Temperatures and Pressures of Ureilite Formation in the Equilibrium Smelting Model
As noted by Warren (2012), in an equilibrium smelting model, selection of any two of the variables TE, PE, and Fo (where the subscript “E” denotes equilibration) automatically determines the third variable. This is the fundamental constraint that has been used in all studies that have discussed an equilibrium smelting model for ureilites (Berkley and Jones 1982; Goodrich et al. 1987a; Sinha et al. 1997; Warren and Kallemeyn 1992; Walker and Grove 1993; Singletary and Grove 2003; Goodrich et al. 2007). The range of ureilite Fo is an observation (∼74–95), and temperatures of equilibration for each Fo (i.e., each ureilite) can be obtained from a variety of mineral geothermometers based on observed compositions of minerals in the meteorites (see Appendix S1). Thus, for each pair of Fo and corresponding TE, pressure (and therefore depth in parent body if an asteroid size is known or assumed) of equilibration can be determined. To put it more explicitly, Fo and TE are input and PE is output. However, Warren (2012, p. 213) states that “advocates of anatectic smelting (Goodrich et al. 2004, 2007; Wilson et al. 2008) have proposed some specific combinations of PE and Fo (Fig. 2) without noting the implied temperatures.” He then argues that those temperatures are not consistent with “actual” ureilite equilibration temperatures and concludes that equilibrium smelting models show poor agreement with ureilites. This argument is flawed because it assumes that Goodrich et al. (2004, 2007) and Wilson et al. (2008) used Fo and PE as the input variables, which is not correct.
Goodrich et al. (2004) was a review paper and simply summarized previous estimates for pressures of ureilite smelting from a number of different authors. It stated that the range of those estimates was ∼15–100 bars (corresponding to Fo approximately 76 to 92 for olivine-pigeonite ureilites). The two endmembers of this range were not intended to constitute a thermodynamically consistent pair (i.e., they did not necessarily come from the same reference). The range of previously published pressure estimates was ∼5–30 bars for the most ferroan ureilite and approximately 50–125 bars for the most magnesian. Goodrich et al. (2004) cited representative values from each of these ranges, which is all that was needed for discussing the implications of the model.
In contrast, Goodrich et al. (2007) did derive a new range of pressures for ureilite equilibration in the smelting model, using a rigorous thermodynamic treatment (simultaneous solution of olivine-silica-iron and C-CO-CO2 equilibria) essentially identical to that used by Warren (2012). The derivation was illustrated on a plot of T versus fO2 in fig. 1 of that paper. As explained in the figure caption, the range of ∼30–100 bars pressure was derived from the input temperature range ∼1250–1275 °C from 2-pyroxene thermometry (Appendix S1) and corresponding Fo values of ∼76–94, respectively: “Equilibration temperatures in the range of ∼1250–1275 °C for ureilites (Fo ∼76–94) indicate that they are derived from pressures of ∼30–100 bars” (Goodrich et al. 2007, p. 2877). This input temperature range was well within the uncertainties of published 2-pyroxene temperatures for the range of ureilite Fo (Appendix S1).
The only significant difference between the pressure derivation of Goodrich et al. (2007) and that of Warren (2012) is the choice of mineral thermometer used to provide input temperatures. Instead of using 2-pyroxene temperatures, Warren (2012) used temperatures obtained from a recently developed pigeonite thermometer (Singletary and Grove 2003), and referred to these as “actual” ureilite equilibration temperatures (in fact, all mineral thermometers are model dependent and this use of the term “actual” is misleading; see Appendix S1). Thus, the input temperature range of Goodrich et al. (2007) was 1250–1275 °C, whereas the input temperature range of Warren (2012) was 1209–1308 °C. However, based on the mistaken assumption that the input variables in Goodrich et al. (2007) were Fo and PE, and therefore TE was output, Warren (2012) compared the two temperature ranges, observed that they disagree, and argued that equilibrium smelting models show poor agreement with “real” ureilites. The flaw in this argument is that the TE of Goodrich et al. (2007) were not output. Therefore, the exercise carried out by Warren (2012) is an interesting test of the sensitivity of the smelting model to uncertainties in equilibration temperatures, but it is not a test of the model itself.
