Parent body depth–pressure–temperature relationships and the style of the ureilite anatexis

Authors


E-mail: pwarren@ucla.edu

Abstract

Abstract– New analyses of mafic silicates from 14 ureilite meteorites further constrain a strong correlation (Singletary and Grove 2003) between olivine-core Fo ratio and the temperature of equilibration (TE) recorded by the composition of pigeonite. This correlation may be compared with relationships implied by various postulated combinations of Fo and pressure P in models for ureilite genesis by a putative process of anatectic (depth-linked, P-controlled) smelting. In such models, any combination of Fo and P together fixes the temperature of smelting. Agreement between the observed correlation and these models is poor. The anatectic smelting model also carries implausible implications for the depth range at which ureilites of a given composition (Fo) form. Actual ureilites (and polymict ureilite clasts: Downes et al. 2008) show a distribution strongly skewed toward the low-Fo end of the compositional range, with approximately 58% in the range Fo76–81. In contrast, the P-controlled smelting model implies that the Fo76–81 region is a small fraction of the volume of the parent body: not more than 3.2%, in a model consistent with the Fo-TE observations; and even ignoring the Fo-TE evidence not more than 11% (percentages cited require optimal assumptions concerning the size of the parent body). This region also must occur deep within the body, where no straightforward model would imply a strong bias in the impact-driven sampling process. The ureilites did not derive preponderantly from one atypical “largest offspring” disruption survivor, because cooling history evidence shows that after the disruption (whose efficiency was increased by gas jetting), all of the known ureilites cooled in bodies that were tiny (mass of order 10−9) in comparison with the precursor body. The Ca/Al ratio of the ureilite starting matter cannot be 2.5 times chondritic, as has been suggested, unless the part of the body from which ureilites come is at most 50% of the whole body. Published variants of the anatectic, P-controlled smelting model have the ureilites coming from a region that is >50 vol% of their parent body; and to invoke a larger body would have the drawback of implying that the Fo76–81 spike represents an even smaller fraction of the parent body’s interior. The ureilites’ moderate depletions in incompatible elements are difficult to reconcile with a fractional fusion model. It is not plausible that melt formed grossly out of equilibrium with the medium-sized ureilite crystals. The alternative to pressure-controlled smelting, i.e., a model of gasless or near-gasless anatexis, has very different implications for the size and evolution of the original parent body. To yield internal pressures prohibitive of smelting in even the shallowest and most ferroan portion of its anatectic mantle, the body would have to be larger than roughly 690 km in diameter. A 400 km body would have approximately 12 vol% of the interior (or 13 vol% of the interior apart from the thermal “skin” that never undergoes anatexis) prone, if both extremely shallow and extremely ferroan, to mild smelting. Gasless anatexis also implies that this large parent body was compositionally, at least in terms of mg, grossly heterogeneous before anatexis, probably (in view of the oxygen isotopic diversity) as a result of mixed accretion.

Introduction

As reviewed by Goodrich et al. (2004), ureilites are extremely aluminum (feldspar, basalt)-depleted asteroidal-mantle peridotites, containing typically about 2/3 olivine and 25% pyroxene (mostly pigeonite). The number of ureilites has reached well over 100, which qualifies them as the second most numerous variety of achondrite (only HEDs are more common). Yet, except for polymict breccias and some exotic (albeit not evidently impact-injected) veins in one meteorite (Elephant Moraine [EET] 96001: Warren et al. 2006b), ureilites are devoid of observable feldspar. Ureilites show great diversity in terms of modal olivine, pigeonite, orthopyroxene and augite proportions, and in the compositions, especially in the mg (≡ mole% Mg/[Mg+Fe]) ratios, of these silicates (e.g., olivine ranges from Fo75 to Fo96). They are remarkably consistent in other respects. They contain important proportions (average 3 wt%) of carbon, present as a variety of phases including amorphous “C-matrix,” graphite and diamond. The rims of the olivines show distinctive FeO reduction: tiny inclusions of Fe-metal scattered amidst olivine that is reverse-zoned toward pure Mg-olivine. In contrast, the mafic-silicate cores in any individual monomict ureilite are uniform in composition. Ureilites exhibit a remarkably discontinuous thermal history: slow cooling (if not heating) early, but later, suddenly, cooling became very rapid (Miyamoto et al. 1985; Takeda et al. 1989; Herrin et al. 2010).

