1. Discordant Estimates of Mass-Loss Rates for O-Type Stars Alex Fullerton STScI /HIA Derck Massa (STScI/SGT) & Raman Prinja (UCL)

2. Mass-Loss Diagnostics H  emission: recombination   2 Thermal radio emission: free-free   2 UV resonance lines: scattering   Kudritzki & Puls 2000, ARAA, 38, 613 O5 If+ 10.0 × 10 -6 M sun /yr 7.5 5.0

3. Mass-Loss Diagnostics H  emission: recombination   2 Thermal radio emission: free-free   2 UV resonance lines: scattering  

4. Mass-Loss Diagnostics H  emission: recombination   2 Thermal radio emission: free-free   2 UV resonance lines: scattering  

5. Mass-Loss Diagnostics Thermal radio emission: free-free   2 H  emission: recombination   2 UV resonance lines: scattering   Constants, Parameters Velocity Law Optical Depth Ionization Fraction: 0  q i  1 Usually Don’t Know Usually Can’t Estimate

6. UV Resonance Lines in Hot-Star Winds P V λλ 1117.977, 1128.008 f blue, f red = 0.473, 0.234 Δ v = 2690 km/s (P/H) solar = 2.8 × 10 -7 (P/C) solar = 8.5 × 10 -4

7. P V Morphology Walborn et al., 2002, ApJS, 141, 443 O6 O4 O2 O9.7

8. Wind Profile Fits to P V 1118, 1128 Fullerton, Massa, & Prinja 2006, ApJ, 637, 1025 O6 O8 O4O5 O7.5 O9.5

9. A Mass Loss Discrepancy Fullerton, Massa, & Prinja 2006, ApJ, 637, 1025

10. Empirical Ionization Fraction of P 4+ Fullerton, Massa, & Prinja 2006, ApJ, 637, 1025

11. Similarly for the LMC Massa, Fullerton, Sonneborn, & Hutchings 2003, ApJ, 586, 996

12. Critique AssumptionsWays Out A P ~ Solar q(P 4+ )~1 somewhere Standard Model

13. Critique AssumptionsWays Out A P ~ Solar A P ≤ 0.1 Solar q(P 4+ )~1 somewhere Standard Model

14. Critique AssumptionsWays Out A P ~ Solar A P ≤ 0.1 Solar q(P 4+ )~1 somewhere q(P 4+ ) << 1 always Standard Model Sutherland & Dopita 1993, ApJS, 88, 253 Puls et al. 2008, ASPC, 388, 101 Collisional Equilibria v / v ∞ O8 IO7 I O6 IO5 I q q

15. Critique AssumptionsWays Out A P ~ Solar A P ≤ 0.1 Solar q(P 4+ )~1 somewhere q(P 4+ ) << 1 always Standard Model Relax Assumptions –Spherically Symmetric –Stationary –Homogeneous –Monotonically expanding –Sobolev Approx. valid –Aspherical (rotation?) –Time-Dependent –Inhomogeneous –Non-monotonic v(r) –[Sobolev valid?]

16. Critique AssumptionsWays Out A P ~ Solar A P ≤ 0.1 Solar q(P 4+ )~1 somewhere q(P 4+ ) << 1 always Standard Model Relax Assumptions –Spherically Symmetric –Stationary –Homogeneous –Monotonically expanding –Sobolev Approx. valid –Aspherical (rotation?) –Time-Dependent –Inhomogeneous –Non-monotonic v(r) –[Sobolev valid?]

