An Accretion Rim Constraint on Chondrule Formation Theories

ICARUS

134, 180–184 (1998) IS985948

ARTICLE NO.

NOTE An Accretion Rim Constraint on Chondrule Formation Theories Gregor E. Morfill Max-Planck-Institut fu¨r Extraterrestrische Physik, D-85740 Garching, Germany E-mail: [email protected]

Richard H. Durisen Max-Planck-Institut fu¨r Extraterrestrische Physik, D-85740 Garching, Germany; Department of Astronomy, SW 319, Indiana University, Bloomington, Indiana 47405

and George W. Turner Department of Astronomy, SW 319, Indiana University, Bloomington, Indiana 47405 Received July 2, 1997; revised March 24, 1998 conversion of orbital or infall kinetic energy into heat. Some local processes which have been suggested are impact melts on planetesimals (Kitamura and Tsuchiyama (Chap. 33 HJS), Sanders (Chap. 34 HJS)), lightning (Horanyi et al. 1995, Horanyi and Robertson (Chap. 31 HJS)), and nebular shocks (Hood and Horanyi 1993, Boss and Graham 1993, Wood (Chap. 7 HJS), Hood and Kring (Chap. 28 HJS)). If the chondrule production site is distant, the energy efficiency can be substantially reduced, but then an efficient transport mechanism is required to carry the chondrules to the parent body formation sites. Protoplanet atmospheres (Podolak et al. 1993), magnetic flares above the nebula (Levy and Araki 1989, Cameron 1995), the accretion shock at the top of the nebula (Wood 1984, Ruzmaikina and Ip 1994 (Chap. 29 HJS)), and the interface between the early solar wind and inner disk (Skinner 1990, Liffman 1992, Liffman and Brown 1995, Cameron 1995, Shu et al. 1996, Liffman and Brown (Chap. 30 HJS)) have all been proposed as distant formation sites. The extreme variety of proposed scenarios indicates that our understanding of chondrule formation is insufficiently constrained. In this Note, we summarize laboratory results on fine-grained chondrule mantles which may provide insight into the nature and extent of chondrule transport between formation and incorporation into parent bodies. We show, using straightforward dust accretion models, that the observed mantle characteristics seem most compatible with scenarios in which the chondrules deplete the dust in a localized volume.

We argue that properties of the fine-grained rims, presumably accreted by chondrules during transport subsequent to their formation, may help differentiate between chondrule production mechanisms which are ‘‘local’’ (at the parent body formation site) and ‘‘distant’’ (e.g., close to the protosun, in accretion shocks, or outside the Solar Nebula). Systematics in the thicknesses of these rims seem most compatible with local production scenarios in which chondrules deplete the dust in a confined volume prior to parent body formation.  1998 Academic Press

Key Words: chondrules, cosmogony, solar nebula

1. Introduction. Chondrules are millimeter-sized, nearly spherical objects which, in some meteorites, account for over 80% of the mass. From the analysis of their chemical composition and from dynamical crystallization experiments, it has been deduced that chondrules were formed in transient heating events of short duration (minutes to about an hour) at temperatures of p1500 to 19008C. Chondrules seem to record a pervasive and energetic cosmogonic process which altered a vast amount of the solid materials in the Solar Nebula but whose nature remains highly in. This complex subject was recently and thoroughly reviewed in Hewins et al. (1996, hereafter HJS). Given the limited scope of this Note, we will cite only recent papers and refer the reader to chapters in HJS for more complete references (see also Wood 1988, Kerridge and Matthews 1988, Morfill et al. 1993). There are two general classes of chondrule formation theory to which we refer as ‘‘local’’ or ‘‘distant,’’ depending, respectively, on whether the chondrules are produced near the site of meteorite parent body formation at p to 5 AU from the protosun or whether they are produced in a distant, more energetic environment and then transported to the chondrite formation region. Local formation scenarios require a very efficient

