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This study explores how "velocity porosity" affects the absorption properties of P-Cygni lines in astronomical contexts. Key issues addressed include the impact of wind clumping on line absorption, comparisons between velocity dispersion and spatial porosity, and the identification of relevant scaling parameters. The research uses dynamical models to emphasize the importance of these factors for phenomena such as the predicted mass loss rates in stellar winds. The results indicate that velocity clumping is essential for accurate modeling of line-driven instabilities and absorption spectra.
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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? • Velocity dispersion vs. Spatial Porosity • What are relevant scaling parameters (cf. fr, 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
porosity length=h Effective opacity
l=0.05r l=0.1r l=0.2r Porous envelopes h=0.5r hºl/f h=r h=2r
Step function Profile-weighted line column depth
b=1 t¥=1/4 1/2 1 2 Line absorption trough
Velocity vs. Mass } DV Velocity filling factor : dv }
Vorosity? “Velocity Porosity”
Absorption reduction f = 1 RA 0.5 0.2 0.1 tx
smooth, b=1 porous, fv = 1-v/2v¥ t=1/4 t=1/4 1/2 1 2 1 2 Line absorption
4 4 Time (days) 0 1 10 radius (R*) 0 1 10 radius (R*) Velocity Instability model Density CAK init. cond.
Profile-weighted line column depth 4 Time (days) 0 CAK init. cond. -1 0 Wavelength (V¥)
Profile-weighted line column depth 4 Time (days) 0 CAK init. cond. -1 0 Wavelength (V¥)
Dynamic absorption spectrum-weak line 4 Time (days) 0 CAK init. cond. -1 0 Wavelength (V¥)
Dynamic absorption spectrum-weak line 4 Time (days) 0 CAK init. cond. -1 0 Wavelength (V¥)
Dynamic absorption spectrum - med. line 4 Time (days) 0 CAK init. cond. -1 0 Wavelength (V¥)
Dynamic absorption spectrum - med. line 4 Time (days) 0 CAK init. cond. -1 0 Wavelength (V¥)
Dynamic absorption spectrum-strong line 4 Time (days) 0 CAK init. cond. -1 0 Wavelength (V¥)
Dynamic absorption spectrum-strong line 4 Time (days) 0 CAK init. cond. -1 0 Wavelength (V¥)
Weak Medium Strong Time-Averaged Absorption Profiles 1 I /Icont 0 -1 0 Wavelength (V¥)
Weak Medium Strong Time-Averaged Absorption Profiles 1 I /Icont 0 -1 0 Wavelength (V¥)
Weak Medium Strong Dynamic absorption spectra 0 -1 0 0 -1 -1 Wavelength (V¥) 0 -1 0
Summary • Spatial porosity for continuum opacity • characterized by “porosity length” h=l/fr • But for line opacity, key is“velocity clumping” • characterized by fvel(and tSob 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
nonlocal structured model 2D Simulation of Co-rotating Interaction Regions D log(Density) c. a. b. nonlocal local smooth CAK model model
Profile-weighted line column depth 8 Time (days) 0 CAK init. cond. -1 0 Wavelength (V¥)
Dynamic absorption spectrum-med. line 8 Time (days) 0 CAK init. cond. -1 0 Wavelength (V¥)
Dyn. abs. spectrum - very strong line 4 Time (days) 0 CAK init. cond. -1 0 Wavelength (V¥)
Dyn. abs. spectrum - very strong line 4 Time (days) 0 CAK init. cond. -1 0 Wavelength (V¥)
Instability model: Mdot 4 Time (days) 0 CAK init. cond. 1 radius (R*) 10