Magnetic reconnection flares in the photoplanetary nebula and the possible origin of meteorite chondrules

I(ARUS 81, 74--91 (1989)

Magnetic Reconnection Flares in the Protoplanetary Nebula and the Possible Origin of Meteorite Chondrules EUGENE

H. L E V Y AND S U G U R U

ARAK1

Lunar and Planetary Laboratory, Department of Planetary Sciences, University of Arizona, Tucson, Arizona 85721 R e c e i v e d S e p t e m b e r 14, 1987; r e v i s e d J a n u a r y 3, 1989

Many primitive meteorites are composed largely of chondrules, small once-molten beads of glassy rock. The existence of chondrules poses a basic problem for our understanding of the protoplanetary nebula inasmuch as the chondrules seem to have been melted by very short-lived, transient heating events in otherwise cool nebular surroundings. In this paper, the possibility is investigated that meteorite chondrules formed as a result of melting of protosolar nebula dust balls by the energy released from magnetic flares in the nebula's corona. Analysis of the energy that could be released by magnetic reconnection events in nebular coronal flares shows that previously existing dust balls could be heated transiently to temperatures sufficiently high (above 1700°K) to cause the short-lived melting events that are needed to account for the existence of chondrules. The release of flare energy at rates sufficient to account for chondrule melting requires that the flares occur in the presence of magnetic fields somewhat in excess of 5 G in a lowdensity coronal region of the disk. Nebular magnetic fields of this strength are in accord with magnetizing fields that have been inferred from the measured remanent magnetization of primitive meteorites. © 1989AcademicPress,Inc.

Various mechanisms have been suggested to account for the formation of chondrules. Among the suggestions that have been put forward are lightning in the nebula (Whipple 1966), impacts (Kieffer 1976), aerodynamic drag heating on dust accreting into the nebula (Wood 1984) or hot shear flows within the nebula (Wood 1986), and magnetic flares in the dense nebula gas (Sonett 1979). Chondrule formation is not understood (Levy 1987). The formation of such violently disequilibrated objects in the protosolar nebula raises important questions about the dynamical state of the nebula during the Solar System's formation and, thus, about the behavior of protoplanetary accretion disks in general. In this paper we explore a possible episodic heating mechanism that could account for chondrule formation. The mechanism that we examine here involves the transient release of energy as a result of magnetic flares in the corona of the proto-

I. I N T R O D U C T I O N

A large fraction of the matter in many of the most primitive meteorites consists of chondrules: small glass-like beads of the order of a millimeter in radius. It is generally believed that chondrules must have formed through the melting of preexisting solids rather than as condensates from gas. To have formed, the chondrules must have been heated to high temperatures, in the range near 1700°K. However, the primitive meteorites give evidence of having formed in a cold region of the protoplanetary nebula, where the sustained temperatures did not exceed several hundreds of degrees Kelvin. Moreover, the presence of retained high-volatility components in the chondrules themselves, and the mineral-grain textures, indicate that the chondrules could not have been heated to the high temperatures needed for melting, except for very short periods. 74 0019-1035/89 $3.00 Copyright © 1989 by Academic Press, Inc. All rights of reproduction in any form reserved.

ORIGIN OF METEORITE CHONDRULES

75

MAGNETICRECONNECTION EVENT

\

HIGH ENERGYR_ASMAFLOW \

/

\_J

l

I

~O.I AU

DUST BALL"

~IAU

MIDPLANE

.

FIG. I. In this paper, the possibility is examined that loose, fluffy dust balls--lofted to high altitudes above the protoplanetary nebula midplane--could have been melted by energy deposited in them by energetic particles produced in magnetic reconnection flares in the disk's corona. This diagram summarizes the quantitative results of the present model: Chondrule melting occurs at about an astronomical unit above the nebular midplane; the chondrule-making flares themselves occur at about a tenth of an astronomical unit above that.

solar nebula. This phenomenon would have been analogous to the flaring events observed today in the solar corona and in Earth's magnetosphere (and probably in a large variety of other astrophysical objects as well). Our aim in this paper is to explore aspects of the possible magnetic behavior of the protosolar nebula. The ideas in this paper, while speculative, are based on what is suggested to us by the meteorite paleomagnetic evidence about the protoplanetary nebula's magnetic field, and on the behavior of magnetic fields in known systems. We explore the possible properties of magnetic disk flares in terms of their ability to deliver the energy needed to account for chondrule melting (Fig. 1). Although magnetic flares are thought to play an important role in producing transient energy release in a variety of astrophysical objects, it is only in the Sun and in Earth's magnetosphere that this phenomenon can be observed at all closely. Because of the small spatial scale of a flaring region and because of its transient, episodic, and

short-lived character, detailed observations of flares still elude us. Moreover, because of the inherently nonlinear character of the flare mechanism, the underlying physics is only imperfectly understood. Nonetheless, physical and semiquantitative arguments give a theoretical picture that is crudely consistent with observed properties of flares. In the present analysis we will be guided by what is known of solar and geomagnetic flares and by the general physical arguments that describe them. In the remainder of this introduction we briefly describe the basic properties of the meteoritic chondrules that we are attempting to explain. In Section II, we describe the presumed physical characteristics of the protosolar nebula that are essential to this discussion, and we review the basic character of the magnetic flare mechanism. Because some aspects of the physics of magnetohydrodynamic flares are unfamiliar in this context, we briefly discuss those basic concepts and the energetics of disk-nebula flares also in Section II. In Section III

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LEVY AND ARAKI

we analyze the thermal balance involved in melting a chondrule precursor dust ball. Conclusions follow in Section IV. Chondrules in Meteorites

Our purpose in this section is not to try to give a comprehensive discussion of chondritic meteorites and chondrules. There are a large variety of known meteorites, and various classification schemes have been brought to bear in attempts to organize them into categories with common histories and genetic relationships. We will be content to define the problem posed by chondrules in a highly simplified form, but one that is commensurate with an understanding of the basic energetics of chondrule formation that we seek to address. Very generally, chondrites are solid aggregates consisting of two classes of materials: chondrules and matrix. Grossly, the chondrules are small pieces of solid, silicate-rich, rocky material (of different compositions in the various detailed classes of meteorites) typically a millimeter in radius, generally spherical in shape, but sometimes irregular. The characteristic chondrule mineralogies, igneous textures, and droplet-like shapes show that they had been either entirely or partially molten at some time before being incorporated into the meteorites (Grossman and Wasson 1983). Heating and cooling time scales associated with the chondrule-forming heating event are estimated indirectly. Mineral structures within the chondrules indicate cooling rates, through the solidus, in the range of a less than a tenth to about one Kelvin per second (Fujii and Miyamoto 1983, Hewins 1983); such rates suggest heating events of minutes to hours in duration. Chondrules retain volatile elements, such as sodium, potassium, and zinc, although with indications of moderate depletions in some species (Grossman and Wasson 1983, Wilkening et al. 1984); this indicates that the length of time during which chondrules remained hot was short in comparison with other nebula time scales (months to millenia), al-