Takeda (1987) proposed that ureilites formed as asteroidal mantle restites, contrary to the then-popular model (e.g., Berkley et al. 1980; Goodrich et al. 1987) of origin as igneous cumulates. The discovery (Clayton and Mayeda 1988; cf. Kita et al. 2004) of great oxygen-isotopic diversity among ureilites has led to a general consensus (e.g., Warren and Kallemeyn 1992; Scott et al. 1993; Singletary and Grove 2003; Goodrich et al. 2004; Kita et al. 2004; Warren and Huber 2006; Herrin et al. 2010) that most, if not all, ureilites formed as mantle restites.

The role of smelting (“the chemical reduction of a metal from its ore by a process usually involving fusion”—Thrush 1968) in ureilite petrogenesis remains controversial. Many authors assume that depth-linked, pressure-controlled smelting was an important aspect of the early anatectic stage of ureilite evolution, during which the ureilites acquired their diverse mafic-silicate core compositions (e.g., Singletary and Grove 2003; Goodrich et al. 2004; Wilson et al. 2008). In addition, those core compositions survive despite a late, abortive very high −dT/dt episode that caused reduction in the rims of nearly all ureilite olivines (e.g., Goodrich et al. 2004); and that late, disequilibrium, −dT/dt, postmelting process is often regarded as a kind of “smelting” in ureilites (e.g., Sinha et al. 1997; Hutchison 2007; Janots et al. 2011).

Detailed models have been developed for anatectic smelting as the main control on ureilite compositional diversity, with various specified combinations of pressure P and composition (silicate-core mg) during smelting (Goodrich et al. 2004, 2007; Wilson et al. 2008; cf. Singletary and Grove 2003). In this work, I put these models to a test. How well do the specified combinations of P and composition (Fo), along with implied combinations of those parameters with equilibration temperature TE, match a correlation between TE and silicate-core mg (Singletary and Grove 2003) among real ureilites? Also, how well do they match with the ureilites’ skewed (toward low mg: Downes et al. 2008) compositional frequency distribution?

Other aspects of the anatectic, pressure-controlled smelting model will also be critiqued. The alternative model, holding that very little smelting occurred apart from the late, rapid −dT/dt episode (Warren and Kallemeyn 1992; Warren 1996), is not only more mundane in terms of the style of anatexis but also more intriguing in terms of implications for heterogeneous accretion of a large, differentiated, and carbon-rich planetesimal.

Samples, Methods, and Results

As part of this work, silicate compositions were determined for 14 previously unstudied, or little-studied, ureilites: Almahata Sitta, EET 90019, Chocolate Mountains, Graves Nunataks (GRA) 98032, LaPaz Icefield (LAP) 03587, Larkman Nunatak (LAR) 04315, Meteorite Hills (MET) 01083, Northwest Africa (NWA) 766, NWA 1462, NWA 1464, NWA 2225, NWA 4852, NWA 6818, and NWA 6820.

For preliminary mineralogical reconnaissance, backscattered electron (BSE) and secondary-electron images and a few semiquantitative (EDS) mineral compositions were acquired using a LEO 1430 SEM or a JEOL JXA-8200 electron probe. Quantitative mineral compositions were determined using wavelength-dispersive detectors on the JXA-8200. Analyses were run at an accelerating voltage of 15 KV, with focused beam and count durations of 15–20 s. Results are shown in Table 1.

Table 1.   Results from electron-microprobe analysis of pigeonite and olivine in 14 ureilites.
 PigeoniteTb degrees COlivine (cores)
SampleSiO2 wt%TiO2 wt%Al2O3 wt%Cr2O3 wt%FeO wt%MnO wt%MgO wt%CaO wt%Sum wt%N. averagedFo mole%N. averaged
  1. aAlmahata Sitta stone 27 is a large clast of unbrecciated ureilite, described by Warren and Rubin (2010).

  2. bTemperature of equilibration estimated from pigeonite composition using method of Singletary and Grove (2003).

  3. cIn GRA 98032, LAP 03587, and especially LAR 04315, pigeonite-localized impact smelting accompanied by minor reduction of olivine (see Warren and Rubin 2010) complicates identification of unsmelted core compositions. For LAR 04315, the listed olivine Fo is based on a slight extrapolation (Warren and Rubin 2010).

  4. Notes: EET = Elephant Moraine; GRA = Graves Nunataks; LAP = LaPaz Icefield; LAR = Larkman Nunatak; MET = Meteorite Hills; NWA = Northwest Africa.

