1. 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

2. WCD Inhibition by non-radial line-forces Vrot (km/s) = 200 250 300 350 400 450 Wind Compressed Disks } “S-350”

3. Vector Line-Force faster polar wind slower equatorial wind r r Flux dv n /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

4. Line-Driven Instability from Perturbed Profile Doppler Shift Instability growth rate:  ~ g/v th ~ vv’/v th ~ v/L >> v/H ~ vv’/v => # e-folds in wind ~ v/v th ~ 100 !!! For ≤ L = v th /(dv/dr), perturbation “optically thin” u=v/v th

5. Clumped density -15 -14 -13 -12 -11 -10 CAK log Density (g/cm 3 ) Radius (R * ) 1D Simulation of Small-Scale Line-Driven Instability

6. Local vs. Nonlocal Line-Force Sobolev approximation Nonlocal ray optical depth Local Sobolev optical depth

7. 3-Ray Grid for 2D Rad-Hydro Diagram: N  = 9 ;  = 10 o Actual code: N  =157 ;  = 0.01 rad Pole  =0 o Equator  =90 o I+I+ IoIo I-I- g  ~ I + - I -

8. Co-Rotating Interaction Region Models local CAK model nonlocal smooth model nonlocal structured model c.  log(Density) b. a.

9. -1000 1000 cm/s 2 -20 1000 km/s -75 75 km/s -16.7 -14 cm -3 CAK with only Radial Forces CAK with nonRadial Forces SSF with nonRadial Forces log Density Radial Velocity Latitudinal Velocity Latitudinal Line-Force

10. CAK with Nonradial Forces -1.e-9 1.e-9 Msun/yr 0 5.e-9 Msun/yr SSF with Norradial Forces Radial Mass Flux CAK with only Radial Forces Latitudinal Mass Flux

11. “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

12. 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 –poleward force mixed, weaker –little net flow to pole or equator –WCD still weak or absent Future work: –improve oblate lbc –2D rad-hydro with short characteristics –mass-ejection models of disk formation