though the actual chondrule formation time scales are hard to pin down on the basis of existing experimental and theoretical data. Altogether, the time during which chondrules remained hot in the formation process seems to be severely limited from above--from the measured presence of volatiles--and with indications of intervals of the order of minutes near the solidus from the mineral structures. This brief duration of the heating argues strongly against the possibility that chondrules formed close to Sun and were subsequently transported farther out where they were incorporated into otherwise cold objects. The chondrules are often found nearly close-packed in chondritic meteorites, thus constituting the major component of many of the meteorites that contain them. This suggests that chondrules were not a minor trace constituent of nebular solid matter, but rather a major component of the solid material, at least in the zone from which the meteorites come. The space between the chondrules is filled with so-called matrix. Generally speaking, the matrix consists of material similar to that of which the chondrules are composed, with the exception that the matrix matter has not been melted into larger consolidated droplets. Although there is considerable compositional variation, the nonvolatile components of the chondrules and matrix typically are reported to have solar-like compositions. Also, there is reported evidence of compositional trends, size sorting, and possible correlations between size, texture, composition, and other measures. For the purpose of this discussion we will not be concerned with such technicalities of chondrule zoology, although they probably contain clues about detailed variations among formation regions. However, we note that the conspicuous variation of chondrule elemental abundances in refractory siderophiles, reduced iron reflecting the degree of oxidation, and other factors, among the several chondrite groups, have been taken to argue for formation in the protosolar nebula rather than formation in

ORIGIN OF METEORITE CHONDRULES

77

some prenebular environment (Wasson from a differentially rotating disk-shaped 1985). In the latter case, it is held to be nebula consisting of gas and dust, which more difficult to retain the heterogeneity itself resulted from the collapse of an interthat is necessary to make the separate me- stellar cloud (Safronov 1969, Cameron teorite groups, unless the meteorites them- 1978, Hayashi 1981). In its early stage of selves were assembled elsewhere and evolution, the nebula was likely to have brought to the Solar System intact. The been dominated by turbulent motions of the strength of this argument is not clear inas- gas and dust, although at later times the much as isotopic heterogeneities--which turbulence must have diminished enough to clearly are of stellar origin--persist in me- allow coalescence of dust into large obteorites. In any case, we accept here the jects, ultimately planets. For this discussimplest interpretation of existing data: that sion, we are concerned with the nebula's meteorites and chondrules are Solar Sys- dust, magnetic field, and simple aspects of tem products. Age dating studies of chon- its physical structure. drules (Swindle et al. 1983a,b) indicate that chondrules formed in an interval of some 5 Prechondrular D u s t × 106 years about 4.55 billion years ago, The transient chondrule heating events coincident with the Solar System's forma- may have been of such short duration that tion. thermodynamic equilibrium was not reached. In addition, in such a transient event as we contemplate, the local environThe Chondrule P r o b l e m ment was likely to have been far from therFor the purposes of this discussion, we modynamic equilibrium. Therefore, the will regard the typical chondrule to be a heating and cooling of chondrule material silicaceous sphere, melted into a solid dropwould, in general, have been dependent on let of about 1-mm radius from a preexisting, such extrinsic properties of the material as loose assemblage of unconsolidated dust the state and shape of the accumulation. grains. We will assume that the unmelted Of course, we have no a priori knowledge precursor of chondrules consisted of accuof the precise physical state of a prechonmulations of dust grains similar to those drular blob beyond our already stated asfound in the chondrite matrix material. The sumption that it consists of unconsolidated retained volatile content of chondrules sugmaterial grossly similar to that seen in gests that they were molten for only a brief chondrite matrix: silicaceous matter, probtime; the presence of apparently preexist- ably dominated by grains several microns in ing, unmelted mineral grains in some chon- diameter. Nor do we yet have any firm emdrules suggests that many grains were only pirical basis for understanding the accumumarginally melted. Thus we define the basic lation of dust blobs under cold, low-denenergetics problem of chondrules: to melt, sity, zero-gravity conditions. However, for an instant and marginally, a few milli- consider the process of early grain accumugrams of silicate matter in an otherwise lation. Grain assemblages accumulate by cool part of the protoplanetary nebula. This sticking together--as a result of electrorequires transient events capable of bring- static and other contact forces--when they ing the chondrule to temperatures of about come into contact during random encoun1700°K in a surrounding thermal environters. Because such small grains must move ment of some several hundred degrees Kelnearly with the fluid in which they are emvin. bedded, the grain-grain encounters occur at low velocities. Under these conditions, it II. THE DUST, THE NEBULA, AND FLARES is reasonable to assume that the grain asIt is now widely believed that our Solar semblages accumulate as very loose, fairy System formed about 4.5 x 10 9 years ago castle-like structures. Moreover, the grains

78

LEVY AND ARAKI

are not subject to large stresses that would cause these structures to collapse; thus we would expect the loose structures to be long-lived in the nebula. In this discussion, we presume that a prechondrular assemblage is a very loose blob--similar to dust accumulations that gather under untended beds--perhaps with a fractal-like structure. The a v e r a g e spatial density of such a loose dust accumulation is on the order of 10 -z g cm -2. Intuitively, this seems like the most likely original physical state of a few-milligram accumulation nebular dust. But we will leave further investigation of that assumption to another time. Nebular Magnetic Field

Evidence for the possible existence of a strong magnetic field in the protoplanetary nebula is found in the remanent magnetization of meteorites (Butler 1972, Sugiura et al. 1979, Sugiura and Strangway, 1983, Levy and Sonett 1978). The most straightforward interpretation of the measurements indicates the presence of a field with intensity in the range of 0.1 to 10 G, although these interpretations are probably not free of uncertainty (Wasilewski 1987). The original of such a large-scale magnetic field is not fully understood, the most serious of the obstacles being the low electrical conductivity of cold gas at nebular densities. However, it has been suggested (Consolmagno and Jokipii 1978) that ionization from the decay of radioactive nuclides could have raised the nebula's electrical conductivity. It has also been shown that dynamo generation of a nebular magnetic field could have occurred with the electrical conductivity produced by the decay of aluminum-26, and that the field intensity could have attained the values indicated by the meteorite remanence (Levy 1978). Recent observations of abundant 26A1 in the interstellar medium (Mahoney et al. 1984) support the possibility that nonthermal energy sources could have influenced the state of the nebular gas. For the purpose of the present discus-

sion, we leave aside further discussion of the origin of the nebula's electrical conductivity, and accept that the presence of a nebular magnetic field with intensity in the range of a few to I0 G is indicated by meteorite remanence as discussed in the references cited above. Because of the strong fluid shear associated with the disk's differential rotation, the dominant magnetic field component is expected to be toroidal, lying in the disk and winding azimuthally around it. The N e b u l a ' s Vertical S t r u c t u r e

For nebular masses substantially smaller than that of the Sun, the gravitational acceleration in the nebula is dominated by the Sun; the local disk mass makes only a small contribution to the vertical gravity. The local vertical acceleration due to gravity, g z , viz., in the Z direction perpendicular to the plane of the disk, is approximately the vertical projection of the Sun's gravitational attraction, gz(Z) =