Almahata Sitta 27a55.170.050.521.028.830.4430.622.4299.0919127585.49
Chocolate Mountains55.430.070.461.0910.050.4428.633.0399.2031125282.25
EET 9001956.510.140.761.016.230.4630.634.54100.2822127689.312
GRA 9803255.020.030.211.0912.400.4126.613.7399.503c122776.56c
LAP 0358754.490.060.951.2013.110.4024.724.9599.8813c120674.724c
LAR 0431555.110.080.711.0810.230.4426.975.1699.7790c1236810c
MET 0108356.850.020.890.864.810.2933.322.6399.6710130491.95
NWA 76653.840.141.891.4111.370.4323.086.9799.1426119676.335
NWA 146253.710.131.931.2311.050.4424.107.0999.679120878.110
NWA 146453.610.131.911.2210.980.4324.086.9899.3616120877.939
NWA 222554.100.090.851.229.840.4127.564.9999.0513124682.318
NWA 485255.690.110.801.067.510.4929.454.6199.7213126487.426
NWA 681853.920.111.861.3611.190.4424.796.0699.742121378.78
NWA 682054.880.050.661.0811.680.4428.013.0299.826124279.78

After olivine, the most common mineral in ureilites (occurring in 5/6 of them) is the clinopyroxene pigeonite. For estimation of TE, I use a pigeonite-based technique developed by Singletary and Grove (2003), whose experiments, specifically simulating ureilitic systems, indicate that

image(1)

where TE is in °C and XMg-Pi and XCa-Pi are the mole% concentrations of MgO and CaO, respectively, in pigeonite. Figure 1a shows results for TE plotted versus olivine-core XMg-Ol (Fo). The nominal 2σ error for these results is generally close to 40°, but Singletary and Grove (2003) state that it recovers experimental temperature to “within ± 20 °C.”

Figure 1.

 Relationship between olivine-core Fo and pigeonite equilibration temperature TE (a) as constrained by ureilite mineral analyses and the method of Singletary and Grove (2003); and (b) as implied by various proposed pressure-controlled smelting models discussed in the text. In (a), open symbols denote four unusual bimodal-textured ureilites that contain augite as well as pigeonite. Labeled symbols denote selected ureilites manifesting diversity: ALH 82106, GRA 95205, LAP 03587, LEW 88774, MET 01083 and NWA 766. Data sources for (a), other than Singletary and Grove (2003) and Table 1, include: Wlotzka (1972), Neuvonen et al. (1972), Berkley et al. (1980), Berkley (1986), Goodrich et al. (1987), Takeda (1987, 1989), Treiman and Berkley (1994), Weber and Bischoff (1998), Tribaudino (2006), Warren et al. (2006), Ikeda (2007), Downes et al. (2008), Warren and Rubin (2010) and Herrin et al. (2010). For LEW 88774, TE is shown as listed by Singletary and Grove (2003), but with a down arrow, because this was probably not a valid application of their method. LEW 88774 is an exceptional ureilite with exsolved pyroxenes; Chikami et al. (1997) estimated from compositional-scale aspects of the exsolution that the equilibration of LEW 88774 terminated at roughly 1160 °C.

As noted by Herrin et al. (2010), another geothermometry technique, “LCP-ol-aug,” is available for application to the handful of ureilites that contain a combination of low-Ca pyroxene, olivine, and augite (Kretz 1982; Brey and Köhler 1990). However, it is difficult to compare the LCP-ol-aug method with Singletary and Grove’s pigeonite-olivine method. Aside from using nonureilitic compositions, Kretz (1982) and Brey and Köhler (1990) designed their methods to fit LCP-ol-aug data obtained at several kilobars of pressure. Also, most of the augite-bearing ureilites are magnesian (Fo>86), and the one ferroan exception (MET 78008; Fo77) shows poor agreement between the two LCP-ol-aug results: 1300 °C per Kretz (1982), 1169 °C per Brey and Köhler (1990). In general, agreement is best (most systematic) between the Brey and Köhler (1990) variant of the LCP-ol-aug method and the pigeonite-olivine method (Singletary and Grove 2003), with the LCP-ol-aug results averaging 68 ± 25° cooler.