Wilson et al. (2008) adopted the results of Goodrich et al. (2007) for pressures of ureilite equilibration (∼30–100 ± 10 bars). Based on these pressures, Wilson et al. (2008) constrained the radius of the ureilite parent body to ∼100 km, and used this size in modeling the thermal history and physics of melt extraction on that body. To evaluate whether an inappropriately small range of input temperatures in Goodrich et al. (2007) led to serious errors in the work of Wilson et al. (2008), we have repeated the thermodynamic derivation of Goodrich et al. (2007) using input temperatures from the pigeonite thermometer (Appendix S1). This calculation yields pressures of 87 bars (Fo 75) to 34 bars (Fo 95), which do not differ grossly from the 30–100 ± 10 bars of Goodrich et al. (2007). As 87 bars is the central pressure for a body of approximately 76 km radius (ρ = 3300 kg m−3), and it seems unlikely that the meteorites have sampled the absolute center of the asteroid, we conclude that approximately 100 km radius (Wilson et al. 2008) is still reasonable for the size of the UPB in the equilibrium smelting model. Thus, the large-scale implications of the equilibrium smelting model do not depend greatly on ureilite equilibration temperatures, within the range of plausible estimates, and we have no disagreement with Warren (2012) as to what those implications are.
The Pigeonite Problem and Ca/Al Ratios of Ureilite Precursor Material
One of the most characteristic, and puzzling, features of ureilites is that in the majority of them the sole pyroxene is pigeonite, where pigeonite is defined compositionally (Deer et al. 1966) as pyroxene of Wo 5–15. Among planetary materials, olivine-pigeonite rocks are almost invariably cumulates, rather than residues, and yet a cumulate model for ureilites (e.g., Berkley et al. 1980; Mittlefehldt 1986; Goodrich et al. 1987a) appears to be ruled out by their oxygen isotope heterogeneity (see Clayton and Mayeda 1988, 1996; Warren and Kallemeyn 1992; Scott et al. 1993). To address this problem, Goodrich (1999) carried out modeling to constrain the chemical composition(s) of precursor materials that could yield ureilite-like olivine-pigeonite assemblages (i.e., correct pyroxene type and olivine/pyroxene ratio for each Fo 75 to 92) as residues of batch partial melting in the system Ol-Pl-Wo-Qtz (Longhi 1991). One of the conclusions of that modeling was that ureilite precursor materials must have had superchondritic Ca/Al ratios (≥2–2.5 × CI). Warren (2012, p. 219) cites this result as “a related postulate” of the equilibrium smelting model. He then argues against superchondritic Ca/Al ratios, and presents these arguments as arguments against smelting. Here, we show that the hypothesis of superchondritic Ca/Al ratios in ureilite precursor materials (more fundamentally, the problem of pigeonite) is independent of the issue of smelting versus nonsmelting.
The modeling of Goodrich (1999) began with a generic chondritic composition, not restricted to a specific chondrite type (in contrast to what is stated in Warren 2012). This composition was then systematically varied in terms of 4 parameters—Si/Mg ratio, Ca/Al ratio, alkali contents, and mg# (FeO content)—and tested using MAGPOX (Longhi 1991) to see whether it could produce ureilite-like assemblages as residues of batch partial melting. The requirement for superchondritic Ca/Al ratios arose because, at constant Ca/Al ratio, the stability of pigeonite (Wo ≥ 5) relative to orthopyroxene (Wo < 5) strongly decreases with increasing mg#, and the olivine-pigeonite ureilites (Fo ∼75–92) are simply too magnesian for pigeonite to be stable at chondritic Ca/Al ratio (Longhi 1991). It is important to note that the variation in FeO content in Goodrich (1999) did not imply smelting. In fact, it was assumed by the author to be nebular: “… the assumption [is] made here that the FeO/MgO ratios of ureilites were established prior to accretion by a nebular process” (p. 111). Nevertheless, the results did not depend on how the FeO contents of the starting materials were established, and so would be applicable in both smelting and nonsmelting models.