GMo Z r2 r '

(1)

and increases linearly with Z, in the thin disk approximation. Mo is the mass of the Sun and r is the radial distance from the Sun. For an isothermal gas, the equation of vertical equilibrium is then dn kT --~ = mgz(Z),

(2)

where n is the gas number density, m the mean molecular mass of the gas, and T the temperature. Thus, the density of nebular matter decreases rapidly away from the plane, approximately as n ( Z ) = n(0) exp(-Z2/A2);

2kTr 3

Az -= - -

GMotn "

(3) Taking the gas temperature to be about 250°K, at about 3 AU from the center of the disk, results in A -~ 4 × 10~2 cm, a few tenths of an astronomical unit. The addi-

ORIGIN OF METEORITE CHONDRULES

79

tional contribution of local disk mass adds Magnetic Flares to the vertical gravity, and A will be diminMagnetic fields store energy which may ished, at altitude, by some 10%, depending be converted explosively in flares to varion the actual nebular mass distribution. ous other forms. Some of the released flare With such a sharply decreasing mass energy appears in the form of heat arising density, we can think of the disk gas as be- directly from the joule dissipation of the asing confined closely to its midplane and sociated electrical currents. Some of the overlain on both sides by a substantially energy emerges in energetic particles accelmore tenuous region that we will call, for erated in the electric fields associated with lack of a better term and with some preju- the rapidly changing flare magnetic field or dice, the disk's corona. accelerated by plasma turbulence. Some of Consider a protoplanetary nebula with a the energy is released as kinetic energy of mass density of 10-9 g cm -3 and a tempera- motion when the highly stressed magnetic ture of 300°K. The gas pressure would be configuration is released and allowed to reapproximately 20 dyn cm -2. A magnetic lax; a homely example of this last effect can field with an intensity of 5 G would have be seen in the kinetic energy that appears magnetic pressure of 1 dyn cm -2, or about when like poles of a magnet are held to5% that of the gas. The magnetic buoyancy gether and then released. of such a field would cause magnetic flux to Observations show that cosmical magrise toward the disk's faces, bursting netic flares release energy in all of the through into the corona, much as magnetic aforementioned forms. In addition, subseflux tubes rise through the Sun's convec- quent interactions can convert the released tion zone to fill the solar corona (Parker energy to yet other forms; the white light 1979). In the disk corona, where the gas part of a solar flare is evidently secondary pressure and energy density are much emission excited near the photosphere by lower than in the disk proper, the magnetic the precipitation of energetic particles profield would be the dominating force acting duced higher in the Sun's corona. Energetic on the gas. Such a coronal magnetic field particles produced by magnetic reconnecwould tend to evolve toward a vacuum or tion flares in the geomagnetic field precipiforce-free configuration because of the ab- tate, along magnetic field lines, to the top of sence of another comparable stress with Earth's atmosphere, in the auroral ovals, which it could equilibrate. This is a situa- where they produce the aurorae. tion analogous to that obtaining in the solar Magnetic flares in Earth's magnetocorona. Thus, if the protoplanetary disk has sphere produce large geomagnetic storms a magnetic field of the strength suggested which release some 1024 ergs of energy in by the meteorite measurements, we would hot plasma and energetic particles over sevexpect that the field would suffuse and eral hours (Axford 1964, Chapman 1964), dominate, dynamically, a corona above the an energy release rate of 1019 to 10 20 ergs disk faces. sec -1. Geomagnetic storms are energized as For the present, we do not address the the solar wind drags magnetic field lines interesting questions that arise in connec- back into the geomagnetic tail, building up tion with the thermal state of the disk's co- magnetic flux in the tail and causing a large rona, although a host of analogies with the deviation from the field's normal, more enSun immediately assert themselves. We ergetically relaxed structure. Geotail magwill assume that the coronal gas is an elec- netic flares occur when the field lines recontrically conducting plasma. Indeed, with nect at the tail's neutral sheetwthe surface the low coronal gas density, a high state of that separates the lobes of oppositely diionization would be more easily maintained rected magnetic field lines in Earth's magthan in the disk itself. netic tail.

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LEVY AND ARAKI

Large magnetic flares in the solar corona can release as much a s 1032 to 1033 ergs over 5 to 10 min, an energy release rate in the range of 1030 ergs sec -1, although less energetic flares are more common. The solar convection zone provides the underlying energy source for solar flares. The coronal magnetic field lines are rooted in the convection zone beneath the photosphere; there the field lines are overwhelmed by the fluid which drags the field lines around with it. Because the field lines are continuous, the coronal magnetic structure becomes entangled as it readjusts to the continually changing magnetic boundary condition below. The result seems to be to concentrate large magnetic field gradients, magnetic stress, and electrical current in regions where the field structure consequently breaks down, leading to a flare (for example, see Low 1979). Generally speaking, cosmical magnetic flares seem to occur when a magnetic field is subjected to external forces that distort it, thus building up high internal magnetic stress and electrical current which can become extremely localized. Indeed, it is the concentration of magnetic stress and electric current in very small regions that induces the usual magnetohydrodynamic conditions to fail, causing a process known as magnetic reconnection. This local failure of idealized magnetohydrodynamics and the associated reconnection of the field lines allow the field lines to move rapidly through the fluid, changing their topology and releasing a large amount of energy in the process (for general background, see Priest 1982). Magnetic reconnection probably occurs in a variety of circumstances and at widely varying rates (see, for example, Parker 1983). However, explosive flares, with large and rapid energy releases, seem to be produced most readily when a magnetic field penetrates from one region of space (I in Fig. 2) in which its motion is controlled by the embedding fluid to a second region of space (II) in which the field itself provides

the dominant force. Energy is stored in the region II magnetic field by the motions of magnetic field lines rooted in region I and is subsequently released in large explosions. For geomagnetic tail flares, the solar wind and magnetopause correspond to region !, while the geomagnetic tail corresponds to region II. In solar flares, the solar convection zone is region I and the corona is region I!. In the protoplanetary nebular flares discussed below, region I corresponds to the disk itself, and region !! is the disk corona. The specific mechanism, for explosive magnetic flares generally, apparently involves magnetic neutral sheet reconnection or closely related processes, involving large local gradients in the magnetic field. The detailed mechanism of neutral-sheet reconnection was first described by Parker (1963) and Petschek (1964) after its suggestion as the mechanism of solar flares (Dungey 1953, 1958). The physical process is illustrated in Fig. 3. Magnetic field and fluid flow toward the center as the overall magnetic structure collapses. In the neutral region, where the magnetic field vanishes, the lines of force "reconnect," relieving the topological constraints that held the field in its highly stressed preflare configuration. The gas is heated locally by the dissipation of electrical currents. Magnetic stress is released by the rapid reconnection of field lines, resulting in the acceleration of fluid to high speeds in the ejected flow. In addition to the hot ejected fluid, energetic particles are accelerated by wave particle interactions in the flare and by the electric field and shock waves in the collapsing magnetic field. Energy Release in a Magnetic Reconneetion Flare