Figure 1a corresponds to fig. 10 of Singletary and Grove (2003) with an expanded database. Figure 1a manifests a strong (= 0.89) correlation between TE and olivine-core Fo. This trend indicates that magnesian ureilites underwent systematically far higher TE than ferroan ureilites. The indicated slope is 5.4 K per mole% Fo, and the range in apparent TE is from 1196 to 1308 °C. An equally good (= 0.89) fit is obtained as TE = 402.48ln(Fo)––528.3, and as this relationship yields a conservatively lower range in TE (from 1209 °C at Fo75 to 1305 °C at Fo95), I utilize it in the following section.

Implications for Models of Ureilite Formation

Comparison with the Anatectic, P-Controlled Smelting Model

If, as the P-controlled smelting model requires, the most ferroan ureilites correspond to the deepest origins, then Fig. 1a implies that the parent body had an inverted geotherm: cooler at deep levels than at shallow levels (Singletary and Grove 2003). Wilson et al. (2008) acknowledge this anomaly, but suggest that it might have developed as a result of the preponderant heat source, 26Al, having migrated as an ingredient in basalts that formed a composite, near-global “sill,” approximately 7 km below the surface of the body. One problem with this model is that basaltic matter is so rare among ureilites, even among polymict ones, that a common model assumes the parent body’s basalt, instead of aggregating at shallow depth, was efficiently lost to space through explosive volcanism (Warren and Kallemeyn 1992; Scott et al. 1993; Goodrich et al. 2004). The minor basaltic component that is found as clasts in polymict ureilites is preponderantly fine grained or glassy (Ikeda et al. 2000; Ikeda and Prinz 2001; Cohen et al. 2004; Goodrich et al. 2004), implying rapid cooling very near the surface of a parent body, not 7 km down.

Singletary and Grove (2006) approximately reproduced the Fig. 1a trend in a series of experimental simulations of their P-linked smelting model. However, their results show only a very feeble relationship, an anticorrelation with r= 0.37, between olivine Fo and P (a complication is that their set of 20 relevant, “saturated with olivine, pyroxene, metal, and liquid” data-pairs is ambiguously defined). The correlation coefficient remains about 0.4, even if the data set is limited to a single experimental T or small range of T (e.g., they list 18 pairs of Fo and P, for T within 30° of 1200 °C). This weak relationship between results for Fo and P seems a major shortcoming, considering that the most basic tenet of the anatectic-smelting model is that the smelting process was controlled by the extremely P-sensitive graphite-CO equilibrium. At magmatic T, the graphite-CO equilibrium should, in principle, have “a strong buffering capacity for reducing oxidized materials to below the CCO buffer” (Medard et al. 2008; cf. Holloway et al. 1992); however, for various reasons, experiments of this type are difficult (Medard et al. 2008).

No single equation could possibly cover the full gamut of ureilite silicate reduction mechanisms. Even in the late rim-reduction process, at least a trace of melt was probably present, especially in those ureilites (Warren and Rubin 2010) in which the terminal redox processing was accompanied by pyroxene-localized impact melting. A common feature of all possible reaction mechanisms is the presence of gas (CO) only on the products side, which implies that the reaction must be extremely pressure-sensitive (Berkley and Jones 1982). The olivine-rim reduction reaction, a form of “smelting” that occurred in virtually all ureilites, can be written in combination with the C–CO reaction in various ways (cf. Warren and Kallemeyn 1992), such as

image(2)

where 3(Mg3FeSi2O8) is an atomistic way of denoting 6 moles of Fo75 olivine. As discussed by Warren and Rubin (2010), ureilites in general feature an excellent correlation between core (unreduced) olivine mg and low-Ca pyroxene mg, but in some cases, shock-melting caused pyroxene to also undergo extensive reduction. That pyroxene reduction process (incontrovertibly smelting) was in molecular terms approximately

image(3)

where a simplified chemical formula, without CaO, is used for pigeonite.

Ureilites formed at such high temperature and low oxygen fugacity (with Fe-metal present) that the gas phase formed by oxidation of C must have been nearly pure CO; i.e., PCOP (Warren and Kallemeyn 1992). The solubility of CO in basaltic melt, at asteroidal pressures, is negligible (Holloway 1998). Thus, in the anatectic smelting model, the C–CO reaction (at any given TE and equilibration pressure PE) fixes the silicates’ FeO contents; in other words, their mg (e.g., olivine Fo) ratios. Selection of any two of TE, PE, and Fo amounts to specification of the third variable. 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.

