dynamical origin of wind structure
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Dynamical Origin of Wind Structure. Stan Owocki Bartol Research Institute Department of Physics & Astronomy University of Delaware. The effect of “velocity porosity” on P-Cygni line absorption strength. Key Issues. What is effect of wind clumping on line-absorption? - PowerPoint PPT PresentationTRANSCRIPT
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Dynamical Origin of Wind StructureThe effect of “velocity
porosity” on P-Cygni line absorption strength
Stan OwockiBartol Research InstituteDepartment of Physics &
AstronomyUniversity of Delaware
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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?
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Spatial Porosity
• Same amount of material
• More light gets through
• Less interaction between matter and light
Incident light
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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
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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
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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
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Line absorption trough
=1
τ
€
τ x =τ ∞
(1− R /r)2β −1
€
Ic (1− e−τ x )
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Velocity vs. Mass
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Velocity vs. Mass
v}
}V
€
fv ≡δv
ΔV
Velocity filling factor :
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Velocity vs. Mass
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“Velocity Porosity”
Vorosity?
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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
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Line absorption
smooth, =1
τ
porous, fv = 1-v/2v
τ
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Line-Driven Instabilty sim (SSF)
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Instability model
CAK init. cond.
radius (R) 1 100
4
Time(days)
1 100
4
radius (R)
Velocity Density
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Profile-weighted line column depth
Wavelength (V) -1 00
4
Time(days)
CAK init. cond.
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Profile-weighted line column depth
Wavelength (V) -1 00
4
Time(days)
CAK init. cond.
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Dynamic absorption spectrum-weak line
Wavelength (V) -1 00
4
Time(days)
CAK init. cond.
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Dynamic absorption spectrum-weak line
Wavelength (V) -1 00
4
Time(days)
CAK init. cond.
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Dynamic absorption spectrum - med. line
Wavelength (V) -1 00
4
Time(days)
CAK init. cond.
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Dynamic absorption spectrum - med. line
Wavelength (V) -1 00
4
Time(days)
CAK init. cond.
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Dynamic absorption spectrum-strong line
Wavelength (V) -1 00
4
Time(days)
CAK init. cond.
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Dynamic absorption spectrum-strong line
Wavelength (V) -1 00
4
Time(days)
CAK init. cond.
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Weak
Time-Averaged Absorption Profiles
Wavelength (V) -1 0
I /Icont
0
1
Medium
Strong
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Weak
Time-Averaged Absorption Profiles
Wavelength (V) -1 0
I /Icont
0
1
Medium
Strong
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Dynamic absorption spectra
Strong
MediumWeak
-1 -1 -100 0Wavelength (V)
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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
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2D Simulation of Co-rotating Interaction Regions
localCAKmodel
nonlocalsmoothmodel
nonlocalstructured
model
c.
log(Density)
b. a.
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Profile-weighted line column depth
Wavelength (V) -1 00
8
Time(days)
CAK init. cond.
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Dynamic absorption spectrum-med. line
Wavelength (V) -1 00
8
Time(days)
CAK init. cond.
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Dyn. abs. spectrum - very strong line
Wavelength (V) -1 00
4
Time(days)
CAK init. cond.
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Dyn. abs. spectrum - very strong line
Wavelength (V) -1 00
4
Time(days)
CAK init. cond.
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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