The basic energy source that drives a magnetic flare is the magnetic field, with an energy density ofB2/8cr erg c m -3. In such a flare, the surrounding magnetic field structure collapses toward the flare site, carrying the magnetic energy with it. Thus, a mag-

ORIGIN OF METEORITE CHONDRULES

81

1T

FIG. 2. Magnetic reconnection flares occur at regions of very high magnetic field gradients. In this highly stylized cartoon, magnetic flux tubes are shown to be entangled as a result of fluid motions (Region I), which randomly move the feet of the flux tubes and braid the field lines, producing magnetic neutral surfaces across which the magnetic field changes sign. Large amounts of energy are stored in such magnetic field structures and high stresses build up in the space dominated by the magnetic field energy (Region II). Dissipative processes in the "singular regions" where the magnetic field stress is concentrated--shown here where the magnetic fields are oppositely directed across the surface of contact between the two flux tubes--cause a breakdown of idealized magnetohydrodynamic conditions. Dissipative reconnection of the magnetic field lines across the neutral surface explosively releases large amounts of energy in the form of hot plasma and energetic particles. After a flare, the magnetic field is shown (inset) to be relaxed to the less stressed, low-energy state consistent with the boundary conditions imposed where the feet of the flux tubes are embedded in the dense gas below. In this diagram, several episodes of flaring and topological reduction of the magnetic field structure might occur before the field finally relaxed to the low-energy state shown in the inset.

n e t i c flare l i b e r a t e s e n e r g y at a r a t e e q u a l to the magnetic energy density times the rate at w h i c h t h e field s t r u c t u r e c o l l a p s e s , integrated appropriately over a surface enclosing t h e flare site. I n F i g . 3, let u b e t h e r a t e at w h i c h t h e s u r r o u n d i n g m a g n e t i c field, B, c o l l a p s e s t o w a r d t h e m a g n e t i c n e u t r a l sheet. If the characteristic transverse linear s c a l e o f t h e flare r e g i o n is L , t h e n t h e r a t e at w h i c h e n e r g y is r e l e a s e d b y t h e flare is a p proximately

dE B2 d---t = uL2 ~ e r g s e c - l .

(4)

I n a s m u c h a s t h e r a t e at w h i c h m a g n e t i c rec o n n e c t i o n flares l i b e r a t e e n e r g y is c o n -

trolled by the collapse speed, one of the b a s i c q u e s t i o n s in u n d e r s t a n d i n g s u c h flares is t o d e t e r m i n e u. E n e r g y r e l e a s e r a t e s o b s e r v e d in s o l a r flares a n d in E a r t h ' s m a g n e tosphere indicate that collapse speeds must a p p r o a c h t h e A l f v r n s p e e d , B / % / ~ p in cgs units. P e t s c h e k (1964) a n d s u b s e q u e n t w o r k e r s ( S o n n e r u p 1970, Y e h a n d A x f o r d 1970, Y e h 1976) s h o w e d t h a t s u c h f a s t collapse speeds can occur as a result of the f a c t t h a t t h e m a g n e t i c t e n s i o n in t h e r e c o n n e c t e d field l i n e s p u l l s fluid r a p i d l y o u t o f the reconnection region. Using Petschek's s i m p l e p h y s i c a l a n a l y s i s , w h i c h s e e m s to capture most of the essential elements of the magnetic reconnection process, we

82

LEVY AND ARAKI

write the Alfv6n speed Mach number of the collapse speed as M = U/VA. The energy flux into the reconnection region is then MVAB2/8rr, inasmuch as the magnetic energy dominates in the flare region. Following Petschek, we take y* to be the dimension of the reconnection region normal to the incoming flow and ~ to be the dimension of the reconnection region normal to the outgoing flow. Energy conservation requires that the incoming and outgoing energy must be equal, so that the ratio of the outgoing energy flux to the incoming energy flux is y* f8" (5)

"0 VAM

and

y*

~ 2 VAM2'

(6)

where rl = c2/4qTO" is the magnetic diffusivity and o- is the electrical conductivity. Using Eqs. (5) and (6) f-

1 2M"

(7)

Putting these results together, the outgoing flux of energy, F, from a reconnection region is given by B2 F ~ ~ MVAf

\\

B3 8-rr4V'-~p erg cm -2 sec -j, (8)

independent of the reconnection rate under the present assumptions. For the purpose of the present discussion, the magnitude of F is our principal concern. Physically, Eq. (8) states the intuitively reasonable result that outgoing energy flux corresponds to a flow of energy equivalent to the original magnetic field energy density moving at the Alfv6n speed. Several important aspects of the question of the adequacy of nebular magnetic flares for melting chondrules emerge immediately from Eq. (8). The two variables that govern the energy flux out of a reconnection flare are the strength of the

/

u

EXTERNAL

i i Y

INFLOW

DIFFUSION REGION

/

/

//

//

\

f ~ f STANDING WAVE

/ l \

/

MAGNETIC LINES OF FORCE

Now, Petschek estimates 6

PLASMA OUTFLOW

\ \\

\\\ \\ BOUNDARY LAYER

FIG. 3. In a magnetic reconnection event, magnetic field regions with opposite polarity collapse toward the neutral sheet that separates the opposite polarity fields. By one way of thinking about the process, the collapsing magnetic fields deposit energy in the neutral region, producing energetic particles and hot plasma. Particles are accelerated in the electric fields produced by the collapsing magnetic structure. Plasma instabilities also accelerate particles and heat the gas. [Adapted from Fig. 50-3 in Petschek (1964).]

magnetic field and the density of the fluid in which the field is embedded. The following discussion will show that such flares are plausible as the energy source for chondrule melting, but that the required conditions are relatively stringent.

Form and Propagation of the Emergent Flare Energy The primary energy produced by such a flare is in the form of energetic particles, protons and electrons. Photon emission-X rays and softer photons--is the secondary result of particle collisions. As we will see, nebular flares with enough energy production to melt chondrules must occur in an extremely tenuous nebular corona, with local mass density in the range of about 10 TM g cm -3. If we assume that, in the flare, most of the magnetic energy is uniformly distrib-

ORIGIN OF METEORITE CHONDRULES uted to the particles, then the average energy of the emergent particles is B 2/87r Ep

p/mp "

(9)

Taking B - 5 G and t9 - 10-18 g c m -3, we find that the typical energy of the particles emerging from the flare is about 1 MeV. This is equivalent to an average energy distribution in which the emerging particles move with the ambient Alfv6n speed. In the following, we will assume that the heating of the chondrule precursors was primarily the result of energy deposition by 1-MeV particles. Inasmuch as the energetic particles emerging from the flare will be electrically charged, they cannot move freely in the corona; instead they are tightly constrained to move along the magnetic field lines in very well-defined channels. We have assumed here that the coronal magnetic field is rooted in the nebula. Thus the particles will move along the magnetic lines of force to the face of the nebula, where they deposit their energy in the nebular matter. This particle precipitation is directly analogous to the processes that channel energetic tail flare particles and deposit them at the feet of the magnetic field lines in Earth's auroral oval to make the aurorae, and to the processes that similarly deposit solar coronal flare particles in the Sun's chromosphere, at the feet of those field lines, to make H,, and white light flares. As the magnetic field traces from the coronal flare sites to the nebular disk below, the field lines of force can be expected to converge somewhat. Thus, some of the downward particles are likely to mirror in the converging field and be reflected away. However, by Liouville's theorem under conditions generally applicable to the situation that we are considering, the particle energy flux will be preserved along the magnetic field lines. The rate at which particles are reflected back by the converging magnetic field is compensated by the spatial compression of the remaining particle flux.