Figure 2.

 Proposed combinations of pressure and olivine-core Fo in three variants of the pressure-controlled smelting model (Goodrich et al. 2004, 2007; Wilson et al. 2008). A key premise of these models is that P-controlled smelting yielded an anticorrelation between olivine-core Fo and the smelting pressure. Polynomial fits to the overall trend are used for extrapolating approximately implied pressures for intermediate Fo values.

A thermodynamics-based (Warren and Kallemeyn 1992) map of the relevant T–PCO–Fo–fO2 space is shown in Fig. 3. This figure incorporates thermodynamic calculations for both the graphite-CO equilibrium (French and Eugster 1965) and for the partitioning of FeO into olivine in the presence of Fe-metal (Williams 1972). The olivine Fo ratio is insensitive to P, but strongly linked to T and fO2. For both sets of equilibria, Fig. 3 is based on activity coefficients rather than assuming ideality. Figure 3 agrees closely, for the graphite-CO buffer as a function of T and fO2, with fig. 1 of Nicholis and Rutherford (2009; cf. Fogel and Rutherford 1995).

Figure 3.

 Curves for the C–CO buffer (light blue curves) and olivine-reduction (dark red curves) shown on a plot of temperature versus log(fO2) for the region of parameter-space relevant to ureilite genesis; based, as discussed in Warren and Kallemeyn (1992), on thermodynamic treatments of French and Eugster (1965) and Williams (1972). With pressure-controlled smelting, any specified combination of pressure and olivine-core Fo implies a unique temperature. The heavy black lines that connect combinations of 2 or 3 points (open symbols) delineate variants of the pressure-controlled smelting model as specified by: Goodrich et al. (2004), two large squares; Goodrich et al. (2007), two small circles; Wilson et al. (2008), three larger circles. The lighter (green, in color) bow-shaped curve shows the trend implied (in a P-controlled smelting scenario) by the temperature-Fo relationship observed for actual ureilites in Fig. 1a.

Figure 3 is not entirely consistent with some detailed experimental results of Walker and Grove (1993). Figure 4 of Walker and Grove (1993) shows an isotherm (for a T variously described as “approximately 1210” or “approximately 1215” °C) on a plot of P versus Fo; this isotherm is reproduced in Fig. 4. However, my diagram also shows two additional data points implied by text on page 633 of Walker and Grove (1993): “At ∼65 bars … [the isotherm] should be near Fo84”; and “We determined … that Fo76 ureilite olivine required P of ∼90 bars to suppress smelting at the experimental temperature.” These two points (which show relatively good agreement with the isotherms implied by thermodynamics; Warren and Kallemeyn 1992) suggest that the locus of the Walker-Grove isotherm is somewhat uncertain. Also, as the dashed curve in Fig. 4 indicates, when the Walker-Grove isotherm is extrapolated from its low-P (30 bar) end to 0 bar, it leaves considerable FeO (Fo97) in olivine. This extrapolated result is not plausible. There is no doubt that as P goes to zero, the fO2 of the high temperature graphite-CO equilibrium goes to extremely low values (cf. fig. 1 of Nicholis and Rutherford 2009). Conceivably, the true isotherm has a complex shape, concave as drawn by Walker and Grove but then convex, and thus does, after all, reach Fo100 at = 0. But it seems more likely that the isotherm as drawn by Walker and Grove (1993), although certainly a noteworthy constraint, is simply not accurate and/or precise enough to meet the test of interpolation between its low-P (30 bar) end and 0 bar. For purposes of this article, Fig. 3 will be assumed to most closely represent the relevant equilibria. Figure 3 has the virtue of internal consistency. It also agrees precisely with fig. 1 of Goodrich et al. (2007).

Figure 4.

 Relationship between the pressure of the graphite-CO stability boundary and olivine Fo (in the presence of silicate melt and smelted Fe-metal). Thick curve (blue, in color) shows the boundary at approximately 1215 °C, as constrained by the experiments of Walker and Grove (1993); the dashed portion of the curve (below 30 bar) is a conservatively drawn (tangential-straight instead of concave-down) extrapolation, which implausibly implies FeO-bearing Fo97 olivine is stable with melt, graphite, and Fe-metal even at zero pressure. Straight black lines show the boundary as determined for a range of temperature (1400–1600 K) from thermodynamics (Warren and Kallemeyn 1992). This diagram is amended from a version shown by Warren (1993), where the thermodynamic model was only roughly drawn, and dubiously followed Walker and Grove (1993) in showing concave-down curvature at low (less than 50 bar) pressures. Regarding the two “W & G page 633” points (referring to Walker and Grove 1993), see text.