The hypothesis of superchondritic Ca/Al in ureilite precursors was challenged by Kita et al. (2004). These authors performed partial melting calculations using MELTS (Ghiorso and Sack 1995), and reported that batch melting of anhydrous silicate CM (chondritic Ca/Al ratio, FeO adjusted to yield Fo 77) produced an olivine-pigeonite residue. They also suggested that fractional melting of chondritic materials might lead to olivine-pigeonite residues. Warren (2012) invoked the arguments of Kita et al. (2004) as evidence against superchondritic Ca/Al ratios in ureilite precursor material.
However, the arguments of Kita et al. (2004) were countered in Goodrich et al. (2007). First, Goodrich et al. (2007) repeated the MELTS calculation of Kita et al. (2004) for the same composition and showed that, although the residual low-Ca pyroxene is pigeonite in the early stages of melting, pigeonite is replaced by orthopyroxene when plagioclase is eliminated and the final residue consists of olivine + orthopyroxene. Second, Goodrich et al. (2007) showed that MELTS is in agreement with MAGPOX that for all Fo greater than 77 (i.e., most of the ureilite range), the residual low-Ca pyroxene is always orthopyroxene. Third, Goodrich et al. (2007) tested fractional melting (using an incremental batch procedure) in both MAGPOX and MELTS and showed that fractional melting of material with a chondritic Ca/Al ratio is no more likely than batch melting to lead to ureilite-like residues.
The predominance of pigeonite in ureilites is an unresolved problem. Ureilite precursor materials with superchondritic Ca/Al ratio could solve this problem. However, as discussed in Goodrich (1999) and Goodrich et al. (2007), it is difficult to explain how such materials could have originated, except in a previous stage of igneous processing (Goodrich et al. 1987a), which appears to be ruled out by the observed oxygen isotope heterogeneity. It is virtually impossible to produce superchondritic Ca/Al ratios with any mix of chondritic components, because all such components have chondritic Ca/Al ratio. Hence, it is unlikely that superchondritic Ca/Al is a primitive feature of the ureilite parent body.
As an alternative, Goodrich et al. (2002) suggested that Ca was concentrated in ureilite source regions during preigneous aqueous alteration on the parent body, as evidenced in some dark inclusions in CV chondrites. This hypothesis was envisioned as a way to solve the problem of pigeonite and simultaneously provide the radial gradient in Δ17O that is required in equilibrium smelting models for the UPB (Goodrich et al. 2002, 2004). Warren (2012) interpreted this to mean that the problem of pigeonite and the issue of smelting versus nonsmelting are intrinsically linked. He argues from mass balance that in the aqueous alteration hypothesis, the part of the UPB from which ureilites come must constitute ≤50% of the whole body, which is not consistent with what is implied (>70 vol%) by equilibrium smelting models (e.g., Wilson et al. 2008). We agree with this argument. It provides a useful constraint on any hypothesis that postulates that superchondritic Ca/Al ratios originated on the parent body, rather than before or during accretion. However, it is a mistake to assume that the inconsistency between aqueous alteration and smelting is an argument against smelting. It could equally well be taken as an argument against aqueous alteration. In fact, Goodrich and Wilson (2011) came to the conclusion that aqueous alteration is not a viable mechanism and abandoned this hypothesis. The solution to the problem of pigeonite in ureilites may or may not involve superchondritic Ca/Al ratios in ureilite precursor material, but in any case it is independent of the issue of smelting. In sum, the occurrence of high-Wo pigeonite as the dominant pyroxene type in ureilites is a major problem for any model in which ureilites are seen as residues of single-stage, equilibrium (batch or fractional) partial melting of chondritic material, including both smelting and nonsmelting models.