2. Fine-grained dust rims in CM chondrites. Metzler and his colleagues (1991, 1992, Chap. 16 HJS) have made a detailed analysis of 14 carbonaceous chondrites of the CM group by scanning electron and optical microscopy of complete thin sections. In these meteorites, all coarse-grained chondritic components, such as chondrules, chondrule fragments, and refractory inclusions, are surrounded by layers of finegrained dust. The following summarizes the observed properties of these rims reported by Metzler and Bischoff (Chap. 16 HJS): (1) The boundaries between the dust mantles and the chondrules are sharp, with no reaction zones. (2) Dust mantles consist mainly of silicates in fine grains which were apparently encountered by the chondrules as solids. (3) The dust mantles also contain embedded mineral assemblages (olivines, sulfides,

180 0019-1035/98 $25.00 Copyright  1998 by Academic Press All rights of reproduction in any form reserved.

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Zolensky et al. 1997). Nevertheless, aqueous alteration does not preclude an accretionary origin for the fine-grained rims themselves, and we adopt it as a working hypothesis. In fact, Paque and Cuzzi (1997) have demonstrated a similar Da(a0 ) relation, but with a smaller K P 0.17, in the anhydrous CV chondrite Allende and also argue for an accretionary origin (Cuzzi et al. in Zolensky et al. 1997). The main focus of this Note is the observed linear correlation between mantle thickness and the enclosed chondrule core size (item 7). 3. Accretion of dust mantles. Consider a chondrule with an initial radius a0 , instantaneous radius a, and an average internal mass density ri moving at a relative velocity d v through a dust population with spatial mass density rd suspended in a gas with density rg , temperature T, and mean molecular mass e. The dust particles are presumed to be much smaller than the chondrules, in accordance with observations. The rate of increase in the chondrule radius due to accretion of dust by surface adhesion is then

FIG. 1. Rim thickness versus chondrule core radius data from Metzler et al. (1992) for four meteorites (Kivesvaara, Murchison, Murray, and Y791198) as digitized from the diagrams in the paper. The solid line is a simple least-squares power-law fit, Da p a0.81 0 , in which the square deviations in log Da are minimized. When such power laws are fit to the data from the individual meteorites, power-law exponents of 0.86, 0.65, 0.79, and 0.83 are obtained, respectively. Shown for comparison by the dashed curve is the least squares fit of a linear relation to this data, Da 5 0.46a0 , in which the square deviations in Da are minimized. There is no obvious difference in the quality of either type of fit. Given the large scatter, due in part to biases introduced by rimmed chondrules which are cut off center in the thin sections, the trend in the rim-thickness data is consistent with a nearly linear Da(a0 ) relation.

etc.) and overall are an unequilibrated mechanical mixture of components with different origin and genesis, including interstellar SiC grains in some cases. (4) Dust mantles are frequently stratified, consisting of two or more concentric dust layers with well-defined boundaries. (5) There is no evidence for solar wind implantation of noble gases in the rims. (6) The texture of some CM chondrites is entirely an agglomoration of chondrules and other refractory inclusions plus their fine-grained rims and no matrix material. (7) There is a linear correlation between the dust mantle thickness Da and the radius of the enclosed chondrule core a0 , Da P Ka0 . The slope K of the linear regression line is about 0.47 6 0.1 for the combined data from all chondrules measured; the variance in the slope among the fourteen meteorites is also only about 60.1. Reanalyzing the combined data for four of the meteorites using a powerlaw fit, we find Da p a 0.81 (see Fig. 1). As we will show elsewhere, the 0 biases introduced by off center cuts in thin sections make the observed Da(a0 ) relation shallower than the true relation; and, within the uncertainties, the power-law fit is consistent with a linear relation. According to Metzler and Bischoff (Chap. 16 HJS), these characteristics suggest that the dust grains were accreted as solids from a generally wellmixed solar nebula environment during the time between the chondrule formation event (items 1, 2, and 3) and the formation of the primary rock from the dust-rimmed chondrules (item 6). The chondrules and dust were probably shielded from solar wind outflow during the rim accretion phase (item 5). At the same time, dust mantle stratification (item 4) suggests passage of some chondrules through dust reservoirs of somewhat different temperature or composition. The status of CM chondrites as primary accretion rock has been recently called into question because they show evidence for extensive aqueous alteration and because they contain phyllosilicates which probably could not have formed in the solar nebular (see articles by Bischoff, Browning, Fegley, and others in

