The variation in sizes of chondrules from one chondrite to the next is thought to be due to some sorting process in the early solar nebula. Hypotheses for the sorting process include chondrule sorting by mass and sorting by some aerodynamic mechanism; one such aerodynamic mechanism is the process of turbulent concentration (TC). We present the results of a series of statistical tests of chondrule data from several different chondrites. The data do not clearly distinguish between various options for the sorting parameter, but we find that the data are inconsistent with being drawn from lognormal or (three-parameter) Weibull distributions in chondrule radius. We also find that all but one of the chondrule data sets tested are consistent with being drawn from the TC distribution.
Chondrites comprise the vast majority of meteoritic falls (Sears & Dodd 1988). Chondrules are the major component of chondrites, and were likely the most ubiquitous object in the solar nebula. An understanding of the formation conditions of chondrules will lead us to a better understanding of the early history of the solar system. It has been known for some time that chondrules vary in size between different classes of chondrites (Dodd 1976;Hughes 1978a;Rubin 1989;Scott & Haack 1993). This phenomenon has been interpreted as arising from some sorting process acting in the solar nebula between the time of chondrule formation and the time of chondrite parent body formation, or from some parent body process. A sorting process has also been proposed as a possible explanation for metal-silicate fractionation by acting on other components of chondrites, including metal and sulfide grains (Dodd 1976;Scott & Haack 1993;Skinner & Leenhouts 1993;Huang et al. 1996;Kuebler et al. 1997;Benoit et al. 1998;Schneider et al. 1998;Akridge & Sears 1999;Kuebler et al. 1999). It is possible that the observed differences simply correspond to variations in the initial distributions of chondrules produced at different times and in different locations in the solar nebula, with no sorting or other post-formation alteration. The observed distribution of chondrules in any chondrite will reflect the initial distribution of chondrules produced, any sorting mechanisms that may have acted on the chondrules between formation and parent body assembly, and any parent body processes affecting the chondrule distribution. Chondrule distributions may vary between chondrite classes, or possibly even within chondrite classes.
Chondrule sizes in various samples have been described as approximately following lognormal (King & King 1979), Rosin (Hughes 1978a;Rubin & Grossman 1987) and Weibull distributions (Hughes 1978b;Eisenhour 1996). In general, a quantity z with a lognormal distribution is described by a probability density
where µ and σ are the mean and standard deviation of ln(z), respectively. For a chondrule size distribution, z is the chondrule radius r. Chondrule distributions in other parameters (e.g. mass, so that z = 4pi 3 ρr 3 , with ρ the chondrule density) can also be considered. The Weibull distribution comes in two-parameter and three-parameter varieties; the threeparameter variant has probability density
for z > α. This distribution is characterized by a location parameter α, shape parameter β, and scale parameter γ. The Weibull location parameter provides a minimum value for z, and corresponds to a constant additive shift in all data values, hence to a shift in the median, mean and mode. The shape parameter characterizes the shape of the distribution, and the scale parameter is a measure of the statistical dispersion of the distribution corresponding to a multiplicative shift of the standard deviation. The shape and scale parameters of the Weibull distribution must be positive. The two-parameter Weibull is equivalent to a threeparameter Weibull with α = 0. The two-parameter Weibull distribution can arise from fractal particle fragmentation, and for constant particle density a two-parameter Weibull distribution in mass (rather than in particle number) is equivalent to the Rosin distribution (Brown & Wohletz 1995). The Rosin distribution gives the mass percentage Y of material passed by a sieve of mesh width
, where β and γ are once again the shape and scale parameters of the distribution. In some of the statistical tests described below, the roles of location, shape, and scale parameters are generalized to other distributions, but they retain the same basic significance.
Hypotheses for a chondrule sorting process operating prior to parent body formation include sorting by mass (Kuebler et al. 1997), sorting due to photophoresis (Wurm & Krauss 2006), sorting due to X-winds (Shu, Shang & Lee 1996), sorting due to disk winds (Teitler, in preparation), and sorting by turbulent concentration (TC; Hogan et al. 1999;Hogan & Cuzzi 2001;Cuzzi et al. 2001). Photophoresis relies on non-uniform desorption of gas molecules from dust grains with non-uniform surface temperatures. Sorting by x-wind or disk winds involves dust grains being entrained in the nascent outflow and then dropping back onto the disk. In the TC scenario, chondrules that encounter turbulence are strongly concentrated in regions of low vorticity where their gas-drag stopping times match the local Kolmogorov eddy turnover time (Cuzzi et al. 2001). Possible sources of turbulence include the magnetorotational instability (Balbus & Hawley 1991, 1998), the Kelvin-Helmholtz instability (Gómez & Ostriker 2005;Chiang 2008), and other mechanisms (Cuzzi & Weidenschilling 2006;Rebusco et al. 2009).
The relevant sorting parameter for photophoresis sorting is the particle density times the thermal conductivity of the particle (Wurm & Krauss 2006). The x-wind, disk wind and TC mechani
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