; Lucy 1984; OR-84,5; ROC-90 Nonlinear sims: OCR-87; Feldmeier 1993; O+Puls-99 Energy equation, X-rays: Feldmeier et. al. 1995, 1997 2D sims: 1998; Dessart+O 02, 03, 05 ; Distant evolution: Runacres+O 02, 05

45. Linear perturbation of time-dependent e.o.m.

46. Inward-propagating Abbott waves v r  g~  v’ Abbott speed Sobolev/CAK: Real  => stable!

47. Line-Deshadowing Instability for  < L sob : i  =  g/  v = +g o /v th = Instability with growth rate  ~ g o /v th ~vv’/v th ~ v/L sob ~100 v/R => e 100 growth!

48. Line-Deshadowing Instability for  < L sob : i  =  g/  v = +g o /v th = Instability with growth rate  ~ g o /v th ~vv’/v th ~ v/L sob ~100 v/R => e 100 growth !

49. Bridging law Abbott/Sobolev limit Instability limit

50. Non-linear structure for pure-absorption model Direct force Integral optical depth OCR 1988

51. Non-linear structure for pure-absorption model Direct force Integral optical depth OCR 1988

52. Line-Scattering in an Expanding Wind

53. Sobolev Approximation purely local! Formal solndirectdiffuse + even Escape prob. in direction

54. Local Line-Force oddeven

55. Direct & Diffuse Intensity vs. Comoving Frame Frequency

56. Direct force line-frequency integration

57. Diffuse Radiation

58. Diffuse Line-Drag

59. Linear Stability Analysis radial instability base stable growth rate relative to pt-star absorption

60. Smooth Source Function (SSF) Method frequency & angle averaged Integral Escape prob. => smooths over structure

61. Smooth Source Function (SSF) Method frequency & angle averaged Integral Escape prob. => smooths over structure

62. Sobolev Approximation l sob =v th /(dv/dr) ~ r(v th /v) >v th v th = Sqrt[kT/m] = Sqrt[0.6/ Α ] a ~ 0.1-0.3 a so is SA good even near sonic point??

63. Sonic region forces

66. Time snapshot of wind instability simulation Velocity Density CAK drag stabilizes but back-scattering also self-excites!

67. Clumping vs. radius Clumping factor Radial velocity dispersion

68. Clumping vs. log radius Velocity-density correlation 1R * 10R * 100R * Clumping factor Radial velocity dispersion

69. SSF sim of LDI CAK init. cond. radius (R ∗ ) 1 10 0 4 Time (days) 110 0 4 radius (R ∗ ) Velocity Density

70. Turbulence- seeded clump collisions Feldmeier et al. 1997 Enhances V disp and thus X-ray emission

71. observer on left isovelocity contours -0.8v inf -0.6v inf -0.2v inf +0.2v inf +0.6v inf +0.8v inf optical depth contours  = 0.3  = 1  = 3

72. Chandra X-ray line-profile for ZPup Fe XVII

73. X-ray emission line-profile

74. Fe XVII Traditional mass-loss rate: 8.3 X 10 -6 M sun /yr Cohen et al. 2010 best fit: 3.5 X 10 -6 M sun /yr

75.  Pup: 3 emission lines Mg Ly  : 8.42 Å Ne Ly  : 12.13 Å O Ly  : 18.97 Å  * = 1  * = 2  * = 3

76. Inferring ZPup Mdot from X-ray lines Traditional mass-loss rate: 8.3 X 10 -6 M sun /yr Cohen et al. 2010 best fit: 3.5 X 10 -6 M sun /yr

77. Extension to 3D: the “Patch Method”

78. 3D “patch” model Dessart & Owocki 2002 patch size ~3 deg WR Star Emission Profile Variability WR 140 Lepine & Moffat 1999

79. R ayleigh-Taylor (heavy over light ) Vishniac & Thin-Shell (gas-ram) (ram-ram) Interface Instabilities Kelvin-Helmholtz (shear) Cooling Overstabilty ga For summary, see J. Pittard Ph.D. thesis

80. 2D Planar Simulation of Interaction Layer Walder & Folini 1998,1999 Density Isothermal case: Thin-shell instability Radiative cooling case: Cooling overstability

81. 2D-H + 1D-R nr=1000 n  =60 Δ  =12deg Dessart & Owocki 2003

82. 2D-H+1D-R Clumping statistics Clumping factor Radial velocity dispersion Density contrast reduced Velocity dispersion increased Chaotic lay-out of wind structures – no pancakes etc… Lateral scale extends down to grid resolution => Result of neglecting lateral diffuse force?

83. 3D Linear Stability Analysis 3 r 1  Rybicki et al. 1990 Instability tensor: radial instability lateral damping base stable

84. Lateral line-drag net radial instability for: lateral damping for:

85. Lateral line-drag net radial instability for: lateral damping for:

86. 3-Ray Grid for 2D Nonlocal Rad-Hydro Diagram: N  = 9 ; Δ  = 10 o I-I- IoIo I+I+ g  ~ I + - I - e.g. for impact parameter Actual code: N  =157 ; Δ  = 0.6 o = 0.01 rad

87. Dessart & Owocki 2005

88. 2nd-Order Sobolev lateral viscosity

89. Dessart & Owocki 2005

90. Lateral radiative viscosity DO-05

91. h “Porous” opacity from optically thick clumps “porosity length” Self-shadowing of optically thick clumps lowers the effective opacity of a clumped medium

92. Porous envelopes h=0.5r h=r h=2r ℓ ℓ =0.05r ℓ ℓ =0.1r ℓ ℓ =0.2r Porosity length ℓ h  ℓ /f clump size vol. fill factor ℓ f  ℓ /L) 3  f cl f =0.1 f =0.2 f =0.05 f =0.025 f =0.4