Melt Porosity and Fractional Melt Extraction on the Ureilite Parent Body
In an asteroid undergoing anatexis, melt porosity (the amount of melt present in the solid matrix at any given time) and melt transit times (source region to surface) are directly linked to the bulk density of the melt. The presence of CO gas produced by smelting increases the buoyancy of the melt and thus reduces melt porosity and transit times. Goodrich et al. (2007) and Wilson et al. (2008) concluded that in a smelting model, melt porosity would be so low and melt transit times so short that the ureilite anatexis could be regarded “from the point of view of geochemical modelling” as “nearly perfect fractional melting.” Thus, Warren (2012) presents arguments against low melt porosity and fractional melt extraction, implicitly suggesting that they are arguments against smelting.
Warren (2012) points out that, in the smelting formulation of Goodrich et al. (2007), gas production does not begin immediately upon the start of melting at all depths in the UPB, and argues qualitatively that this makes low melt porosities and near-perfect fractional melting implausible. However, this qualitative argument does not survive scrutiny, as shown quantitatively by Wilson et al. (2008). Using the relationships developed in their equations (21) through (27), Wilson et al. (2008) calculated total melt transit times that included the effects of delayed smelting in deeper source regions. The resulting most conservative (largest) transit times for even the deepest ureilite source regions were only a few months. Goodrich et al. (2007) calculated that these short melt times would have led to preservation of pre-existing oxygen isotope heterogeneity in the residues (i.e., ureilites).
The assumption made by Warren (2012) was that if there is no gas production due to smelting, then melt porosities will be significantly higher and melt extraction will be much closer to batch than to fractional conditions. However, Wilson and Goodrich (2012) extended the calculations of Wilson et al. (2008) to nonsmelting models, and showed that this assumption is not correct. Table 1 summarizes the effects of melt buoyancy (which is dependent on amount of CO present) on melt porosity and total melt transit time, for the 100 km radius asteroid size inferred by Wilson et al. (2008) for the UPB. Goodrich et al. (2007) predicted that, in the case in which smelting takes place at all depths where melting is occurring, CO would reduce the bulk density of the silicate melt to approximately 200 kg m−3, making the density difference between host rocks and melt equal to approximately 3100 kg m−3 and leading to a melt transit time of approximately 30 days; approximately 2% by volume of melt would be present in the melting zone at any one time (Table 1). In the opposite case of no smelting at any depth, and hence no gas production, the density difference between the solid and the melt is approximately 300 kg m−3. Under these conditions, the total melt transit time is approximately 3× longer (91 days versus 28 days) than when ubiquitous smelting occurs (Table 1). The difference between approximately 1 month (with smelting) and approximately 3 months (without smelting) is too small to have any significant effect on the conclusions of Goodrich et al. (2007) and Wilson et al. (2008).
Table 1. Variation in the time taken by magma to reach the surface from the deepest part of the melt zone of a 100 km radius UPB, together with the total volume% of melt present in the melt zone at any one time, as a function of melt buoyancies (determined by CO mass fraction) covering the entire range of physical possibilities
|CO mass abundance/ppm||Volume % melt||Δρ/(kg m−3)||Transit time/days|
The transit times and melt percentages in Table 1 would change if a different size were postulated for the UPB. As discussed by Warren (2012), in nonsmelting models, all ureilites must have equilibrated at sufficiently high pressure that smelting was suppressed (assuming that the carbon in ureilites is primary; see Berkley and Jones 1982 and Goodrich and Berkley ). Warren (2012) estimated that this would require a minimum of 80 bars, based on the most ferroan (approximately Fo 75) precursor material and equilibration at 1205 °C. Following the same reasoning, but using a peak T of approximately 1300 °C (Appendix S1) leads to a minimum pressure of approximately 150 bars. Assuming further that ureilites are more likely to have been excavated from shallow (rather than deep) regions on their parent body (Warren 2012), the UPB must have been at least 250 km in radius (implying a minimum depth for the most ferroan ureilites of approximately 30 km). Inserting 250 km radius into the equations used to derive Table 1 yields melt transit times of ∼13 months. This is still short compared with the time scales needed to achieve oxygen isotope equilibration (Goodrich et al. 2007). Thus, quantitative modeling of melt extraction on asteroids leads to the conclusion that melt extraction on the ureilite parent body was a rapid, near-fractional process in which original oxygen isotope heterogeneity would have been preserved, whether smelting occurred or not.
