Introduction Methodology Results Summary Appendix References

Oral Comprehensive Magnetic Reconnection as a Chondrule Heating Mechanism Samuel A. Lazerson University of Alaska, Geophysical Institute

January 29, 2008

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Introduction Methodology Results Summary Appendix References

Motivation Previous Theories The Question Conditions Plasma Parameters

Motivation Chondrules are the millimeter sized spherical inclusions found in chondrites (meteorites). The process by which they formed in largely unknown. They are discussed as the first 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.

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Motivation Previous Theories The Question Conditions Plasma Parameters

Existing Theories There have been multiple attempts to explain the properties of chondrules through plasma and astrophysical processes Impact Melts

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Introduction Methodology Results Summary Appendix References

Motivation Previous Theories The Question Conditions Plasma Parameters

Existing Theories There have been multiple attempts to explain the properties of chondrules through plasma and astrophysical processes Impact Melts Meteor Ablation

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Introduction Methodology Results Summary Appendix References

Motivation Previous Theories The Question Conditions Plasma Parameters

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

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Introduction Methodology Results Summary Appendix References

Motivation Previous Theories The Question Conditions Plasma Parameters

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

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Introduction Methodology Results Summary Appendix References

Motivation Previous Theories The Question Conditions Plasma Parameters

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

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Introduction Methodology Results Summary Appendix References

Motivation Previous Theories The Question Conditions Plasma Parameters

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]) Oral Comprehensive

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Introduction Methodology Results Summary Appendix References

Motivation Previous Theories The Question Conditions Plasma Parameters

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]) Oral Comprehensive

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Introduction Methodology Results Summary Appendix References

Motivation Previous Theories The Question Conditions Plasma Parameters

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]) Oral Comprehensive

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Introduction Methodology Results Summary Appendix References

Motivation Previous Theories The Question Conditions Plasma Parameters

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]) Oral Comprehensive

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Motivation Previous Theories The Question Conditions Plasma Parameters

The Scientific Question Can magnetic reconnection in a dusty plasma explain the heating necessary for chondrule properties? 4.5 By old

Stereotypical Chondrite (Sears, 2004)

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Introduction Methodology Results Summary Appendix References

Motivation Previous Theories The Question Conditions Plasma Parameters

The Scientific Question Can magnetic reconnection in a dusty plasma explain the heating necessary for chondrule properties? 4.5 By old nm to mm size

Stereotypical Chondrite (Sears, 2004)

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Motivation Previous Theories The Question Conditions Plasma Parameters

The Scientific Question Can magnetic reconnection in a dusty plasma explain the heating necessary for chondrule properties? 4.5 By old nm to mm size Heating rates in the range of 2000 − 5000K /hr

Stereotypical Chondrite (Sears, 2004)

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Motivation Previous Theories The Question Conditions Plasma Parameters

The Scientific Question Can magnetic reconnection in a dusty plasma explain the heating necessary for chondrule properties? 4.5 By old nm to mm size Heating rates in the range of 2000 − 5000K /hr Multiple heating events are recorded. Stereotypical Chondrite (Sears, 2004)

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Introduction Methodology Results Summary Appendix References

Motivation Previous Theories The Question Conditions Plasma Parameters

The Scientific Question Can magnetic reconnection in a dusty plasma explain the heating necessary for chondrule properties? 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 field on the order of 1[G ]. Lazerson ([email protected]) Oral Comprehensive

Stereotypical Chondrite (Sears, 2004)

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Motivation Previous Theories The Question Conditions Plasma Parameters

What the the conditions for chondrule formation?

I propose the following criterion for a process that is responsible for chondrule thermal processing: Proper heating rates.

Chondrules in the Grassland Meteorite

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Introduction Methodology Results Summary Appendix References

Motivation Previous Theories The Question Conditions Plasma Parameters

What the the conditions for chondrule formation?

I propose the following criterion for a process that is responsible for chondrule thermal processing: Proper heating rates. Produce multiply rimmed structures.

Chondrules in the Grassland Meteorite

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Introduction Methodology Results Summary Appendix References

Motivation Previous Theories The Question Conditions Plasma Parameters

What the the conditions for chondrule formation?