83

Altogether then, we will take the value in Eq. (8) to represent the flare particle energy flux entering the disk and available to heat chondrule precursor dust assemblages. It is important to realize that any direct photon energy from a flare will not effectively heat the dust some large distance away. While the particle energy flux can be expected to be nearly preserved as the particles move along magnetic field lines, radiant energy flux would diminish with the square of distance from the flare site. Even at short distances away from the flare site, the energy flux would be too low to cause melting of silicates. For the energetic flare particles to reach the protochondrular dust balls, then the dust must be relatively unshielded from the coronal regions in which the energetic particles are produced. This means that the dust must be exposed to the precipitating particles at relatively high altitudes in the nebula, where the intervening material is sufficiently tenuous to allow the particle beams to penetrate. Thus, only dust lofted to high altitudes can be heated by this process. Generally speaking, the path length through gas (in g cm -2) intervening between the site of particle generation and the locale in which the chondrules can be produced by flare must be less than the stopping distance of the particles. For the 1-MeV particles that would be expected from the flares described in this analysis, the gas overburden must be less than 10 mg cm -2. The chondrule formation would necessarily occur during a turbulent phase of the nebula, when dust globs were being lofted to high altitude and when things were sufficiently stirred up to expose a large fraction of the dust to flare particles over time. We will return to this point in the conclusions. IIl. CHONDRULEMELTING Assume that the specific heat of a chondrule dust ball is approximately constant during the melting process and obeys the Dulong-Petit law for solid materials at high

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LEVY AND ARAKI

t e m p e r a t u r e s , so that the specific heat of chondrule material is Cmol = 2 x 109 erg K -1 mol -l.

(10)

The typical density o f chondrule m a t t e r is 3 g c m -3 (Kluger et al. 1983) and the volume o f a chondrule is a b o u t 4 x 10 -3 cm 3, so that a c h o n d r u l e ' s m a s s is about 10 -2 g. If we a s s u m e that the chemical compositions of dust balls and chondrules are similar, the m e a n m o l e c u l a r weight of a dust ball is on the order of that of olivine, (Fe, Mg)2SiO4 140-204 and ortho-pyroxene, (Fe, Mg)2Si206 - 200-264. Thus we estimate that a typical dust ball has the m a s s of m 10 -2 g - 5 x 10 -5 mol. Therefore, the heat capacity of a typical chondrule p r e c u r s o r dust ball is C = mfmol - 105 erg K -~.

(11)

The variation of the prechondrule dust bali's t e m p e r a t u r e is given simply by balancing the heat deposited by the bombarding particles against the heat lost by radiation into a b a c k g r o u n d effective temperature To. L e t the total s u r f a c e area, o v e r which the dust glob radiates, be S. Also, let the p r o j e c t e d s u r f a c e area, the part of the surface that intercepts the incoming b e a m of energetic particles, be Sp. The variation of the dust glob's t e m p e r a t u r e is then given by C d T = FS p - cr(T 4 - T4)S; dt

(12)

here tr = 5.67 × 10 -5 erg sec -j cm 2 K 4 is the S t e f a n - B o l t z m a n n constant. We have a s s u m e d that the dust radiates as a black body. This is a c o n s e r v a t i v e assumption; to the extent that the dust glob radiates less efficiently than a black b o d y , the cooling rate will be slower and the dust will heat m o r e easily. The analytic expression in Eq. (12) neglects the effect of the latent heat of melting on the t e m p e r a t u r e variation. H o w ever, as will b e c o m e evident, this does not affect any of our conclusions. N o w , to use Eq. (12), we need to have expressions for the total and projected sur-

face areas of the dust glob. We have presumed that the dust glob is an open, loose, fairy castle-like structure. To derive a specific magnitude for its surface area, a s s u m e that the 10-mg dust accumulation can be modeled as a long cylinder of length l and d i a m e t e r d, gathered into a loose tangle so that the entire surface of the cylinder is exp o s e d to the surrounding space. I f the volume of the tangled dust glob is equivalent to that of a sphere of radius r, then the effective length of the tangled cylinder is 16 r 3 I - -~- dT.

(13)

Setting d - l 0 / z m , a few dust grain diameters thick, and r - l m m , the size o f a chondrule, yields l - 5 × l03 cm. N o t e that, because d ~ r ~ l, the effective surface area of the fluffy dust glob is very m u c h greater than that of the melted and consolidated chondrule. This crude model of a fluffy dust glob gives S ~ ~rld ~ 15 cm 2

and

Sp ~ ld - 5 cm 2.

(14) O f course, we do not expect that real dust accumulations will h a v e a string-like structure; this arithmetic model is used only to give specificity to the mass-to-surface area ratio. The important point is that, with this loose, open structure, the projected mass density of the prechondrule dust glob is about 10 mg c m -2. I n a s m u c h as the penetration depth of I - M e V photons is about 10 mg cm -2, the bulk of the energetic particles assumed to be produced by the nebular flares are effectively stopped in the dust and deposit their energy rather uniformly throughout the dust volume. This justifies the use of the simple heat balance expression in Eq. (12). The ratio of S to Sp depends very weakly on the structural details of the p r e c u r s o r y dust blob; however, the saturation t e m p e r a t u r e varies only with the fourth root of the ratio. T h e r e f o r e such uncertainty does not affect any of the conclusions in this paper. In any case, once the

ORIGIN OF METEORITE CHONDRULES

First consider the maximum temperature to which the dust glob can be heated. Putting dT/dt = 0 in Eq. (12), and denoting the maximum saturation temperature by T=, we find

chondrule is melted, it becomes spherical and its subsequent thermal evolution is independent of the initial physical structure. While the steady-state saturation temperature of the chondrule dust glob depends only very weakly on the initial structure and morphology of the accumulation, the heating time scale depends more strongly on it, by the ratio of the surface areas. Thus, other things being equal, a fluffy dust glob will heat more rapidly than a solid sphere holding the same mass, by a factor of approximately ld/r 2. In the present example, the loose dust accumulation heats about 500 times faster than would a consolidated sphere. In everything that follows we will use the relations defined by Eq. (14) to describe the dust accumulation in Eq. (12). We shall see presently that while the specific picture of the precursor dust is of only secondary importance with respect to the questions of heating times, it is very important in controlling the dynamics of the dust and determining whether the dust can be lofted to altitudes high enough to be exposed to energetic flare particles.