d a rd Q 5 d v, dt 4 ri

[1]

where Q is the sticking efficiency. Only the geometric cross section of the chondrule has been included explicitly. We express the internal density ri as an average because, during the accretion process, the dust rim may be uncompacted. Hence, generally, ri 5 ri (a), with ri (a0 ) 5 rs , where rs is the density of the chondrule core. The relative velocity d v between dust and chondrules in the protoplanetary disk can be calculated for various situations. The dust particles are sufficiently small that they effectively move with the nebular gas, so that d v is also the relative velocity between the gas and the chondrules. A millimeter-sized particle in a solar nebula environment will typically achieve a steady-state drift, or terminal velocity, with respect to the gas given by

d v 5 2 Atf ,

[2]

where A is the acceleration term due to differences between forces acting on the particle and the gas (Weidenschilling 1977, Morfill 1985). The quantity tf is the dust–gas frictional coupling time scale. For a Maxwellian distribution using Epstein Drag (a ! mean free path in the gas), tf 5 2Ïfri a/3rg cth , where cth 5 (2kT/e)1/2 is the thermal speed of the gas. The relative velocity d v is proportional to the total chondrule radius a, including the mantle, through the factor tf . We will now show that two simple models for dust–mantle accretion, namely, accretion over a fixed amount of time in a constant background and growth limited by depletion of dust in a localized volume, are both compatible with the observed correlation between mantle thickness and chondrule radius. Uniform accretion time. With (2), the integration of Eq. (1) gives Da 5 a0 (e t/ta 2 1),

[3]

where the subscript zero designates an initial value and ta 5 4rs a0 / rd Q d v0 is the characteristic mantle accretion time scale. The Da in (3) is the thickness of the uncompacted rim, but it can be shown that this is related to the thickness of the compacted rims in chondrites by a factor which depends only weakly on a0 . So, for simplicity, we hereafter assume ri 5 rs 5 constant. Then, because a0 / d v0 is independent of a0 , (3) gives Da p a0 for the compacted rims, provided that the accretion time t/ta is the same for all chondrules. A similar result was obtained independently by Cuzzi et al. (1998b) in the context of weak turbulence. A uniform chondrule accretion age t/ta , independent of both chondrule size and parent body, seems most compatible with episodic chondrule formation (or injection) over a short time scale followed, after t/ta , by

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almost complete, simultaneous chondrule removal from the dusty nebula before the next formation (or injection) episode. We note that the observed Da/a0 P 0.5 implies a ratio of the dust rim mass to chondrule mass mr /mc P 2.4. So the chondrules accrete a large amount of dust, and a constant t/ta P 0.4 is required. The observed accretion rim thicknesses are thus on the edge of the exponential regime for (3). This tightens the constraint on t/ta because upward fluctuations in t/ta by more than a factor of two would overproduce relatively thick rims. In fact, most of the scatter in the rim-thickness data probably arises simply because the thin sections used to measure rim thicknesses and diameters were noncentral for most chondrules (Sears et al. 1993). Local dust depletion. In principle, a constant chondrule age could be mimicked by depletion of the dust due to accretion. The requirement is a short episode of chondrule formation (or injection) in a confined volume of gas and dust, followed by mantle accretion. The rimmed chondrules must then be incorporated into meteorite parent bodies without passing through more dust-laden gas. For this case, we must supplement Eq. (1) with the dust depletion equation drd 52 dt