Partitioning of Rare Earth Elements During Ureilite Anatexis
Ureilites show only modest fractionations of rare earth elements (REE), which in equilibrium models would be more consistent with batch than with fractional melt extraction (Warren and Kallemeyn 1992; Goodrich et al. 2007). However, Goodrich et al. (2007) suggested that the observed REE patterns of ureilites could be explained by disequilibrium partitioning, limited by slow diffusion in pyroxenes during fractional melt extraction (e.g., Van Orman et al. 2001), and do not necessarily indicate a large grain-scale porosity (i.e., near-batch conditions) during anatexis. Warren (2012) argues that the parameters used in the modeling of Goodrich et al. (2007) are unrealistic, and that disequilibrium partitioning of the REE is implausible. He therefore concludes that ureilite REE patterns support moderate porosity and batch melt extraction, implicitly suggesting that the smelting framework of Goodrich et al. (2007) is wrong.
Warren (2012) argues that the REE diffusion coefficients used by Goodrich et al. (2007) are too small by a factor of 100 because they neglect the effects of premelting in pyroxene, which was previously inferred to enhance the diffusivity of some cations as the temperature approaches the melting point. Warren (2012, p. 221) states that “Goodrich et al. (2007) modeled diffusion based on simple Arrhenius-plot extrapolations from data … obtained for solid diopside no hotter than about 200 K below its melting temperature.” This statement is incorrect. The experimental data for diffusion of REE in diopside at 1 atm (Van Orman et al. 2001) were obtained at temperatures between 1050 and 1300 °C, a range that extends to within 90 K of the diopside melting temperature and encompasses the temperatures at which ureilites equilibrated (see Appendix S1). Hence, no extrapolation in temperature was needed in Goodrich et al. (2007) to obtain the diffusion coefficients used in numerical modeling of disequilibrium melting. The speculation by Warren (2012) that the REE diffusion coefficients are enhanced by premelting at temperatures relevant to ureilite anatexis is directly contradicted by the experimental diffusion data (Van Orman et al. 2001).
Warren (2012) also suggested that the initial spherical grain radius of 1 mm used in the numerical modeling by Goodrich et al. (2007) was too large. The grain size relevant during ureilite anatexis has considerable uncertainty and therefore we performed additional numerical modeling to address the influence of grain size on diffusion-controlled REE partitioning. The results are shown in Fig. 1, for a melting time scale of 2 Myr. Changing the initial grain radii from 1 to 0.3 mm has only a modest influence on the REE patterns in the residual solid. Light REE become strongly depleted in the solid residue during near-fractional melting only when the initial grain radii are on the order of ∼0.1 mm or smaller. It is possible that such small grain sizes are relevant during ureilite anatexis, but this seems unlikely unless grains overdissolve and reprecipitate actively during melting, in which case the relevant grain size is that of the unreacted mineral cores (Lo Cascio et al. 2008). Although some overdissolution during melting is inevitable for minerals like pyroxenes that have solid solution (Liang 2003), it is not clear whether this would be sufficient in the case of ureilites to expose ∼0.1 mm mineral cores. Thus, even taking into account the uncertainties in grain size pointed out by Warren (2012), quantitative modeling indicates that ureilite REE patterns are consistent with disequilibrium partitioning during anatexis. This conclusion is independent of the smelting hypothesis. Neither melt transit time nor total melt porosity, as defined in Wilson et al. (2008) and given in Table 1 in this paper, are parameters in the diffusion-limited partitioning model (Van Orman et al. 2001). The relevant parameters are total melting time scale (on the order of Myr) and the fraction of melt present along grain boundaries on the finest melt-conduit scale (on the order of 0.1–0.2%), neither of which is dependent on smelting.
