Ph.D Thesis Defense: Magnetic Reconnection as a Chondrule Heating Mechanism

• 1.Introduction Methodology Results Summary References Appendix Ph.D. Thesis Defense Magnetic Reconnection as a Chondrule Heating Mechanism Samuel A. Lazerson University of Alaska, Geophysical Institute November 6, 2008 Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense

2. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma Introduction The process by which chondrules, the rst solid objects in the solar system, formed is widely disputed. A series of numerical experiments were performed in order to determine if magnetic reconnection in the dusty plasma of the protosolar nebula could be responsible. The following were achieved: The rst simulations of magnetic reconnection in a dusty plasma were conducted A self-consistent model was forwarded for chondrule formation via magnetic reconnection in a dusty plasma. Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 3. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma Motivation Chondrules are the millimeter sized spherical inclusions found in chondrites (stony meteorites). Chondrules in the Grassland chondrite. The process by which they formed is largely unknown. They are discussed as the rst solids in the solar system. They are the transitional material between dust and meter sized stones. They present a geological record of the conditions present in the protosolar nebula. Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 4. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma The Scientic Question Can magnetic reconnection in a dusty plasma explain the heating necessary for chondrule properties? Stereotypical Chondrite (Sears, 2004) 4.5 By old Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 5. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma The Scientic Question Can magnetic reconnection in a dusty plasma explain the heating necessary for chondrule properties? Stereotypical Chondrite (Sears, 2004) 4.5 By old nm to mm size Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 6. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma The Scientic Question Can magnetic reconnection in a dusty plasma explain the heating necessary for chondrule properties? Stereotypical Chondrite (Sears, 2004) 4.5 By old nm to mm size Heating rates in the range of 2000 5000K/hr Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 7. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma The Scientic Question Can magnetic reconnection in a dusty plasma explain the heating necessary for chondrule properties? Stereotypical Chondrite (Sears, 2004) 4.5 By old nm to mm size Heating rates in the range of 2000 5000K/hr Multiple heating events are recorded. Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 8. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma The Scientic Question Can magnetic reconnection in a dusty plasma explain the heating necessary for chondrule properties? Stereotypical Chondrite (Sears, 2004) 4.5 By old nm to mm size Heating rates in the range of 2000 5000K/hr Multiple heating events are recorded. Exposed to a magnetic eld on the order of 1[G]. Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 9. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma Existing Theories There have been multiple attempts to explain the properties of chondrules through plasma and astrophysical processes Impact Melts Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 10. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma Existing Theories There have been multiple attempts to explain the properties of chondrules through plasma and astrophysical processes Impact Melts Meteor Ablation Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 11. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma Existing Theories There have been multiple attempts to explain the properties of chondrules through plasma and astrophysical processes Impact Melts Meteor Ablation Hot Inner Nebula Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 12. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma Existing Theories There have been multiple attempts to explain the properties of chondrules through plasma and astrophysical processes Impact Melts Meteor Ablation Hot Inner Nebula Fu Orionis Outburst Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 13. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma Existing Theories There have been multiple attempts to explain the properties of chondrules through plasma and astrophysical processes Impact Melts Meteor Ablation Hot Inner Nebula Fu Orionis Outburst Bipolar Flows Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 14. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma Existing Theories There have been multiple attempts to explain the properties of chondrules through plasma and astrophysical processes Impact Melts Meteor Ablation Hot Inner Nebula Fu Orionis Outburst Bipolar Flows Nebular Lightning Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 15. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma Existing Theories There have been multiple attempts to explain the properties of chondrules through plasma and astrophysical processes Impact Melts Meteor Ablation Hot Inner Nebula Fu Orionis Outburst Bipolar Flows Nebular Lightning Accretion Shocks Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 16. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma Existing Theories There have been multiple attempts to explain the properties of chondrules through plasma and astrophysical processes Impact Melts Meteor Ablation Hot Inner Nebula Fu Orionis Outburst Bipolar Flows Nebular Lightning Accretion Shocks Nebular Shocks Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 17. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma Existing Theories There have been multiple attempts to explain the properties of chondrules through plasma and astrophysical processes Impact Melts Meteor Ablation Hot Inner Nebula Fu Orionis Outburst Bipolar Flows Nebular Lightning Accretion Shocks Nebular Shocks Magnetic Flares Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 18. Introduction Methodology Results Summary References Appendix Introduction Motivation The Question Previous Theories The Dusty Plasma The Dusty Plasma Dust Ions Electrons Neutrals Units Number Density nk 0.1 1001 1 1x1012 m3 Charge Number Zk 10, 000 1 1 Mass mk 1x1016 1.67x1027 9.11x1031 1.67x1027 kg Temperature Tk 500 500 500 500 K Plasma Frequency pk 0.017 41.7 56.4 s1 Cyclotron Frequency ck 0.0016 9600 17.6x106 s1 Neutral Collision Frequency kn 0.0004 102 4352 s1 Debye Length Dk 49 49 1543 m Inertial Length Scales c pk 17.6x109 7.2x106 5.3x106 m Magnetization c ck 187x109 31, 000 17 m Plasma Parameter 1 Plasma Beta 1 Coulomb Coupling c 1 We make the following assumptions: n = 5x1011 cm2 , vTn = 2030 m/s, B = 104 T, and rd = 106 m. Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 19. Introduction Methodology Results Summary References Appendix Organization DENISIS Simulation Parameters The Numerical Experiment A numerical experiment is conducted using the DENISIS 4-Fluid Dusty MHD code. Harris-like Current Sheet Ballistic Relaxation Reconnective Mode Test Particle Simulation Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 20. Introduction Methodology Results Summary References Appendix Organization DENISIS Simulation Parameters The DENISIS Code The DENISIS (Dust Electron Neutral Ion Self-consistent Integration Scheme) code has proven useful in studying dusty plasmas in the space environment. (Schroer et al., 1998). Fluid Code Dust, Ion and Neutral Continuity Equations Electron Density (Quasineutrality) Dust and Neutral Equations of Motion Dust, Ion, Electron and Neutral Energy Equations Induction Equation (intertialess Ion EOM) Leap-Frog and Dufort Frankel Integration Schemes 3-D Nonuniform Cartesian Grid Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 21. Introduction Methodology Results Summary References Appendix Organization DENISIS Simulation Parameters Continuity Equations d t = (d vd ) i t = (i vi ) n t = (nvn) e = me i mi Zd d md Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 22. Introduction Methodology Results Summary References Appendix Organization DENISIS Simulation Parameters Momentum Equations (d vd ) t = (d vd vd ) (pe + pi + pd ) + 1 4 B B dnd (vd vn) ini (vi vn) ene (ve vn) (nvn) t = (nvnvn) pn +dnd (vd vn) + ini (vi vn) + ene (ve vn) Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 23. Introduction Methodology Results Summary References Appendix Organization DENISIS Simulation Parameters Electron Velocity The electron and ion velocities are related to eachother through mobilities (). The current density carried by the ions and electrons thus becomes w = j Zd end vd = e (ni vi neve) . It should now become evident that for low electron densities this may be rewritten w = eni vi Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 24. Introduction Methodology Results Summary References Appendix Organization DENISIS Simulation Parameters Energy Equations 1 i 1 pi t = 1 i 1 (pi vi ) pi vi + mn mi +mn i in (vi vn)2 + md md +mi i id (vi vd )2 + mi mi +me i ie (vi ve)2 2 i in mi +mn kB Ti i 1 kB Tn n1 2 i id mi +md kB Ti i kB Td d 1 2 i ie mi +me kB Ti i kB Te d 1 Ion Energy Equation shown for reference. Similar equations exist for each of the 4 species. Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 25. Introduction Methodology Results Summary References Appendix Organization DENISIS Simulation Parameters Induction Equation B t = mi c e pi i + vi B 2B mi c e [id (vi vd ) + in (vi vn) + ie (vi ve)] Which for a depleted electron regime may be written B t = mi c e pi i + mi md Zd d i vd B +mi c 4e B i B 2B mi e {nd ni Zd ni nd id + Zd in vd invn} Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 26. Introduction Methodology Results Summary References Appendix Organization DENISIS Simulation Parameters Simulation Parameters Normalizations B-Field = 0.1 G Mass Density = 1 1017 kg Time = 180 s Length = 500 106 m Smallest Grid Scale = 12.5 106 m Velocity = 3 106 m/s Normalized Values Dust Mass Density = 1.0 Dust Charge Number = 10 Ion Mass Density = 0.1 Ion Charge Number = 1 Neutral Mass Density = 1.0 Dust Mass = 1.00 Current Sheet Thickness = 0.2 Ion Mass = 0.01 Grid Dimensions NX = 49 x [10, 10] Equidistant Xmin = 0.41 NY = 49 y [2, 2] Non-Equidistant Ymin = 0.0125 NZ = 15 z [0, 10] Equidistant Zmin = 0.67 Collision Frequencies Dust-Neutral = 0.026 Dust-Electron = 0.0000001 Ion-Neutral = 1000 Ion-Dust = 0.00128 Electron-Neutral = 0.00 Ion-Electron = 0.00 Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 27. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Ballistic Relaxation The simulation begins with a Harris like current sheet prole. (Harris, 1962) Due to collisional interactions and pressure variations this is not an equilibrium. An equilibrium is achieved through the use of a ballistic relaxation technique.(Hesse et al., 1993) Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 28. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Ballistic Relaxation: Final Proles I Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 29. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Ballistic Relaxation: Final Proles II Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 30. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Reconnetive Mode Three choices of reconnective mode were examined. These included a Sweet-Parker, Local Alfven, and Diusive Equilibrium modes. Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 31. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Sweet-Parker Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 32. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Local Alfven Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 33. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Diusive Equilibrium Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 34. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Sweet-Parker Movie Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 35. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Resistivity The eects of various resistivities on magnetic energy Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 36. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Resistivity: (Parameter Dependence) (e) Global Resistivity = 0.01 (f) Collisional Terms On Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 37. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Collision Frequencies The eects of various choices for the collision frequencies were evaluated Dust-electron collision frequency (de) showed little eect Dust-neutral collision frequency (dn) showed some sensitivity for values greater than 0.001 Ion-dust collision frequency (id ) showed little eect Ion-neutral collision frequency (in) had the greatest eect Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 38. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Dust-Neutral Collision frequency The eects of various choices for the dust-neutral collision frequency (dn) Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 39. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Ion-Dust Collision frequency The eects of various choices for the ion-dust collision frequency (id ) Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 40. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Ion-Neutral Collision frequency The eects of various choices for the ion-neutral collision frequency (in) Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 41. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Ion-Neutral Movie Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 42. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Adiabatic Index Variation of the Adiabatic Index for the species yielded little eect Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 43. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Chondrule Heating So what is the eect of reconnection on the dust particles themselves (chondrules)? Neutral heating on the order of 20%. Large dust-neutral relative velocities on the order of the Alfven velocity. Enhancements of the current sheet. Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 44. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Aerodynamic Heating We may calculate the heating of a dust particle in terms of aerodynamic heating due to neutral drag via (Wood, 1984) mdustCdust dTdust dt = 2 r2 dustgasv3 4r2 dust T4 dust T4 0 Given our parameters velocities as low as 3000 m/s will begin to heat the dust at necessary rates for chondrule formation. Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 45. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Testparticle Subcode Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 46. Introduction Methodology Results Summary References Appendix Ballistic Relaxation Reconnective Mode Resistivity Collision Frequencies Adiabatic Index Chondrule Heating Testparticle Heating Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 47. Introduction Methodology Results Summary References Appendix Summary Chondrule Formation Model Future Work Summary The following has been accomplished Multi-uid quasi-equilibrium Harris-like dusty current sheet First simulations of magnetic reconnection in a dusty plasma First self-consistent dusty plasma explanation of chondrule heating Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 48. Introduction Methodology Results Summary References Appendix Summary Chondrule Formation Model Future Work Chondrule Formation Model This model of chondrule heating has succeeded in the following ways Produces heating of chondrules necessary for formation Process is associated with the nebular environment Magnetic elds are relevant to the process The dust is accounted for as a charge carrier Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 49. Introduction Methodology Results Summary References Appendix Summary Chondrule Formation Model Future Work Future Work The following future work has begun Testing and development of a fully ionized dusty plasma code (MHDust) Inclusion of a neutral gas component (nMHDust) Simulations of magnetic reconnection in other dusty plasmas Evaluation of variable dust charge Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 50. Introduction Methodology Results Summary References Appendix References 1 D. Sears. The Origin of Chondrules and Chondrites. Cambridge Planetary Science, Cambridge (2004). 2 M. K. Joung, M. M. Low and D. S. Ebel. Astro. J.. 606 (2004). 3 A. Schroer, G. T. Birk and A. Kopp. Comp. Phys. Comm. 112 (1998). 4 E. G. Harris. Il Nuovo Cimento. 23 (1962). 5 M. Hesse and J. Birn. J. Geo. Res. 98 (1993). 6 J. A. Wood. Earth and Plan. Sci. Lett. 70 (1984). Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 51. Introduction Methodology Results Summary References Appendix The Protosolar Nebula Mobilities The Protosolar Nebula Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense 52. Introduction Methodology Results Summary References Appendix The Protosolar Nebula Mobilities Electron and Ion Mobilities Parallel Hall Pederson EB Electron 4.04 107 9990 2.47 Ion 9.39 105 9960 106 vi /ve 0.232 0.997 42.9 ji /je 23.2 998 42900 Mobilities given in units of Cs kg . Lazerson ([email protected]) UAF GI Ph.D. Thesis Defense