E

y

0

f (a)fa 2 d vrd Q da,

[4]

where f (a) is the chondrule size distribution function. When d v p a, the integrand on the right-hand side contains a 3f (a); and so, if ri 5 rs 5 constant, the integral is proportional to rc , the spatial mass density of the chondrules. If we assume that the confinement volume remains constant and isolated, then rc 5 rc0 1 rd0 2 rd , and (4) becomes 3d v0 rdQ drd 52 ( rc0 1 rd0 2 rd ), dt 4rs a0

[5]

which has the solution [1 1 ( rc0 / rd0 )]e2t , ( rc0 / rd0 ) 1 e2t

rd 5 rd0

[6]

where t 5 3(1 1 rc0 / rd0 )t/ta . Substituting (6) into (1) and integrating yields Da 5 a0

FS

rc0 1 rd0 rc0 1 rd0 e2t

D G 1/3

21 .

[7]

If chondrules with the same a0 had a range of lifetimes, the corresponding Da’s would also scatter over some range. However, if the dust is depleted, i.e., t * 3, we may neglect the e2t term in (12), and lifetime variations are unimportant. Expression (7) then simplifies to the observed linear relation Da p a0 . Several other constraints follow from this model. The linear regression lines from the studies by Metzler et al. (1991, 1992) give K 5 0.47 6 0.1, as confirmed by Figure 1. Combining this with (7) for t R y gives 1.6 & rd0 / rc0 & 2.9 for the conditions in the Solar Nebula at the time and location of chondrule formation. This indicates that there must have been comparable initial volume mass densities of dust and chondrules. The depletion condition t * 3 also yields t * ta (1 1 rc0 / rd0 )21. Confinement of chondrules while they deplete the dust in a localized volume of gas is an appealing simple result, because it is no longer necessary to guarantee that all chondrules in all CM chondrite parent bodies accreted their mantles for the same amount of time. On the other hand, there are a number of plausible confinement mechanisms, such as gravitational instabilities (cf., Weidenschilling and Cuzzi 1993), large-scale convective cells (e.g., Kley et al. 1993, Lin et al. 1993), vortices generally (e.g., Adams and Watkins 1995, Klahr and Henning 1997), and confinement to stagna-