-13

,

i

i

85

T~-= T(oo) =

T4 +

,

having used the incident energy flux from Eq. (8). Inasmuch as To, the surrounding temperature, is in the range of several hundred degrees, very much smaller than the approximately 1600°K needed to make chondrules, To has no substantial effect on the conclusions. Within the assumptions of the present model, the temperature to which a dust glob can be heated depends essentially on the strength of the flare magnetic field and the ambient matter density in which the flare occurs. Figure 4 shows the combinations of flare magnetic field intensity and flare ambient matter density that lead to three temperatures T~ = 1000°K, 1500°K, 2000°K, which bracket the chondrule melting range. (In Fig. 4 the surround-

i

I

I

I

I

Too (K) -i5

/ '~

-17

-i9 ._1

-21

-23

(15)

167r

I

I

I

I

I

I

I

I

2

5

4

5

6

7

8

9

iO

B (Gouss) FIG. 4. The equilibrium temperature of dust heated by energetic particles from magnetic flares, under the model assumptions in this paper, is determined by the magnetic field strength and the local mass density in the flare region. In this figure are shown combinations of magnetic field intensity, B, and mass density, p, that lead to three characteristic temperatures spanning the range of interest for ehondrule melting. In this example, To is taken to be 100°K.

86

LEVY AND ARAKI

ing temperature into which the particle loses radiative energy is taken to be 100°K. Changing the surrounding temperature to 600°K allows the flare ambient density to be about 30% higher in Fig. 4.) Figure 4 shows that only a portion of the (B, p) parameter plane can yield temperatures in the rock-melting range. For a magnetic field as high as I0 G - - i n the range of the highest nebular fields ever inferred from primitive meteorite measurements--even a mass density of l 0 -14 g cm -3 will not allow flares to heat the dust to as much as 1000°K. With a flare magnetic field as low as I G, the ambient mass density at the flare site would have to be as low as 10 22 g cm-3, an implausibly low ambient density in a starforming region. A 5- to 7-G field could easily produce chondrule-melting flares in an ambient density of 10 -18 g cm -3, perhaps a not unreasonable coronal mass density. Applying Eq. (3), one finds that the simple nebular model used there gives the requisite mass density at about 1 AU above the disk's midplane. At nebular densities of 10 -9 or 10-j° g cm -3, however, this analysis indicates that the dust could not be heated by more than a few hundred degrees. Altogether then, flares that yield a sufficiently high energy flux to melt chondrules require a combination of high magnetic field intensity and low ambient mass density--at values that are plausible for a protoplanetary nebular corona. From this analysis, it is clear that magnetic flares within the main part of the disk itself would not have been able to produce energy fluxes of a magnitude needed to melt chondrules (cf. Sonett 1979). It is interesting to take note of this last fact: The values for the mass density and magnetic field strength in the nebular corona needed to produce flares that can account for chondrule melting are near the edge of plausibility in terms of what is inferred about the Solar System's precursor nebula. As we discussed earlier, chondrules seem to have been exposed to a heating source only marginally able to melt

them. These two factors are in seeming agreement. Now turn to the heating time scale. For fixed parameters (B, p, To), and using Eq. (14), the general solution of Eq. (12) is t =

4crT~'ld

In T ~ - To T~ + T T_

a,c'an )l.

(16)

Figure 5 plots the heating curves, T(t), for several representative values of the relevant parameters (B, p). As shown in Fig. 5, the heating times are very short, less than a tenth of a second to reach the maximum temperature. This is, of course not surprising. Inasmuch as the saturation temperature occurs where the incoming energy flux balances the heat lost to radiation, the time scale for heating must be of the order of the cooling time at the saturation temperature. Consequently, the heating time scale must be of the order of the radiative cooling time at the saturation temperature, and that is just the numerical factor leading the right-hand side of Eq. (16). The fact that the heating time scale is so short makes our results largely insensitive to assumptions about the physical structure of the precursor dust accumulations. As noted earlier, a fully consolidated sphere would heat more slowly, taking on the order of a minute to reach its highest temperature under the conditions discussed here. If the precursor assemblages of dust contained some larger particles, as is indicated by chondrule structures, this would have altered, slightly, the heating and melting rates, but not the final temperatures. In the foregoing discussion we have neglected the latent heat absorbed by the chondrule as it melts. Because the quantity of heat required for the actual melting is of the same magnitude as the heat required to raise the temperature of the dust, and because the time scales are already inherently short, taking account of the latent heat of melting has no effect on the temperature

ORIGIN OF METEORITE CHONDRULES 1800

I

TIn(K) = 1676

i

I

I

I

I

I

87 I

.

1500

1200

~1257

~__ 900

600

300

I

l

I

I

l

I

I

I

20

40

60

80

I00

120

140

160

180

t (millisecond) FIG. 5. Chondrules exposed to energetic particles from the disk coronal flares heat rapidly, in about 0.1 sec. The curves in this figure are labeled with the equilibrium temperatures, which are in turn determined by the magnetic field and mass density at the flare site. Typical correspondences of equilibrium temperature with flare magnetic field and mass density, T=(K), [B(gauss), p(g cm-3)], are, for the four temperatures, 1676(5, 10-18), 1585(10, 10-16 or 1, 10-22), 1257(5, 10-17), and 1189(10, 10-~5 or 1, 10-21).

attained by a nascent chondrule and does not significantly alter any of our conclusions.

IV.DISCUSSIONANDCONCLUSIONS Studies of star-forming regions reveal a host of unexpected energetic dynamical phenomena apparently associated with the protostellar disks that are ubiquitously found in such regions. Such manifestations as high-speed bipolar outflows and HerbigHaro objects associated with protostars indicate that these systems are far more dynamically active than the usual picture of a cold Keplerian disk might imply. From a broad view of the behavior of cosmical systems, this dynamical activity is not surprising. Observations of a wide range of objects in the Solar System and elsewhere show us that cosmical systems with large amounts of free energy to dissipate do it in unexpected and surprising ways (Levy 1987). Large explosions in the solar corona and in planetary magnetospheres are examples of

nature's creativity in finding amazing ways to expend energy. The abundance of meteorite chondrules indicates that the protoplanetary nebula was able to alter significant amounts of primitive matter through transient processes that departed far from the prevailing thermal equilibrium. In this paper we have put forward and examined the possibility that chondrules are markers of magnetic flares associated with the protoplanetary nebula. Meteorites carry magnetic remanence that suggests the presence of a strong magnetic field in the protoplanetary nebula. Although such a strong field is somewhat surprising, it is not unreasonable either dynamically or in terms of the kinds of magnetic fields that could conceivably be produced by such a nebula (Levy 1978). Such a magnetic field, escaping buoyantly to the disk's corona could be expected to make flares with sufficient outgoing energy flux to melt dust accumulations and make chondrules. The flares would have to occur

