Dynamical Origin of Wind Structure The effect of “velocity porosity” on P-Cygni line absorption strength Stan Owocki Bartol Research Institute Department of Physics & Astronomy University 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 porosity length=h

Porous envelopes h=0.5r h=r h=2r l=0.05rl=0.1rl=0.2r h  l/f

Profile-weighted line column depth Step function

Line absorption trough  =1      

Velocity vs. Mass

vv } } VV Velocity filling factor :

Velocity vs. Mass

“Velocity Porosity” Vorosity?

Absorption reduction 0.5 f = 1 xx RARA

Line absorption smooth,  =1     porous, f v = 1-v/2v    

Line-Driven Instabilty sim (SSF)

Instability model CAK init. cond. radius (R  ) Time (days) radius (R  ) Velocity Density

Profile-weighted line column depth Wavelength (V  ) Time (days) CAK init. cond.

Profile-weighted line column depth Wavelength (V  ) Time (days) CAK init. cond.

Dynamic absorption spectrum-weak line Wavelength (V  ) Time (days) CAK init. cond.

Dynamic absorption spectrum-weak line Wavelength (V  ) Time (days) CAK init. cond.

Dynamic absorption spectrum - med. line Wavelength (V  ) Time (days) CAK init. cond.

Dynamic absorption spectrum - med. line Wavelength (V  ) Time (days) CAK init. cond.

Dynamic absorption spectrum-strong line Wavelength (V  ) Time (days) CAK init. cond.

Dynamic absorption spectrum-strong line Wavelength (V  ) Time (days) CAK init. cond.

Weak Time-Averaged Absorption Profiles Wavelength (V  ) 0 I /I cont 0 1 Medium Strong

Weak Time-Averaged Absorption Profiles Wavelength (V  ) 0 I /I cont 0 1 Medium Strong

Dynamic absorption spectra StrongMediumWeak Wavelength (V  )

Summary Spatial porosity for continuum opacity –characterized by “porosity length” h=l/f  But for line opacity, key is“velocity clumping” –characterized by f vel (and  Sob of smoothed wind) Line-driven instability suggests: – f vel ~= (maybe 0.5 if seeded by low freq. pert) – Mdot misunderestimated by f vel, i.e – Maybe upto a factor 2 of the ca. 10 needed for PV

2D Simulation of Co-rotating Interaction Regions local CAK model nonlocal smooth model nonlocal structured model c.  log(Density) b. a.

Profile-weighted line column depth Wavelength (V  ) Time (days) CAK init. cond.

Dynamic absorption spectrum-med. line Wavelength (V  ) Time (days) CAK init. cond.

Dyn. abs. spectrum - very strong line Wavelength (V  ) Time (days) CAK init. cond.

Dyn. abs. spectrum - very strong line Wavelength (V  ) Time (days) CAK init. cond.

Instability model: Mdot radius (R  ) Time (days) CAK init. cond.