93. Porous envelopes h=0.5r h=r h=2r ℓ ℓ =0.05r ℓ ℓ =0.1r ℓ ℓ =0.2r Porosity length ℓ h  ℓ /f clump size vol fill fac ℓ f  ℓ /L) 3  f cl f =0.1

94. h Pure-abs. model for “blob opacity”

95. Expanding Porous envelopes h=0.5r h=r h=2r l=0.05rl=0.1rl=0.2r Porosity length h  l/f

96. “Clumping” – or micro-clumping: affects density-squared diagnostics; independent of clump size, just depends on clump density contrast (or filling factor, f ) visualization: R. Townsend

97. The key parameter is the porosity length, h = (L 3 /ℓ 2 ) = ℓ/f But porosity is associated with optically thick clumps, it acts to reduce the effective opacity of the wind; it does depend on the size scale of the clumps Lℓ f = ℓ 3 /L 3

98. h = ℓ /f clump size clump filling factor (<1) The porosity length, h: Porosity length increasing  Clump size increasing 

99. Effect of Porosity on X-ray line- profiles

100. Porosity only affects line profiles if the porosity length (h) exceeds the stellar radius

101. But large optical thickness of line opacity suggests it could be much more sensitive to porosity May help solve “PV problem” (Fullerton et al. 2006)

102. Spatial variation of velocity & density

103. Velocity vs. Mass

104. vv } } ΔVΔV Velocity filling factor :

105. Velocity vs. Mass

106. “Velocity Porosity” Vorosity ?

107. Dynamic absorption spectra from 1D SSF sim StrongMediumWeak 0 0 0 00 Wavelength (V ∞ ) Time

108. Weak Line-Desaturation => lower Mdot est. Wavelength (V ∞ ) 0 F /F cont 0 1 Medium Strong

109. How is line-driven wind affected by: Pulsation Rotation Magnetic field To answer, back to Sobolev/CAK

110. Pulsation-induced wind variability Velocity Radius radiative driving modulated by brightness variations “kinks” velocity “plateaus” shock compression

111. Wind variations from base perturbations in density and brightness log(Density) Velocity Radius wind base perturbed by  ~ 50 radiative driving modulated by brightness variations “kinks” velocity “plateaus” shock compression

112. Wind variations from base perturbations in density and brightness log(Density) Velocity Radius wind base perturbed by  ~ 50 radiative driving modulated by brightness variations “kinks” velocity “plateaus” shock compression

113. BW Vul: Observations vs. Model C IVModel line

114. HD64760 Monitored during IUE “Mega” Campaign Monitoring campaigns of P-Cygni lines formed in hot-star winds also often show modulation at periods comparable to the stellar rotation period. These may stem from large-scale surface structure that induces spiral wind variation analogous to solar Corotating Interaction Regions. Radiation hydrodynamics simulation of CIRs in a hot-star wind Rotational Modulation of Hot-Star Winds

115. WR6 - wind modulation model m=4 dynamical model NIV in WR 6

116. How is line-driven wind affected by: Pulsation Rapid Rotation Magnetic field

117. How is a line-driven wind affected by (rapid) stellar rotation?

118. Wind Compressed Disk Model Bjorkman & Cassinelli 1993

119. Vrot (km/s) = 200 250 300 350 400 450 Hydrodynamical Simulations of Wind Compressed Disks Note: Assumes purely radial driving of wind with no gravity darkening

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

121. Gravity Darkening increasing stellar rotation

122. Radial line-force; No gravity dark.

123. Vector line-force; No gravity dark.

124. 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:

125. Vector line-force; With gravity dark.

126. Effect of rotation on flow speed *

128. Smith et al. 2003

129. Eta Carinae

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

132. Power-law porosity At sonic point:

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

135. Flow Stagnation

137. Photon Tiring & Flow Stagnation

138. How is line-driven wind affected by: Pulsation Rotation Magnetic field

139. Magnetic confinement vs. Wind + Rotation Alfven radius Kepler radius Rotation vs. criticalWind mag. confinement

140. MHD Simulation of Wind Channeling Confinement parameter Isothermal No Rotation R A ~  * 1/4 R *  * =10

141. Field aligned rotation RKRK RARA V rot =250 km/s = V crit /2  * =32

142. Radial Mass Distribution

143. Radial Distribution of equatorial mass Stronger Magnetic Confinement ---> More Rapid Rotation --->

144. RRM model for  Ori E B * ~10 4 G tilt ~ 55 o  * ~10 6 !

145. EM +B- field polarimetry ΗΗ photometry RRM model for  Ori E B * ~10 4 G tilt ~ 55 o  * ~10 6 !

147. Summary Lines have lots of locked-up opacity Acceleration desaturates => acceleration Direct instability vs. scattering line-drag Compressive turbulence => clumped wind “Vorosity” more important than “porosity” Rot, puls, B-fields=> large-scale structure

150. X-ray lightcurve for  Car

151. Accretion Disk Winds from BAL QSOs

153. Wind rotation spindown from azimuthal line-torque g  (10 3 cm/s 2 ) [V  (nrf) - V  (wcd)] *sin(  )*r/R eq (km/s) a. b. -10 -30 -50 -70 -90 -0.1 -0.3 -0.5 -0.7 -0.9 azimuthal line-force ang. mom. loss

154. Azimuthal Line-Torque Δ V + <  Δ V_ g  ~  Δ V + -  Δ V_ < 

155. Line-Force in Keplerian Disk

156. Line-Driven Ablation g lines ~ dv l /dl Net radiative Flux = 0, but g lines ~ dv l /dl > 0 !

157. Wolf-Rayet Wind Driving