88

LEVY AND ARAKI

at high altitudes in the disk's corona, where the local mass density was l ow - - i n the r a n g e 10 -16 to 10-18 g cm-3--and, at the same time, the coronal magnetic field intensity would have to be in the range of the values inferred from meteorite magnetic remanence for the disk field. The chondrules themselves would have also to be made at high altitudes in the disk, to where the flare particles could penetrate. Lofting o f Dust to High Altitudes: The Locus o f Flares, the Locus o f Melting The requirement that the precursor dust accumulations be exposed to the flare particles across little intervening matter imposes a rigid constraint on the possibility that chondrules might have melted as a result of magnetic flares--the projected mass density of the nebula itself was probably five orders of magnitude greater than the allowed intervention of material, To quantify the implications of this requirement, consider that the energetic protons, produced by the flares considered in this paper, have a range of approximately 10 mg cm-2; therefore, the matter intervening between the flare site and the site of chondrule melting must not be substantially larger than this value. Taking the path length to be of the order of 2 × 10!2 cm (which, as we will see, leads to a consistent picture), then the average number density of hydrogen molecules must not exceed about l 0 9 c m -3. Thus, a question that must be addressed is whether we could reasonably expect dust to be lofted to such an altitude in the nebula. A complete answer to this question would require more detailed knowledge of nebular conditions than is presently available. Here we will confine ourselves to a crude analysis that suggests, within the context of the ideas presented in this paper, it is not unreasonable to expect that dust might indeed have been lofted to such an altitude. The vertical distribution of dust in the nebula is dominated by the balance between the confining vertical component of

gravity and the vertical mixing due to turbulence. Crudely, for the dust to be able to reach some altitude, it is necessary that the vertical drag force in rising convective eddies be at least as large as the vertical gravity, which acts downward. We can crudely estimate the vertical gravity by taking the local Z component of gravity from a central solar mass, as given by Eq. (1). Taking Z to be about 10 J3 cm, in Eq. (1), and r to be about 3 AU, then gv ~ 10-2 cm sec -I. Now consider the drag force on a dust accumulation, produced by vertical motions. Take the vertical velocity of rising convective gas to be vz, the density to be p = nm, where n is the number density, and m the mean molecular weight. Let (7"m be the projected surface density of a precursor dust glob. Now, balancing the vertical drag force with the vertical gravity (each taken per unit projected surface area of the dust accumulation), O'mgv ~- nmv~.

(17)

In the present model, the dust has been taken to have a loose, fractal-like structure with a projected average surface density of a few milligrams per square centimeter. The ambient mass density to which dust accumulations can be lofted is given by n 10~9/v~ cm -3. To estimate the actual density level to which the dust can be lifted, it is necessary to know the velocity of vertical motions. The value of this velocity is unknown, especially as it depends on altitude in the low-density regions above the nebula. However, a kilometer per second (the sound speed in the disk below) is a not unreasonable estimate for this number, yielding n ~ 10 9 cm -3. In that case, comparing this estimate with the previous one, we see that the dust might indeed be lifted high enough by gas motions to be exposed to energetic disk coronal flare particles, at least during vigorously turbulent stages of nebular evolution. As noted earlier, assuming a midplane nebular density of 10 -9 g cm -3 surrounding a one-solar-mass central star, the density

ORIGIN OF METEORITE CHONDRULES would have fallen low enough to expose the dust to energetic flare particles at about 1 AU above the midplane. The density would have fallen low enough to allow rock-melting flares to occur at about a tenth of an AU above that--consistent with our earlier estimate of the path length intervening between the flare and the chondrule-melting sites. The character of the gas motions at such an altitude is problematic and depends on unknown details of a nebular corona. Under the conditions hypothesized in this paper, magnetic stresses would dominate the gas motion in this region, in which case it is likely that velocities could far exceed the kilometer-per-second value found earlier to be sufficient to raise dust accumulations to high altitudes. This would reinforce our previous conclusion that dust could be raised to altitudes in the nebula high enough to expose them to energetic flare particles. It is illuminating to realize that the precursor dust accumulations would be lifted to such high altitudes only in the loose fluffy form that we have assumed; more highly compacted dust would not make it. The vertical distribution of such fluffy dust accumulations is dominated by the extent to which the dust globs are tied to the gas; the dust falls freely only in the regime where the force of gas drag drops below the force of gravity. It is conceivable that the high concentration of chondrules in many chondrites reflects a settling process that concentrated the chondrule beads toward the nebular midplane after the melting events. Altogether, the conditions needed for magnetic flare particles to produce chondrule melting are plausible, but there seems not to be a great margin of excess in terms of the nebula's capacity to make chondrules in this way, at least in the context of conventional ideas about nebular structure and dynamics. The fact that it is not easy to make disk flares with energy fluxes large in comparison with that needed to melt the chondrules, and to expose the dust to these flares, might provide some comfort in view

89

of the fact that the chondrule-making events seem to have been marginal in their capacity to heat the chondrules beyond the melting point. The chondrules are not rare and incidental features of meteorites; the chondrules constitute a significant component of those meteorites that survive to the present. Chondrule formation seems to require conditions far different from those usually ascribed to the protoplanetary nebula. The existence of chondrules as a dominant component of meteorites must be telling us that the nebula was a dynamically exciting place in ways that the standard picture does not describe. We are inclined to suspect that subtle clues preserved in the primitive meteorite record may point the way toward a picture of the nebula far richer in dynamical behavior than is generally assumed. The primary purpose of this paper has been to examine the questions of energetics associated with the hypothesis of chondrule melting by disk coronal flares. There are many additional questions involved in understanding the formation of chondrules and their accumulation into meteorites. Some of these questions will be taken up in subsequent work. Gross Energetics of a Nebular Flare Because the characteristic chondrule heating and cooling response times are so short, and under the assumptions discussed above that the chondrule melting region is optically thin and uninsulated, the heating and cooling history of a chondrule is controlled entirely by the variation in the incident energy flux. The inferred severalminute time scale of chondrule melting suggests that the hypothetical nebular flares proposed in this paper were minutes in duration. It is possible to use the inferred time scale of the chondrule heating events to characterize the nebular flares that could cause the chondrule melting. Indeed, the character of such flares is rather well constrained. Consider that the magnetic field in

90

LEVY AND ARAKI

the flare region must be several Gauss in magnitude and that the ambient matter density must be in the range 10 -18 g cm -3. Then the Alfvrn speed in the flare region is of the order of 109 cm sec -1. For the sake of illustration, suppose that the flare involves the collapse of the preexisting magnetic structure at a rate of 0.1 VA. If the duration of the flare event is "/'f in the range of 10 2 to 10 3 seconds, then the volume of involvement in the actual flare would be expected to be about (0.1 VArf) 3. Taking these results together and using Eq. (4), the energy of the flare would be expected to be B5 Ef ~ 10 -3 6477.5/2p3/2 7 3.