I propose the following criterion for a process that is responsible for chondrule thermal processing: Proper heating rates. Produce multiply rimmed structures. Magnetic fields of 1G .

Chondrules in the Grassland Meteorite

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Introduction Methodology Results Summary Appendix References

Motivation Previous Theories The Question Conditions Plasma Parameters

What the the conditions for chondrule formation?

I propose the following criterion for a process that is responsible for chondrule thermal processing: Proper heating rates. Produce multiply rimmed structures. Magnetic fields of 1G . Must cease at planetary formation. Chondrules in the Grassland Meteorite

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Motivation Previous Theories The Question Conditions Plasma Parameters

Plasma Parameters

Number Density Charge Number Mass Temperature Plasma Frequency Cyclotron Frequency Neutral Collision Frequency Debye Length Inertial Length Scales Magnetization

nk Zk mk Tk ωpk ωck νkn λDk c ωpk c ωck

Dust 0.1 10, 000 1x10−16 500 0.017 0.0016 0.0004 49 17.6x109

Ions 1001 1 1.67x10−27 500 41.7 9600 102 49 7.2x106

Electrons 1 1 9.11x10−31 500 56.4 17.6x106 4352 1543 5.3x106

187x109

31, 000

17

Neutrals 1x109

Units m−3

1.67x10−27 500

kg K s −1 s −1 s −1 m m m

Plasma Parameter Λ 1 Plasma Beta β 1 Coulomb Coupling Γc 1 We make the following assumptions: σn = 5x10−11 m−2 , vTn = 2030 m/s, B = 10−4 T , and rd = 10−6 m.

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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 Static Resistive Region Gradient in Resistivity Nonlinear Ohms Law

Test Particle Simulation

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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. (Schr¨ oer et al., 1998). Fluid Code Dust, Ion and Neutral Continuity Equations Dust and Neutral Equations of Motion Dust, Ion, Electron and Neutral Energy Equations Ohms’s Law (intertialess Ion EOM) Electron Density (Quasineutrality)

Leap-Frog and Dufort Frankel Integration Schemes 3-D Nonuniform Cartesian Grid Lazerson ([email protected]) Oral Comprehensive

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Organization DENISIS Simulation Parameters

Simulation Parameters Normalizations B-Field Time Smallest Grid Scale Normalized Values Dust Mass Density Ion Mass Density Neutral Mass Density Current Sheet Thickness Grid Dimensions NX = 49 NY = 49 NZ = 15 Collision Frequencies Dust-Neutral Ion-Neutral Electron-Neutral

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= = =

0.1 G 180 s 12.5 × 106 m

= = = =

1.0 0.1 1.0 0.2 x ∈ [−10, 10] y ∈ [−2, 2] z ∈ [0, 10]

= = =

0.026 1000 0.00

Mass Density Length Velocity

= = =

1 × 10−17 kg 500 × 106 m 3 × 106 m/s

Dust Charge Number Ion Charge Number Dust Mass Ion Mass

= = = =

10 1 1.00 0.01

Equidistant Non-Equidistant Equidistant Dust-Electron Ion-Dust Ion-Electron

∆Xmin = 0.41 ∆Ymin = 0.0125 ∆Zmin = 0.67 = = =

0.0000001 0.00128 0.00

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Ballistic Relaxation Reconnection Chondrule Heating

Ballistic Relaxation I begin with a Harris like current sheet profile. (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)

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Ballistic Relaxation Reconnection Chondrule Heating

Static Resistive Region

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Ballistic Relaxation Reconnection Chondrule Heating

Perpendicular Gradient

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Ballistic Relaxation Reconnection Chondrule Heating

Non-Linear Ohm’s Law

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Ballistic Relaxation Reconnection Chondrule Heating

Chondrule Heating So what is the effect of reconnection on the dust particles themselves (chondrules)?

(a) Static Resistivity

(b) Gradient Resistivity

(c) Nonlinear Ohm’s Law

Examination of the neutral gas shows around a 3% increase in temperature. Lazerson ([email protected]) Oral Comprehensive

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Ballistic Relaxation Reconnection 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)  
π 2 dTdust 2 4 = αrdust ρgas v 3 − 4πβrdust σ Tdust − T04 mdust Cdust dt 2 Given our parameters velocities as low as 3000 m/s will begin to heat the dust at necessary rates for chondrule formation.

