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...

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

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

Radiative acceleration vs. gravity Gravitational Force Radiative Force

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 Γ lines ~ 10 3  Γ el  1 for high Quality Line Resonance, cross section >> electron scattering

Driving by Line-Opacity Optically thin Optically thick

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

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

Sobolev approximation for radial acceleration from single line purely local!

Direct force line-frequency integration

CAK power-law ensemble line-force

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

CAK wind in zero-gas-pressure limit

inertiaeff. gravityline-acceleration

Graphical solution 2 Solns 1 Soln No solns

Critical solution

Wind Momentum Luminosity Relation

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

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

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

Finite-disk reduction of CAK mass loss rate

FDCF for  velocity law

Finite-disk reduction of CAK mass loss rate

Enhanced acceleration

High-speed of finite-disk-corrected wind

CAK vs. FD velocity law

FD CAK

Finite Disk Correction FD CAK

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

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:

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

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

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

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

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

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

Multi-line scattering

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

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

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

Mdot increases with Γ Edd Graefner & Hamman

Mdot increases with Γ e Graefener & Hamman 2005

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, D sims: 1998; Dessart+O 02, 03, 05 ; Distant evolution: Runacres+O 02, 05

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

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

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!

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 !

Bridging law Abbott/Sobolev limit Instability limit

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

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

Line-Scattering in an Expanding Wind

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

Local Line-Force oddeven

Direct & Diffuse Intensity vs. Comoving Frame Frequency

Direct force line-frequency integration

Diffuse Radiation

Diffuse Line-Drag

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

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

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

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

Sonic region forces

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

Clumping vs. radius Clumping factor Radial velocity dispersion

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

SSF sim of LDI CAK init. cond. radius (R ∗ ) Time (days) radius (R ∗ ) Velocity Density

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

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

Chandra X-ray line-profile for ZPup Fe XVII

X-ray emission line-profile

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

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

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

Extension to 3D: the “Patch Method”

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

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

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

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

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?

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

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

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

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

Dessart & Owocki 2005

2nd-Order Sobolev lateral viscosity

Dessart & Owocki 2005

Lateral radiative viscosity DO-05

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

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

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

h Pure-abs. model for “blob opacity”

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

“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

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

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

Effect of Porosity on X-ray line- profiles

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

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)

Spatial variation of velocity & density

Velocity vs. Mass

vv } } ΔVΔV Velocity filling factor :

Velocity vs. Mass

“Velocity Porosity” Vorosity ?

Dynamic absorption spectra from 1D SSF sim StrongMediumWeak Wavelength (V ∞ ) Time

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

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

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

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

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

BW Vul: Observations vs. Model C IVModel line

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

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

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

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

Wind Compressed Disk Model Bjorkman & Cassinelli 1993

Vrot (km/s) = Hydrodynamical Simulations of Wind Compressed Disks Note: Assumes purely radial driving of wind with no gravity darkening

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

Gravity Darkening increasing stellar rotation

Radial line-force; No gravity dark.

Vector line-force; No 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:

Vector line-force; With gravity dark.

Effect of rotation on flow speed *

Smith et al. 2003

Eta Carinae

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

Power-law porosity At sonic point:

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

Flow Stagnation

Photon Tiring & Flow Stagnation

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

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

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

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

Radial Mass Distribution

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

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

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

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

X-ray lightcurve for  Car

Accretion Disk Winds from BAL QSOs

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 azimuthal line-force ang. mom. loss

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

Line-Force in Keplerian Disk

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

Wolf-Rayet Wind Driving