Taking the inferred values o f B - 5 G and p 10 -18 g cm -3, then Ef ranges from about 1030 to 1033 e r g s p e r flare as "rf r a n g e s f r o m 102 to 103 s e c . Thus, the e n e r g y production

in these hypothetical nebular flares falls into exactly the same range as solar flares observed today. ACKNOWLEDGMENTS The authors are grateful to J. T. Wasson for his critical comments. This work was supported in part by the National Aeronautics and Space Administration under Grant NSG-7419. REFERENCES AXFORD, W. I. 1964. Viscous interaction between the solar wind and the Earth's magnetosphere. Planet. Space Sci. 12, 45-53. BUTLER, R. F. 1972. Natural remanent magnetization and thermomagnetic properties of the Allende meteorite. Earth Planet. Sci. Lett. 17, 120-128. CAMERON, A. G. W. 1978. Physics of primitive solar nebula and of giant gaseous protoplanets. In Protostars & Planets (T. Gehrels, Ed.), pp. 453-487. Univ. of Arizona Press, Tucson. CHAPMAN, S. 1964. The energy of magnetic storms. Geophys. J. R. Astron. Soc. 8, 514-536. CONSOLMAGNO, G. J., AND J. R. JOKIPII 1978. 26AI and the partial ionization of the solar nebula. Moon Planets 19, 253-259. DUNGEV, J. W. 1953. Conditions for the occurrence of electrical discharges in astrophysical systems. Phil. Mag. 44, 725-738. DUNGEY, J. W. 1958. Cosmical Electrodynamics. Cambridge Univ. Press, Cambridge.

FUJll, N., AND M. MIYAMOTO 1983. Constraints on the heating and cooling processes of chondrule formation. In Chondrules and Their Origins (E. A. King, Ed.), pp. 53-60. Lunar and Planetary Institute, Houston. GROSSMAN, J. N., AND J. T. WASSON 1983. The compositions of chondrules in unequilibrated chondrites: An evaluation of models for the formation of chondrules and their precursor materials. In Chondrules and Their Origins (E. A. King, Ed.), pp. 88121. Lunar and Planetary Institute, Houston. HAYASHI, C. 1981. Structure of the solar nebula, growth and decay of magnetic fields and effects of magnetic and turbulent viscosities on the nebula. Prog. Theor. Phys. Suppl. 70, 35-53. HEWINS, R. H. 1983. Dynamic crystallization experiments as constraints on chondrule genesis. In Chondrules and Their Origins (E. A. King, Ed.), pp. 122133. Lunar and Planetary Institute, Houston. KIEFFER, S. W. 1976. Droplet chondrules. Science 189, 333-339. KLUGER, F., H. H. WEINKE, AND W. KIESL 1983. Chondrule formation by impact? The cooling rate. In Chondrules and Their Origins (E. A. King, Ed.), pp. 188-194. Lunar and Planetary Institute, Houston. LEVY, E. H. 1978. Magnetic field in the primitive solar nebula. Nature 276, 481. LEVY, E. H. 1987. Energetics of chondrule formation. In Meteorites (J. Kerridge and M. Matthews, Eds.), pp. 697-711. Univ. of Arizona Press, Tucson. I.EVY, E. H., AND C. P. SONETT 1978. Meteorite magnetism and early solar system magnetic fields. In Protostars & Planets (T. Gehrels, Ed.), pp. 516532. Univ. of Arizona Press, Tucson. Low, B. C. 1979. Evolving force-free magnetic fields. I. The development of the preflare stage. Astrophys. J. 212, 578-585. MAHONEY, W. m., J. C. LING, W. A. WHEATON, AND A. S. JACOBSON 1984. HEAO-3 discovery of Z6A1in the interstellar medium. Astrophys. J. 286, 578-585. PARKER, E. N. 1963. The solar-flare phenomenon and the theory of reconnection and annihilation of magnetic fields. Astrophys. J. Suppl. 8, 177-211. PARKER, E. N. 1979. Cosmical Magnetic Fields. Their Origin and Their Activity. Oxford Univ. Press (Clarendon), London. PARKER, E. N. 1983. Heating of the outer solar atmosphere, I, I1. In Solar-Terrestrial Physics. Principles and Theoretical Foundations (R. L. Carovillano and J. M. Forbes, Eds.), pp. 129-154. Reidel, Dordrecht. PETSCHEK, H. E. 1964. Magnetic field annihilation. In A A S - N A S A Symposium on the Physics o f Solar Flares (W. N. Hess, Ed.), NASA SP-50, pp. 425439. N A S A , Washington, DC. PRIEST, E. R. 1982. Solar Magnetohydrodynamics. Reidel, Dordrecht.

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WASILEWSKI,P. 1987. Magnetic record in chondrite

tary Cloud and Formation o f the Earth and Planets. Nauka Press, Moskow. (Also SAFRONOV, V. S. 1972. NASA TTF-677. NASA, Washington, DC.) SONNERUP, B. U. 0 . 1970. Magnetic-field re-connection in a highly conducting incompressible fluid. J. Plasma Phys. 4, 161-174. SONETT, C. P. 1979. On the origin of chondrules. Geophys. Res. Lett. 6, 677-680. SUGIURA, N., M. LANOIX, AND D. W. STRANGWAY 1979. Magnetic fields of the solar nebula as recorded in chondrules from the Allende meteorite. Phys. Earth Planet. Inter. 20, 342-349. SUGIURA, N., AND D. W. STRANGWAY 1983. A paleomagnetic conglomerate test using the Abee E4 meteorite. Earth Planet. Sci. Lett. 62, 169-179. SWINDLE, T. D., M. W. CAFFEE, AND C. M. HOHENBERG 1983a. Radiometric ages of chondrules. In Chondrules and Their Origins (E. A. King, Ed.), pp. 246-261. Lunar and Planetary Institute, Houston. SWINDLE, Z. D., M. W. CAFEEE, C. M. HOHENBERG, AND M. M. LINDSTROM 1983b. I-Xe studies of individual Ailende chondrules. Geochim. Cosmochim. Acta 47, 2157-2177.

meteorites--Microstructure, magnetism, and the FeNi phase diagram. Proc. Meteor. Soc. 50, 183. WASSON, J. T. 1985. Meteorites: Their Record o f Early Solar-System History. Freeman, New York. WHIPPLE, F. L. 1966. Chondrules: Suggestion concerning their origin. Science 153, 54-56. WILKENING,L. L., W. V. BOYNTON, AND D. H. HILL 1984. Trace elements in rims and interiors of Chainpur chondrules. Geochim. Cosmochim. Acta 48, 1071-1080. WOOD, J. A. 1984. On the formation of meteoritic chondrules by aerodynamic drag heating in the solar nebula. Earth Planet. Sci. Lett. 70, 11-26. WOOD, J. A. 1986. High temperatures and chondrule formation in a turbulent shear zone beneath the nebula surface. Lunar Planet. Sci. 17, 956-957. YEH, T. 1976. Reconnection of magnetic field lines in viscous conducting fluids. J. Geophys. Res. 81, 4524-4530. YEH, T., AND W. I. AXEORD 1970. On the re-connection of magnetic field lines in conducting fluids. J. Plasma Phys. 4, 207-229.