Figure 1. Influence of grain size on the REE patterns of the residual solid after 30% near-fractional melting. The solid curves represent average concentrations within the mineral grain, as simulated numerically assuming that mineral surfaces maintain equilibrium with grain-scale residual melt at all times and that element transfer to the melt is controlled by diffusion within the mineral grains. For more detail on the model see Goodrich et al. (2007) and Van Orman et al. (2002). The residual melt fraction, i.e., the fraction of melt that remains with the solid on the scale of the mineral grains is 0.2% in the simulations, and the time to reach 30% melting, based on thermal models that consider heating by 26Al, latent heat of fusion, and melt transport, is 2 Myr (Goodrich et al. 2007; Wilson et al. 2008). The leached residue of Kenna (Spitz and Boynton 1991) is shown as a dashed curve for comparison with the simulation results.
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The Fate of Melts on the Ureilite Parent Body
Conductive cooling dictates that all differentiated asteroids must have had a “cold” outer shell, with an initially very steep gradient in temperature (increasing from approximately 200 K at the surface) that became less steep with depth until a nearly constant temperature (the peak temperature experienced by the asteroid) was reached. The thickness of this outer shell would be controlled by the compaction and porosity of the outer layers of the asteroid, and has been estimated to be in the range of 6–10 km (Ghosh and McSween 1998; Merk et al. 2002; Wilson et al. 2008; Warren 2011; Wilson and Keil 2012). The physical modeling of Wilson et al. (2008) indicated that rising melts on the UPB would encounter a density trap at the base of this outer shell, and be emplaced there to form shallow intrusive bodies. Warren (2012) argues that emplacement of UPB melts in shallow intrusions is not consistent with properties of the rare, feldspathic clasts in polymict ureilites (presumed to be samples or products of such melts), and implies that the smelting model behind the shallow intrusion scenario (Wilson et al. 2008) is therefore wrong. However, Keil and Wilson (2012) have shown that emplacement of melts as intrusions below the density trap of the outer shell is a necessary feature of all small (<200 km radius) differentiated asteroids, regardless of smelting, and is a likely feature of all differentiated asteroids. Thus, even nonsmelting models for the UPB (e.g., Warren 2012) need to consider the possibility that the feldspathic clasts in polymict ureilites are derived from shallow intrusions.
As the alternative to formation in shallow intrusions, Warren (2012) invoked the hypothesis that the majority of melts produced on the UPB were lost to space due to explosive volcanism (Warren and Kallemeyn 1992; Scott et al. 1993; Goodrich et al. 2004). However, Wilson et al. (2008) showed that explosive volcanism and formation of shallow intrusions are not mutually exclusive. Wilson et al. (2008) describe how the changing pressure and smelting-produced gas content in intrusions can cause stress changes at the intrusion roof as magma is accumulated. Wilson and Keil (2012) treated the more general case of gas from sources other than smelting, including the case in which no gas is present, and showed that similar stresses are produced irrespective of gas content. These stresses can lead to intermittent dike propagation feeding eruptions at the surface. If the intervals between eruptions are long enough, the eruptions can take place at volume fluxes greatly exceeding the average melt production rate in the asteroid interior. Warren (2012, p. 215) argued that feldspathic clasts in polymict ureilites are preponderantly fine grained and/or glassy, “implying cooling very near the surface of a parent body, not 7 km down.” In fact, the most abundant population of feldspathic materials in polymict ureilites, the “albitic lithology,” is largely crystalline, consisting of moderately sized grains (up to approximately 500 μm) of Na-rich plagioclase and pyroxene, with fine-grained accessory phases and glass occurring only as late mesostasis (Cohen et al. 2004; Ikeda et al. 2000). Considering that even within intrusive bodies there may be a large range of cooling rates (e.g., upper, lower, and lateral margins versus interiors), it does not seem a foregone conclusion that these clasts could not have cooled at 7–10 km depth. Also, fine-grained or glassy clasts could be derived from the chilled margins of dikes feeding surface eruptions. Furthermore, the clasts of the albitic lithology show an extreme range of normal igneous fractionation (Ikeda et al. 2000; Cohen et al. 2004; Goodrich et al. 2010), which implies crystallization over a finite period of time. As discussed by Wilson et al. (2008, p. 6174), it is much more likely that this crystallization occurred in a “slowly” cooled intrusion than during an explosive eruption to space. Finally, Warren (2012) implied that the rarity of feldspathic ureilite materials (a few percent of the material in approximately 10% of all ureilites) supports the hypothesis that the vast majority of ureilitic melts were lost during explosive volcanism. However, Wilson et al. (2008) calculated that even with the formation of intrusive bodies at the base of the cold outer shell, only ∼15–25% of all UPB melts were retained on the asteroid. The sampling of only a small fraction of these retained melts is not grossly inconsistent with our low sampling of the most magnesian main group ureilites (Goodrich et al. 2004; Downes et al. 2008; Warren 2012), which at least in the smelting model would have formed just below the intrusions.
