Effect of Clumping on WCD Inhibition Stan Owocki Bartol Research Institute University of Delaware • Bjorkman & Cassinelli (1992) proposed kinematic Wind Compressed Disk (WCD) paradigm for Be disks. • General idea confirmed by dynamical CAK models with only central line- forces (OCB 1994). • But WCD inhibited in CAK models with nonradial line-force. • What is effect of instability- generated clumping on WCD inhbition?? • Here apply new “3-Ray” SSF method for 2D instability simulations with nonlocal line-force. • Key problem: artificial structure from grid staircase along oblate surface BC • Results still tentative. Outline
12
Embed
Effect of Clumping on WCD Inhibition Stan Owocki Bartol Research Institute University of Delaware Bjorkman & Cassinelli (1992) proposed kinematic Wind.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Effect of Clumping on WCD Inhibition
Stan Owocki
Bartol Research Institute
University of Delaware
• Bjorkman & Cassinelli (1992) proposed kinematic Wind Compressed Disk (WCD) paradigm for Be disks.• General idea confirmed by dynamical CAK models with only central line-forces (OCB 1994).• But WCD inhibited in CAK models with nonradial line-force.
• What is effect of instability-generated clumping on WCD inhbition??• Here apply new “3-Ray” SSF method for 2D instability simulations with nonlocal line-force.• Key problem: artificial structure from grid staircase along oblate surface BC• Results still tentative.
Outline
WCD Inhibition bynon-radial line-forces
Vrot (km/s) = 200 250 300 350 400 450
Wind Compressed Disks
}“S-350”
Vector Line-Force
fasterpolarwind
slower equatorial wind
r
rFl
ux
r g line ~ dΩ
Ω*
∫ r n I*
r n⋅[∇(
r n⋅ r v)]α
dvn/dn
Max
[dv n
/dn]
Net poleward line force from:
(1) Stellar oblateness => poleward tilt in radiative flux
(2) Pole-equator aymmetry in velocity gradient
N
Line-Driven Instability from Perturbed Profile Doppler Shift
Instability growth rate:
Ω ~ g/vth ~ vv’/vth ~ v/L >> v/H ~ vv’/v
=> # e-folds in wind ~ v/vth ~ 100 !!!
For ≤ L = vth/(dv/dr), perturbation “optically thin”
u=v/vth
0.0 0.5 1.0
0
500
1000
1500
Clumped density
-15
-14
-13
-12
-11
-10
CAK
log
Den
sity
(g/
cm3 )
Radius (R*)
1D Simulation of Small-Scale Line-Driven Instability
Local vs. Nonlocal Line-Force
gκ ~κ dp0
R*
∫ I* dx−∞
∞
∫ ϕ (x−vz /vth)e−t(x,p, z)
t(x, p, z) ≡ dz'κρϕ (x−vz' / vth)z*
∞
∫
≈τ z dx'x−vz / vth
∞
∫ ϕ (x' )
τz ≡κρvth
dvz / dz
Sobolev approximation
Nonlocal ray optical depth
LocalSobolev optical depth
3-Ray Grid for 2D Rad-Hydro
Diagram: N = 9 ; = 10o
Actual code: N =157 ; = 0.01 radPole =0o
Equator =90o
I+
Io
I-
g ~ I
+ - I-
Co-Rotating Interaction Region Models
localCAKmodel
nonlocalsmoothmodel
nonlocalstructuredmodel
c.
log(Density)
b. a.
-1000 1000cm/s2
-20 1000km/s
-75 75km/s
-16.7 -14cm-3
CAK withonly RadialForces
CAK withnonRadialForces
SSF withnonRadialForces
logDensity
RadialVelocity
LatitudinalVelocity
LatitudinalLine-Force
CAK withNonradial
Forces
-1.e-9 1.e-9Msun/yr
0 5.e-9Msun/yr
SSF withNorradial
Forces
RadialMass Flux
CAK withonly Radial
Forces
LatitudinalMass Flux
“Grid Staircasing” along Oblate Lower Boundary
• A vexing problem in WCD simulations has been the tendency for wind to form artificial stream structure.
• This stems from irregular “staircase” of spherical grid along the lower boundardary defined at the oblate stellar surface.
• The problem worsens with increased number of latitudinal zone.
• It is particularly acute in the 3-ray grid models here, which have N, = 157.
Mdot in CAK (g =0) model of WCD using 3-ray SSF grid
Preliminary Result Summary
• WCD model– assumes radial driving
• Poleward line-force in CAK models– results from stellar oblateness &
asymmetric velocity gradient
– reverses equatorward flow
– inhibits WCD
• Nonlocal 2D SSF models– global asymmetries disrupted