tion regions in turbulent flows (Cuzzi et al. (Chap. 5 HJS), Cuzzi et al. 1998a). Uniform column density. Although it is beyond the scope of this Note to consider a wide variety of alternative accretion models, it is instructive to give one example of a plausible dust-rim accretion model that does not work. Suppose all chondrules encounter roughly the same column density of dust prior to incorporation into parent bodies, as might occur for some distant formation theories. By writing da/dt 5 dv da/dx in Eq. (1) where x is the path length along the drift direction, it is easy to show that Da 5 od Q/4rs . Here od is the column mass density of dust encountered by the chondrule along the path. Constant od would mean that accretion mantle thicknesses should be independent of chondrule size, which they are not. 4. Discussion. Admittedly, our accretion models make a number of simplifications that could be questioned. For instance, the presence of layered rims around some chondrules (item 4 in Section 2) and the report by Sears et al. (1993) of two chemically distinct classes of chondrule in the same CM chondrite (Murchison) with different linear relations between Da and a0 suggest that some modifications to a simple local confinement model might be required, such as temperature fluctuations or gradients as well as limited mixing with neighboring volumes and populations. However, such higher-order refinements should not obscure the fact that dust depletion in a confined volume provides a straightforward interpretation of the near constancy of Da/a0 in many chondrites. Consider now the distant formation scenarios that have chondrules produced in energetic environments outside or on the surface of the solar nebula. The chondrules must then be injected or precipitated into the nebula at high altitudes above the midplane. It is difficult to imagine how the chondrules can have a sufficiently uniform t/ta or be confined under such conditions. In fact, whenever chondrule formation is distantly separated from either dust depletion or parent body formation, an intermediate phase of transport through dust-laden gas is hard to avoid. Also, steady injection from a distant formation site leading to gradual dust depletion will not produce the correct systematics in Da/a0 . It seems rather that, if dust depletion followed by parent body formation can be invoked at all in injection theories, it must happen globally over a wide range of radial distances after a few, highly episodic, massive, shortduration chondrule formation events. It is tempting to relate these characteristics to FU Orionis events (Hartmann et al. 1993, Hartmann (Chap. 2 HJS), Wood (Chap. 7 HJS)), but it is not at all clear that global dust depletion will produce the same Da/a0 as a more uniform, localized dust depletion. As an alternative to rim accretion within the solar nebula, Shu et al. (1996), in their magnetocentrifugally driven wind model, suggest that the fine-grained dust rims condense onto the chondrules while they are still entrained in the early solar wind outflow. Although they do not treat this in detail, they do discuss accretion of such rims for CAIs. Their Eq. (13) gives basically Da/a0 p Do /a0 , where Do is the gas surface density as the rim accretes. It is unlikely that there would be enough systematics in their model to correlate Do linearly with a0 for all chondrules delivered to the same nebular radius. This model also faces difficulties with other known rim properties (items 1, 2, 3, and 5 in Section 2). Simplicity favors dust depletion within a locally confined volume as the explanation for the constancy of Da/a0 . This is most compatible with local production of the chondrules themselves by either lightning discharges or nebular shocks. Recent work on the interplay between particles and nebular turbulence no longer favors the idea that small particles can settle directly into a thin, gravitationally unstable midplane disk (Cuzzi et al. 1993, Dubrulle et al. 1995). Simulations of dust-laden turbulence by Cuzzi and his collaborators (Chap. 5 HJS) are particularly exciting because they demonstrate size-selective but transient local confinement of particles near stagnant points in Kolmogorov turbulence to very high concentration factors. They also show that the mechanism in fact selectively confines chondrule-sized particles for plausible nebula

NOTE parameters (Paque and Cuzzi 1997). This may provide the kind of leaky confinement mechanism required to produce the systematics of Da/a0 , while allowing for some mixing or other anomalies. Cuzzi et al. (Chap. 5 HJS) even suggest how this confinement might lead, in turn, to parent body formation. Although dust depletion under local confinement works best for the CM chondrites, other types of chondrites have rather different mechanical structures. These might be accommodated by relaxing the constraints conducive to CM chondrite formation, while still remaining within the context of a local picture. For instance, if the dust component is not depleted before compaction of the meteorite parent body, this would result in more matrix material filling the space between mantled chondrules, as observed in other types of chondrites. Such an outcome might be more likely in a nebular region where the energetics did not happen to favor copious chondrule formation. Also, if chondrule formation were a protracted process rather than a short initial burst, the mantle size distribution would show larger spread. Such alternatives may provide the flexibility necessary to incorporate explanations for the mechanical structures in other chondrite classes into a single unified picture. 5. Conclusions. Analyses of the fine-grained dust rims of chondrules in some chondrites have shown that there is a linear correlation between dust rim thickness Da and chondrule core radius a0 . We have considered several simple models for the accretion of dust rims and find that the most straightforward way of achieving the observed relation between rim thickness and chondrule core radius is for the chondrules to form locally and deplete the dust component in a confined volume prior to meteorite parent body formation.

ACKNOWLEDGMENTS The authors acknowledge useful comments from A. Bischoff, T. E. Bunch, J. N. Cuzzi, T. Hartquist, E. Levy, and K. Metzler. We especially thank our referees, including A. Rubin, for providing important input (and skepticism). Portions of this research were completed while G.E.M. was a fellow of Indiana University’s Patten Foundation and Institute for Advanced Study and while R.H.D. was a Humboldt Fellow at the MaxPlanck-Institute for Extraterrestrial Physics. This work was also supported in part by Grants NAGW-3399 and NAGW5-4342 from NASA’s Origins of Solar Systems Program.

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