In summary, we agree with Warren (2012) that there are many uncertainties about the origin of the feldspathic clasts in polymict ureilites, and it is not clear whether their properties are consistent with formation in shallow intrusions. However, these uncertainties apply equally to the case of no smelting, and thus do not constitute an argument against smelting.
Selective Sampling of UPB Materials by Catastrophic Impact Disruption and Reassembly
The distribution of Fo values among main group ureilites (Fig. 2a) has a strong peak at approximately Fo 78–80, near the low end of the observed range (Goodrich 1992; Mittlefehldt et al. 1998; Goodrich et al. 2004; Warren 2010, 2012). In the equilibrium smelting model, a distribution in Fo implies a distribution in depth (pressure) of derivation. Thus, the obvious implication of the ureilite distribution (in this model) is that the majority of ureilites are derived from “deep” source regions (Goodrich et al. 2004). Quantifying this statement based on the recent ureilite statistics shown in Fig. 2a (234 unpaired main group ureilites) and the smelting formulation described above (temperatures from the pigeonite thermometer), leads to the distribution of depths shown in Fig. 2b. As can be seen from this figure, approximately 78% of all main group ureilites would have been derived from approximately 30–35 km depth. Warren (2010, 2012) argued that “no straightforward model” for impact-driven removal of material would imply such selective sampling of a small volume of the parent body, particularly a deep volume, and therefore that the observed distribution of Fo values among ureilites constitutes evidence against smelting. In contrast, Hartmann et al. (2011) and Goodrich et al. (2011) argued that selective sampling is a likely result of impact processes.
Figure 2. a) Histogram of Fo values of olivine cores among 234 unpaired main group ureilites. The distribution shows a strong peak at approximately Fo 79–80. b) Corresponding depths of derivation in a 100 km radius ureilite parent body (UPB) in the equilibrium smelting model. Based on the smelting formulation (temperatures from the pigeonite thermometer of Singletary and Grove 2003) described in this work and a constant density of 3300 kg m−3.
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If individual ureilites had been chipped off their parent body in a series of subcatastrophic impacts and delivered directly to Earth-crossing orbits, the argument that ureilites should be dominantly derived from shallow depths (Warren 2010) would have merit. However, there is strong evidence in ureilites that this was not the case. All ureilites show mineralogical evidence of extremely rapid cooling (approximately 0.05–10 °C h−1), accompanied by a drop in pressure, through the range approximately 1100–600 °C (Mittlefehldt et al.  and references therein; Herrin et al. 2010). This is widely interpreted to result from catastrophic disruption of the UPB while it was still hot, due to a large impact (Takeda 1987; Warren and Kallemeyn 1992; Goodrich et al. 2004). An age date of approximately 5 Ma after CAI may record this event (Goodrich et al. 2010). From the 0.05–32 Ma exposure ages of ureilites (Eugster 2003), it is clear that this event was not immediately responsible for delivery of ureilites to Earth. Thus, after breakup of the UPB, the ureilitic materials that have arrived on Earth in recent times must have been stored somewhere. The existence of polymict ureilites, and the observation that they show the same distribution of ureilite Fo values as the main group ureilites, suggest that they were stored in a single, reasonably large daughter body that formed in the aftermath of the catastrophic disruption (Goodrich et al. 2004; Downes et al. 2008).
