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
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σ eff ≈ l2 [1− e−τ b ]
€
l
€
τ b ≡ κρ bl = κρl / f
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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
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t(x,r→∞) = κρ φ(x − v(r') /v th ) dr'R
∞
∫
€
≈τ x φ(x') dx 'x
∞
∫
€
τ x=κρv thdv /dr
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=κv thdv /dm
€
=τ∞
(1− R /r)2β −1
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τ∞ =κM
•
v th4πRv∞
2
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Ix = Ic (1− e−τ x )
€
x = v /v th
Step function
Line absorption trough
=1
τ
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τ x =τ ∞
(1− R /r)2β −1
€
Ic (1− e−τ x )
Velocity vs. Mass
Velocity vs. Mass
v}
}V
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fv ≡δv
ΔV
Velocity filling factor :
Velocity vs. Mass
“Velocity Porosity”
Vorosity?
Absorption reduction
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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