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Progress Accomplishments

Progress

First Simulations of Magnetic Reconnection in a Dusty Plasma Dust Neutral relative velocities high enough to explain heating Work has begun on testparticle simulations to evaluate heating of dust

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Progress Accomplishments

Accomplishments

The proposed 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 fields are relevant to the process The dust is accounted for as a charge carrier The process requires a nebular environment

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The Protosolar Nebula DENISIS Equations Reconnective Mode

The Protosolar Nebula

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The Protosolar Nebula DENISIS Equations Reconnective Mode

Continuity Equations ∂ρd = −∇ · (ρd v~d ) ∂t ∂ρi = −∇ · (ρi v~i ) ∂t ∂ρn = −∇ · (ρn v~n ) ∂t   Z d ρd ρi − ρe = m e mi md

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The Protosolar Nebula DENISIS Equations Reconnective Mode

Momentum Equations

∂(ρd v~d ) ∂t

=

−∇ ·(ρd v~d v~d) − ∇ (pe + pi + pd ) ~ ×B ~ + 1 ∇×B 4π

−νdn ρd (v~d − v~n ) − νin ρi (~ vi − v~n ) ∂(ρn v~n ) ∂t

=

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−∇ · (ρn v~n v~n ) − ∇pn +νdn ρd (v~d − v~n ) + νin ρi (~ vi − v~n )

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The Protosolar Nebula DENISIS Equations Reconnective Mode

Energy Equations

1 ∂pi γi −1 ∂t

− γi 1−1 ∇ · (pi v~i ) − pi ∇ · v~i d n ρi νin (~ vi − v~n )2 + mdm+m ρ ν (~ v − v~ )2 + mim+m n    i i id i  d ρi νid kB Ti kB Ti kB Td i νin −2 mρi +m γi −1 − 2 mi +md γi − γd −1 n Ion Energy Equation shown for reference. Similar equations exist for each of the 4 species. =

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The Protosolar Nebula DENISIS Equations Reconnective Mode

Induction Equation

∂B ∂t

=

− me i ∇ × + me i ∇ × − me i ∇ ×

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∇pi mi ~ +m Zd ∇ × ρρdi v~d × B d  ρi  ~ ∇×B ~ − η∇2 B ~ ×B ρh i  i { nndi Zd − nndi νid + Zd νin v~d

− νin v~n }

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The Protosolar Nebula DENISIS Equations Reconnective Mode

Reconnective Mode We perturb the current sheet through a reconnective mode. It is assumed that there is an outflow from the reconnective region along the current sheet at the Alfv´ en velocity. An inflow is also applied perpendicular to the current sheet. The inflow velocity is chosen so as not to compress the plasma in the reconnective region. The ion velocities are chosen so as not to generate any new currents in the system.

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Introduction Methodology Results Summary Appendix References

The Protosolar Nebula DENISIS Equations Reconnective Mode

A Simple Run To illustrate the dynamics of reconnection a test-run’s were conducted to evaluate the reconnective mode applied.

Sweet-Parker Perturbation

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Introduction Methodology Results Summary Appendix References

The Protosolar Nebula DENISIS Equations Reconnective Mode

A Simple Run To illustrate the dynamics of reconnection a test-run’s were conducted to evaluate the reconnective mode applied.

Sweet-Parker w/ Vinflow = .44Vin−sp

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Introduction Methodology Results Summary Appendix References

The Protosolar Nebula DENISIS Equations Reconnective Mode

A Simple Run To illustrate the dynamics of reconnection a test-run’s were conducted to evaluate the reconnective mode applied.

Small Perturbation w/ Vout = .1 and Vinflow = .01 ∗ d/L

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The Protosolar Nebula DENISIS Equations Reconnective Mode

Magnetic Energy Comparison

(j) Sweet-Parker

(k) 44% Sweet-Parker

(l) Low Velocity

Magnetic Energy Evolution for each perturbation. Application of a Sweet-Parker like reconnective mode to a Harris like current sheet results in a compression of the plasma (and field lines) due to density variations not accounted for in the Sweet-Parker (or Petscheck) modes.

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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. Schr¨ oer, 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).

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