Catastrophic collisions have been modeled numerically (e.g., Michel et al. 2001, 2002, 2004). These events involve shattering, fragmentation, and dispersal of the target, followed by gravitational reaccumulation of some of the fragments to form a family of offspring. The simulations of Michel et al. (2001, 2002, 2004) showed that the reaccumulation is not a random mixing process. Rather, each of the reaccumulated bodies is dominated by materials derived from a well-defined, restricted region within the original body. In particular, the few largest fragments may be dominated by materials derived from deep regions, such as the core or the midmantle (Michel et al. 2002). Thus, Hartmann et al. (2011) and Goodrich et al. (2011) argued that the highly selective sampling of the UPB that is implied by the equilibrium smelting model (Fig. 2b) is not unlikely.
However, Warren (2012) argues that the modeling of Michel et al. (2001, 2002, 2004) is “ill-suited” to the ureilite problem because it assumes a monolithic parent body, whereas in the ureilite case the target was a “weak mass of partially molten mush.” This objection is only partially germane. Michel et al. (2001, 2002) assumed a monolithic target, but Michel et al. (2004) extended the model to the more realistic case of a preshattered body. In the latter, the conclusion that the offspring would be highly selective samples was unchanged. The point that the UPB was partially molten when it was disrupted is a good one, but we do not agree that it can be described as “a partially molten mush.” The physical and thermal modeling discussed above indicates that at 5 Ma after CAI, melting on the UPB was in its final stages (Wilson et al. 2008), with only ∼0.1% total melt remaining in the residual mantle matrix and ∼5–8% melt (both relative to the original volume of the body) residing in sill-like intrusions at the base of the cold outer shell. We have recently begun (Michel et al. 2013) to extend the modeling of Michel et al. (2001, 2002, 2004) to targets in various partially molten states, including a case (solid except for a molten layer at 10 km depth) that approximates this picture of the UPB. Although the work is in early stages (only a small part of the relevant parameter space has been explored), initial results indicate that the largest bodies still preferentially sample distinct regions (depths) of the parent body, with detailed differences depending on amount and location of melt.
Warren (2012) also argues that the modeling of Michel et al. (2001, 2002, 2004) is inconsistent with the very high cooling rates inferred for ureilites. Warren (2012) points out that in the smelting model ureilites sample most of the mantle depth range of an original ureilite body that was approximately 100 km in radius (i.e., Fig. 2b), and notes that this size is “a factor of 1010 to 1012 times more voluminous” than the sizes that ureilite fragments are inferred to have been (on the order of tens of meters; Herrin et al. 2010) in the postdisruptive phase. However, this argument overlooks the fact that in the modeling of Michel et al. (2001, 2002, 2004), the parent body is completely shattered into fragments that are at least as small as the numerical resolution of the simulations (particle size approximately 1 km) before reaccumulating to form the offspring. Although the resolution of the simulations (determined by practical considerations of time) gives only an upper limit on the size of the intact fragments surviving the collision, early tests (to particle sizes as small as a few tens of meters) demonstrated that this resolution limit has little effect on the outcome of the gravitational reaccumulation phase (Michel et al. 2001). Thus, the relevant size for cooling rate arguments is not the entire volume of sampled UPB, but rather the size of the shattered fragments (Michel et al. 2002). The cooling rates of these fragments are likely to be of similar magnitude to those inferred for ureilites.
In summary, modeling of catastrophic collisions involving fragmentation and gravitational reaccumulation of offspring bodies is directly relevant to ureilites. For solid targets, such modeling (Michel et al. 2001, 2002, 2004) predicts that the few largest offspring will be selective samples, derived from discrete depth ranges in the parent body. Initial modeling for partially molten targets, such as inferred for the UPB, points to a similar conclusion (Michel et al. 2013). Such modeling has the potential to distinguish between a smelting versus nonsmelting petrogenesis for ureilites.