1. Size and density of chondrule formation regions from missing isotopic fractionation J. Cuzzi and C. M. O’D. Alexander

2. Size and density of chondrule formation regions from missing isotopic fractionation J. Cuzzi and C. M. O’D. Alexander Chondrules & analogs heated in a vacuum preferentially lose their lighter isotopes, as expected (Rayleigh fractionation)

3. Size and density of chondrule formation regions from missing isotopic fractionation J. Cuzzi and C. M. O’D. Alexander Chondrules & analogs heated in a vacuum preferentially lose their lighter isotopes, as expected (Rayleigh fractionation) Chondrules, however, exhibit only very small fractionations!

4. Size and density of chondrule formation regions from missing isotopic fractionation J. Cuzzi and C. M. O’D. Alexander Chondrules & analogs heated in a vacuum preferentially lose their lighter isotopes, as expected (Rayleigh fractionation) Chondrules, however, exhibit only very small fractionations! High local vapor pressure (or total gas pressure) can erase or preclude fractionation (Alexander et al 2000, Galy et al 2000, Alexander 2004,Young & Galy 2004)

5. Size and density of chondrule formation regions from missing isotopic fractionation J. Cuzzi and C. M. O’D. Alexander Chondrules & analogs heated in a vacuum preferentially lose their lighter isotopes, as expected (Rayleigh fractionation) Chondrules, however, exhibit only very small fractionations! High local vapor pressure (or total gas pressure) can erase or preclude fractionation (Alexander et al 2000, Galy et al 2000, Alexander 2004,Young & Galy 2004) We present a physical model that constrains two properties of the chondrule formation region: chondrule volume densities and the size of the heated region

6. Size and density of chondrule formation regions from missing isotopic fractionation J. Cuzzi and C. M. O’D. Alexander Chondrules & analogs heated in a vacuum preferentially lose their lighter isotopes, as expected (Rayleigh fractionation) Chondrules, however, exhibit only very small fractionations! High local vapor pressure (or total gas pressure) can erase or preclude fractionation (Alexander et al 2000, Galy et al 2000, Alexander 2004,Young & Galy 2004) We present a physical model that constrains two properties of the chondrule formation region: chondrule volume densities and the size of the heated region Scenario suggests new measurements and modeling efforts

7.  sat v th,2 v th,1 v th,2 v th,1  1,2 Evaporation into a vacuum: Rayleigh fractionation  x v th,1 and v th,2 : slightly different thermal velocities for two isotopes with different masses at same T Lighter isotopes preferentially lost

8. v th,2 v th,1 v th,2 v th,1  1,2 Evaporation into a vacuum: Rayleigh fractionation v th,1 and v th,2 : slightly different thermal velocities for two isotopes with different masses at same T When local  x   sat fractionation is erased  sat

9. v th,2 v th,1 v th,2 v th,1  1,2 Evaporation into a vacuum: Rayleigh fractionation v th,1 and v th,2 : slightly different thermal velocities for two isotopes with different masses at same T When local  x   sat fractionation is erased  sat

10. Cosmic spherules Rayleigh Chondrule analogs show Rayleigh behavior Cosmic spherules Actual chondrules do not Alexander 2004, GCA Galy et al 2000 data Alexander 2000, GCA Also: Humayan & Clayton 1995, Yu & Hewins 1997, Yu et al 1998, Nagahara & Ozawa 2000, Galy et al 2001 Davis et al 2005, CPD book Alexander et al 2000

11. Isolated clouds case

12. =  sat 2 Richter et al 2002

13. =  sat 2 Richter et al 2002 P > 10 bars For t h = 2 x 10 4 sec

14. Overlapping clouds case

15. R = (D t) 1/2

16. Overlapping clouds case R = (D t) 1/2

17. R  (R,t)

18. R1R1

19. R1R1

20. Extending R integral to ∞ assumes R 1 > 3-4 (D t) 1/2 R1R1

21. R1R1

22. R1R1

23. R1R1

24. R1R1 Local P~10 -3 -10 -5 bar: R 1 ~ 0.5-5 km; CF region 300x larger

25. Extending R integral to ∞ assumes R 1 > 3-4 (D t) 1/2 R1R1 Local P~10 -3 -10 -5 bar: R 1 ~ 0.5-5 km; CF region 300x larger

26. Calibrate a from kinetic models ( Alexander 2004, GCA ) a ~6 ± 1

27. Calibrate a from kinetic models ( Alexander 2004, GCA ) a ~6 ± 1 n c ~10 m -3  Alexander 2004 Ebel & Grossman Wood & Hashimoto

28. How achieve C  ~ 200/f c (not all solids in chondrule sizes)? Settling to midplane? h Turbulence diffuses particles, limits settling Dubrulle et al 1995, Cuzzi et al 1996, Cuzzi & Weidenschilling 2006 H H/h = C = (t s  /  ) 1/2  

29. Turbulence diffuses particles, limits settling   H Settling to midplane? Particles of all sizes are melted together; and, growth time << Myr H/h = C = (t s  /  ) 1/2 h(C=200) Dubrulle et al 1995, Cuzzi et al 1996, Cuzzi & Weidenschilling 2006 How achieve C  ~ 200/f c (not all solids in chondrule sizes)?

30. H/h = C = (t s  /  ) 1/2 Turbulence diffuses particles, limits settling H Particles of all sizes are melted together; and, growth time << Myr Settling to midplane?   h(C=200) Dubrulle et al 1995, Cuzzi et al 1996, Cuzzi & Weidenschilling 2006 How achieve C  ~ 200/f c (not all solids in chondrule sizes)?

31. P(C>200) ~ few 10 -1 Concentration factor follows a probability distribution under turbulent concentration - P(>C) depends on C,  Cuzzi et al 2001 ApJ & work in progress Turbulence can selectively concentrate chondrule-sized precursors

32. P(C>200) ~ few 10 -1 Cuzzi et al 2001 ApJ & work in progress ? Concentration factor follows a probability distribution under turbulent concentration - P(>C) depends on C,  Turbulence can selectively concentrate chondrule-sized precursors

33. Conclusions Chondrule precursor number densities ≥ 10 m -3 Radius of heated volume > 150-1500 km (P=10 -3 -10 -5 bar ) Mass enrichment factor ~ 200x over solar; C ch ~ 200/f ch These same conditions allow stable melts, a prior concern

34. Conclusions Chondrule precursor number densities ≥ 10 m -3 Radius of heated volume > 150-1500 km (P=10 -3 -10 -5 bar ) Implications & future work Mass enrichment factor ~ 200x over solar; C ch ~ 200/f ch Small lengthscale chondrule heating processes precluded (lightning, small planetesimal bow shocks) Implications for redox properties from enhanced FeO, H 2 O Chondrule diversity from single event (n c spatial variations) correlated redox/isotopic properties where are the fractionated chondrules? Can turbulent concentration provide needed P(C,scale)? Elements of differing volatility may provide more constraints Problems for low-density processes (high altitude X-ray flares) These same conditions allow stable melts, a prior concern

36. And since R 1 > 3-4 (D t) 1/2, and D =D o /  g, CFR > 1500 km Problem for low density regime Basic criteria can be written: n c r c 2 > K 1 ;  /r c > K 2 /  g For  g 2000

37. Chondrules

38. log normalized eddy vorticity log  Mass loading truncates TC for  p >100  g Different approach: cascade model Generally consistent with  p ~  g (C ~ 200) at P( C ) ~ 0.3 for lengthscale shown (scale depends on nebula  ) (Hogan & Cuzzi, Phys Rev subm.)

39. 2 Richter et al 2002

40. 2 =  sat