Dynamical Origin of Wind StructureThe effect of “velocity

porosity” on P-Cygni line absorption strength

Stan OwockiBartol Research InstituteDepartment of Physics &

AstronomyUniversity of Delaware

Key Issues

• What is effect of wind clumping on line-absorption?

• Velocity dispersion vs. Spatial Porosity

• What are relevant scaling parameters (cf. f, h=l/f)?

• In dynamical model, how important for, eg. PV?

Spatial Porosity

• Same amount of material

• More light gets through

• Less interaction between matter and light

Incident light

Effective opacity

€

σ eff ≈ l2 [1− e−τ b ]

€

l

€

τ b ≡ κρ bl = κρl / f

€

κeff≡σ effmb

= κ1− e−τ b

τ b

€

≈κτ b

; τ b >>1

€

l

€

l

porosity length=h

Porous

envelopes

QuickTime™ and aCinepak decompressor

are needed to see this picture.

h=0.5r

h=r

h=2r

l=0.05r l=0.1r l=0.2r

hl/f

Profile-weighted line column depth

€

t(x,r→∞) = κρ φ(x − v(r') /v th ) dr'R

∞

∫

€

≈τ x φ(x') dx 'x

∞

∫

€

τ x=κρv thdv /dr

€

=κv thdv /dm

€

=τ∞

(1− R /r)2β −1

€

τ∞ =κM

•

v th4πRv∞

2

€

Ix = Ic (1− e−τ x )

€

x = v /v th

Step function

Line absorption trough

=1

τ

€

τ x =τ ∞

(1− R /r)2β −1

€

Ic (1− e−τ x )

Velocity vs. Mass

Velocity vs. Mass

v}

}V

€

fv ≡δv

ΔV

Velocity filling factor :

Velocity vs. Mass

“Velocity Porosity”

Vorosity?

Absorption reduction

€

RA (τ , fv ) = fv1− e−τ / fv

1− e−τ

0.5

f = 1

τx

RA

€

≈1− e−τ / fv

τ / fv; τ <<1

0.20.1

Line absorption

smooth, =1

τ

porous, fv = 1-v/2v

τ

Line-Driven Instabilty sim (SSF)

Instability model

CAK init. cond.

radius (R) 1 100

4

Time(days)

1 100

4

radius (R)

Velocity Density

Profile-weighted line column depth

Wavelength (V) -1 00

4

Time(days)

CAK init. cond.

Profile-weighted line column depth

Wavelength (V) -1 00

4

Time(days)

CAK init. cond.

Dynamic absorption spectrum-weak line

Wavelength (V) -1 00

4

Time(days)

CAK init. cond.

Dynamic absorption spectrum-weak line

Wavelength (V) -1 00

4

Time(days)

CAK init. cond.

Dynamic absorption spectrum - med. line

Wavelength (V) -1 00

4

Time(days)

CAK init. cond.

Dynamic absorption spectrum - med. line

Wavelength (V) -1 00

4

Time(days)

CAK init. cond.

Dynamic absorption spectrum-strong line

Wavelength (V) -1 00

4

Time(days)

CAK init. cond.

Dynamic absorption spectrum-strong line

Wavelength (V) -1 00

4

Time(days)

CAK init. cond.

Weak

Time-Averaged Absorption Profiles

Wavelength (V) -1 0

I /Icont

0

1

Medium

Strong

Weak

Time-Averaged Absorption Profiles

Wavelength (V) -1 0

I /Icont

0

1

Medium

Strong

Dynamic absorption spectra

Strong

MediumWeak

-1 -1 -100 0Wavelength (V)

Summary• Spatial porosity for continuum opacity

– characterized by “porosity length” h=l/f

• But for line opacity, key is“velocity clumping” – characterized by fvel (and τSob of smoothed wind)

• Line-driven instability suggests:– fvel ~= 0.7-0.8 (maybe 0.5 if seeded by low freq. pert)

– Mdot misunderestimated by fvel , i.e. 0.5-0.8– Maybe upto a factor 2 of the ca. 10 needed for PV

2D Simulation of Co-rotating Interaction Regions

localCAKmodel

nonlocalsmoothmodel

nonlocalstructured

model

c.

log(Density)

b. a.

Profile-weighted line column depth

Wavelength (V) -1 00

8

Time(days)

CAK init. cond.

Dynamic absorption spectrum-med. line

Wavelength (V) -1 00

8

Time(days)

CAK init. cond.

Dyn. abs. spectrum - very strong line

Wavelength (V) -1 00

4

Time(days)

CAK init. cond.

Dyn. abs. spectrum - very strong line

Wavelength (V) -1 00

4

Time(days)

CAK init. cond.

Instability model: Mdot

radius (R)

1 100

4

Time(days)

CAK init. cond.

0 5

250000

height

0.0e+00 5.0e-06 1.0e-05md4