1. The Outer Evolution of Wind Structure Stan Owocki, Bartol/UDel Mark Runacres, Royal Obs./Brussels David Cohen, Bartol/UDel Outline Line-Driven Instability of Inner Wind Acceleration Direct extension to ~40 R * Quasi-Periodic Models to ~150 R * Pseudo-Planar Simulation to >1000 R * Main Result: Energy Balance Crucial Oral Presentation at workshop on: “Thermal & Ionization Aspects of Flows from Hot Stars”, Tartu, Estonia, Aug. 1999

2. Clumped density -15 -14 -13 -12 -11 -10 CAK log Density (g/cm 3 ) Height (R * ) Self-Excitation of Line-Driven Instability in Wind Acceleration Region no base perturbation

3. t=430 ksec Time (ksec) 010203040 430 450 470 490 Height (R * ) log Density (g/cm 3 ) 400102030 430 450 470 490 Time (ksec) 010203040 Height (R * ) Velocity (km/s) 010203040 Extended Evolution to r~ 41 R *

4. log Density (g/cm 3 ) t=430 ksec m(r,t) Time (ksec) r=R * Velocity (km/s) m(r,t) r=R * r=41R * t=430 ksec Extended Evolution vs. Lagrangian Mass Time (ksec) r=41R *

5. Statistical Properties of Wind Structure Sqrt(Clumping factor) 010203040 1 2 3 4 5 1 2 3 4 5 Height (R * ) 010203040 0 1 0 1 Height (R * ) Vel.-Den. Correlation 10203040 0 100 200 300 400 Height (R * ) RMS Vel. 010203040 0 1 2 0 1 2 Height(R * ) RMS log(Den.)  v (km/s) C f ¥ ≠ Ω 2 Æ hΩi 2

6. Quasi-Periodic Extension to r~165 R * Height Repeat structure at r=41 R * 50100150 0 -22 -20 -18 -16 -22 -20 -18 -16 log Density (g/cm 3 ) -22 -20 -18 -16 Time 10 * P o 11 * P o log Density over Quasi-Period P o = 2 16 ~ 65 ksec 50100150 0 1 2 3 4 5 1 2 3 4 5 50100150 Sqrt[C f ] 0

7. Spherical Conservation Equations reduce to: Mass Momentum Energy Pseudo-Planar Equations Galilean transformation Rescaled variables only non-planar terms needed to account for sphericity position velocity density pressure internal energy ~Ω¥Ω(r=R) 2 ~ P¥P(r ) 2 ~ E¥E(r ) 2 @~Ω @t + @(~Ωw) @x =0 @(~Ωw) @t + @(~Ωw 2 ) @x =° @ ~ P @x + 2 ~ P r @ ~ E @t + @( ~ Ew) @x =° ~ P @w @x ° 2 ~ P(V o +w) r x¥r°R°V o t w¥v°V o adiabatic cooling

8. Pseudo-planar evolution Adiabatic evolution of Periodic pulse Quasi-Periodic pulse train : Adiabatic cooling allows structure to persist 0 Time (Msec) 12 Density 0 x (R * ) 30 Density snapshots 0 Radius (R * ) 30 0 x (R * ) 3 0 Time (Msec) 12 Density  t ~ 4 months  r ~ 2000 R *

9. for r > few R*, decline of radiative driving for r >~ 10 R*, pressure expansion but also photoionization heating & line cooling by gas law: with net result Dissipation of Structure So Energy balance key: need  T > 0 Two possibilities: suppress heating => cold clumps: T cold << T * suppress cooling => hot X-ray em: T hot >> T *  0  T  0  P  0  v  0

10. X-rays from Hot +Warm Wind Observe : L x ~ 10 -7 L bol. by scaling analysis (Owocki & Cohen 1999) : L x ~ C s 2 f v (M/v    where : C s =  hot /<  f v = Volume filling fraction hot gas C s f v = f m = Mass filling fraction for : L x / L bol ~ 10 -7 & T hot ~ 5 MK need : C s 2 f v ~ 0.01 for  P=0 : f v ~ 0.9 ; C s ~ 0.1 => f m ~ 0.1 lower  reduces line cooling 

11. Summary Line-driven instability => structure within few R * But by few 10 R * :  v,  P,  T,   0 Energy balance is key to extended structure reduce photoionization heating: cold clumps reduce line-cooling: hot gas + X-rays Pseudo-Planar approach allows: modelling of quasi-periodic structure extension to r > 1000 R *, perhaps to pc Future work instability models as input to pseudo-planar improved photoionization heating & line cooling 2D & 3D models in periodic box Application to: X-ray thermal & non-thermal radio nebulae structure

12. Clumping factor 020406080100 0 20 40 60 80 100 1/(1-f v )  hi ---  lo *  hi /  lo =T hot / T warm =100 1-f v =0.1 C f 1/2 = 2.9 Sqrt[C f ] For hot + warm wind model:

13. Periodic shock tube Initial condition: Temperature constant Factor 4 Density jump