17. Consequences of Clumping (1) “Direct”: Mass-loss rates determined from ρ 2 diagnostics are over-estimated. “Indirect”: The ionization stratification of the wind is altered by enhanced recombination in the clumps. If all the P V - ρ 2 discrepancy is assigned to the ρ 2 diagnostics, then 1)The ρ 2 mass-loss rates must be reduced by factor of at least 10; and 2)Volume filling factors of << 0.01 are implied. CMFGEN Model of HD 190429A (O4 If+) Bouret, Lanz, & Hillier 2005, A&A, 438, 301 q(P 4+ ) smooth wind q(P 4+ ) clumped wind f ∞ = 0.04

18. Consequences of Clumping (2) Spatial Porosity : When clumps become optically thick, the effective opacity of the wind decreases because star light can find an unattenuated channel through the wind. Material can be hidden in the clumps. “Macroclumping”: Not all transitions have the same optical depth, so porosity affects some lines more than others. “Velocity Porosity”: For line transfer, gaps in the velocity profile (“vorosity”) permit star light to leak through the wind, irrespective of the spatial porosity. This effect also weakens an absorption trough. Oskinova, Hamann, & Feldmeier 2007, A&A, 476, 1331 ζ Puppis O4 I(n)f

19. Consequences of Clumping (2) Spatial Porosity : When clumps become optically thick, the effective opacity of the wind decreases because star light can find an unattenuated channel through the wind. Material can be hidden in the clumps. “Macroclumping”: Not all transitions have the same optical depth, so porosity affects some lines more than others. “Velocity Porosity”: For line transfer, gaps in the velocity profile (“vorosity”) permit star light to leak through the wind, irrespective of the spatial porosity. This effect also weakens an absorption trough. Owocki 2007 “Clumping in Hot-Star Winds” (Potsdam)

20. Summary 1)The discrepancy between mass-loss rates estimated from P V and  2 diagnostics is very important. –The paradigm is evolving: winds are significantly structured. –But on what scale[s]? By what process[es]? 2)Consequently: –Mass-loss rates derived from  2 diagnostics are biased : too large. –Mass-loss estimates from P V are biased if the “clumps” are optically thick: too small(?) –We don’t know what the mass-loss rates are to within ??? –Concordance will likely require inclusion of several effects. –We need to use all available diagnostics to break multiple degeneracies.

21. Good Science Opens Doors “…the reasonable assumption that the mass loss rate for any star should be the same irrespective of which line is used …” Conti & Garmany (1980, ApJ, 238, 190) Questions!

22. Back-Up Slides

23. Why Was Clumping Ignored? 1.Absence of variability on flow time scale. 2.Mass fluxes determined at different radio wavelengths (i.e., radial distances) agreed. 3.The mass fluxes obtained from H  (formed near the star) and the radio free-free continuum (formed far from the star) agree. Since it is unlikely that the clumping factor would be the same at both radii, it must be unity; i.e., no clumping. Lamers & Leitherer (1993, ApJ, 412, 771): Eversberg, Lépine, & Moffat 1998, ApJ, 494, 799 Lépine & Moffat 2008, AJ, 136, 548 ζ Puppis O4 I(n)f He II 4686

24. Why Was Clumping Ignored? 1.Absence of variability on flow time scale. 2.Mass fluxes determined at different radio wavelengths (i.e., radial distances) agreed. 3.The mass fluxes obtained from H  (formed near the star) and the radio free-free continuum (formed far from the star) agree. Since it is unlikely that the clumping factor would be the same at both radii, it must be unity; i.e., no clumping. Lamers & Leitherer (1993, ApJ, 412, 771): Blomme et al. 2003, A&A, 408, 715 ζ Puppis O4 I(n)f

25. Why Was Clumping Ignored? 1.Absence of variability on flow time scale. 2.Mass fluxes determined at different radio wavelengths (i.e., radial distances) agreed. 3.The mass fluxes obtained from H  (formed near the star) and the radio free-free continuum (formed far from the star) agree. Since it is unlikely that the clumping factor would be the same at both radii, it must be unity; i.e., no clumping. Lamers & Leitherer (1993, ApJ, 412, 771): Puls et al. 2006, A&A, 454, 625 ζ Puppis O4 I(n)f

26. Summary: Effects of Clumping

27. Sk -67°166 O4 If+

28. Wind Profile Fits to P V 1118, 1128 Fullerton, Massa, & Prinja 2006, ApJ, 637, 1025 O7.5 III O7 Ib(f) O7 II(f) O7 V ((f))