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 & IonizationAspects of Flows from Hot Stars”, Tartu, Estonia, Aug. 1999

0.0 0.5 1.0

0

500

1000

1500

Clumped density

-15

-14

-13

-12

-11

-10

CAK

log

Den

sity

(g/

cm3 )

Height (R*)

Self-Excitation of Line-Driven Instability in Wind Acceleration Region

no base perturbation

t=430 ksec

t=430 ksec

Tim

e (k

sec)

0 10 20 30 40

430

450

470

490

Height (R*)

log Density (g/cm3)

400 10 20 30

-22

-20

-18

-16

-14

-12

-10

430

450

470

490

Tim

e (k

sec)

0 10 20 30 40

Height (R*)

Velocity (km/s)

0 10 20 30 40

0

1000

2000

3000

Extended Evolution to r~ 41 R*

log Density (g/cm3)

125 100 75

-22

-20

-18

-16

-14

-12

-10

t=430 ksec

m(r,t)125 100 75

490

480

470

460

450

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430

Tim

e (k

sec) r=

R*Velocity (km/s)

m(r,t)

125 100 75

0

1000

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3000

125 100 75

490

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430

r=R

*

r=41

R*

t=430 ksec

Extended Evolution vs. Lagrangian MassT

ime

(kse

c)

r=41

R*

Statistical Properties of Wind Structure

Sqrt(Clumping factor)

0 10 20 30 401

2

3

4

5

1

2

3

4

5

Height (R*)0 10 20 30 40

-1

0

1

-1

0

1

Height (R*)

Vel.-Den. Correlation

10 20 30 400

100

200

300

400

Height (R*)

RMS Vel.

0 10 20 30 400

1

2

0

1

2

Height(R*)

RMS log(Den.)

v (

km

/s)

C f ¥≠Ω2Æ

hΩi2

Quasi-Periodic Extension to r~165 R*

Height

Repeat structure at r=41 R*

50 100 1500-22

-20

-18

-16

-22

-20

-18

-16

log Density (g/cm3)

-22

-20

-18

-16

Tim

e

10 * Po

11 * Po

log Density

over

Quasi-Period

Po = 216 ~ 65 ksec

50 100 150

01

2

3

4

5

1

2

3

4

5

50 100 150

Sqrt[Cf]

0

• Spherical Conservation Equations reduce to:

• Mass

• Momentum

• Energy

Pseudo-Planar Equations

• Galilean transformation

• Rescaled variables

only non-planar terms needed to account for

sphericity

positionvelocity

density

pressure

internal energy

~Ω ¥ Ω(r=R)2

~P ¥ P(r=R)2

~E ¥ E(r=R)2

@~Ω@t

+@(~Ωw)

@x= 0

@(~Ωw)@t

+@(~Ωw2)

@x= °

@~P@x

+2~Pr

@~E@t

+@(~Ew)

@x= ° ~P

@w@x

°2~P(Vo +w)

r

x ¥ r ° R ° Vot

w ¥ v ° Vo

adiabaticcooling

Pseudo-planar evolution

Adiabatic evolutionof Periodic pulse

Quasi-Periodic pulse train :

Adiabatic cooling allows structure to persist

0

Tim

e (M

sec)

12

Density

0 x (R*) 30

Density snapshots

0 Radius (R*) 30

0 x (R*) 3

0

Tim

e (M

sec)

12

Density

t ~ 4 months

r ~ 2000 R*

• 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: Tcold << T*

• suppress cooling => hot X-ray em: Thot >> T*

0

T 0

P 0

v 0

¢ΩΩ=¢PP°¢TT

X-rays from Hot +Warm Wind• Observe : Lx ~ 10-7 Lbol .

• by scaling analysis (Owocki & Cohen 1999) :

Lx ~ Cs2 fv (M/v

• where :

Cs= hot/<fv = Volume filling fraction hot gas

Cs fv = fm = Mass filling fraction

• for : Lx / Lbol ~ 10-7 & Thot ~ 5 MK

• need : Cs2 fv ~ 0.01

• for P=0 : fv ~ 0.9 ; Cs ~ 0.1 => fm ~ 0.1

lower reduces line cooling

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

Clumping factor

0 20 40 60 80 1000

20

40

60

80

100

2

3

5

4

1/(1-fv)

hi---lo

*

hi/lo=Thot / Twarm =100

1-fv=0.1Cf

1/2 = 2.9

Sqrt[Cf]

For hot + warm wind model:

Periodic shocktube

Initial condition:Temperature constantFactor 4 Density jump