The sets of olivine-core Fo and P combinations specified in three different models of pressure-controlled anatectic smelting (Goodrich et al. 2004, 2007; Wilson et al. 2008) imply, through Fig. 3, sets of Fo and TE combinations that are shown in Fig. 1b. Significantly, for two of the three specific models (Goodrich et al. 2004; Wilson et al. 2008), the implied overall T versus Fo trend is an anticorrelation. Even in the third model (Goodrich et al. 2007), the Fig. 1b trend is almost flat, with TE varying only from 1254 to 1273 °C. The results from pressure-controlled smelting models thus show decidedly poor agreement with the positive correlation, and at least 100 °C range in TE, of the actual ureilite trend (Fig. 1a).

The fO2, P, and TE combinations implied by Fig. 1a and P-controlled smelting are shown by the bow-shaped curve in Fig. 3. Significantly, the correlation (Fig. 1a) between Fo and TE, in conjunction with the high rate of change in Fo as a function of log(fO2) while Fo is of order 80 mole%, implies that the trend on Fig. 3 starts out (from Fo75 to about Fo85) keeping almost constant P (i.e., the trend shows a slight positive slope on Fig. 3). Only later, as the rate of change in Fo as a function of log(fO2) becomes much less (beyond about 1260 °C and Fo85) does the implied trend show a sharp decrease in P with increasing Fo.

The only way for pressure-controlled smelting to (1) yield a range in TE that approaches 100 °C, (2) match the Fo range (75–95 mole%), and (3) have the most magnesian (highest Fo, highest TE) ureilites form at the shallowest depths (lowest P), would be to contrive a variant of the model that implies a near-flat slope for the ureilite trend on Fig. 3; i.e., a much smaller range in P (total range a factor of about 2) than assumed in any of the three anatectic smelting models (Goodrich et al. 2004, 2007; Wilson et al. 2008). However, as the next section will show, when assessed in view of realistic parent-body P versus depth relationships and ureilite olivine-core Fo statistics, even those existing anatectic smelting models imply an implausibly limited pattern of diversity in P.

Depth-Sampling Relationship Implied by the Anatectic, P-Controlled Smelting Model

Statistics for olivine-core Fo distribution among ureilites are available from two sources: whole ureilites (e.g., Mittlefehldt et al. 1998) and clasts from polymict-breccia ureilites (Downes et al. 2008). Results from the two approaches agree well (Downes et al. 2008; cf. fig. 6a of Goodrich et al. 2004) and indicate a clustering near the low end of the Fo range, such that approximately 50% of ureilites have Fo < 79 mole% and only 25% have Fo > 83 mole%. A composite distribution, based on equal weighting for clasts and whole ureilites, is shown in Fig. 5. In addition, feldspathic clasts in polymict ureilites (i.e., suspected products of melts complementary to the normal ureilites) have yielded oxygen-isotopic data (Kita et al. 2004, 2006) that suggest a similar bias toward ferroan (higher Δ17O) sources. Wilson et al. (2008) proposed a sill-emplacement model to account for a ferroan bias among basaltic materials retained on the parent body (i.e., not lost by explosive volcanism). Ferroan sources, undergoing lesser degrees of smelting, generated gas-poor, moderate-buoyancy magmas that were less prone to explosive blow-off, Wilson et al. (2008) argued. However, this model of divergent magma fates does nothing to explain why the final distribution of the complementary restites (ureilites, per se) should show the observed (Fig. 5) ferroan bias.

Figure 5.

 Histogram of olivine-core Fo compared with relative amounts expected from unbiased sampling of a mantle in which ureilites form by pressure-controlled smelting. As explained in the text, if olivine composition (Fo) is determined by pressure, as assumed by Wilson et al. (2008), then any given set of assumed combinations of Fo and P will carry direct implications regarding the volume distribution of Fo, because pressure-depth (and thus, implicitly, pressure-volume) relationships within the body are constrained by Equations 4–7. The database for observed ureilites is taken from Downes et al. (2008), assigning equal weight to 108 whole ureilites and 317 clasts. Dashed curves show extrapolations to the distribution implied for the original totality of ureilites (i.e., ureilites assuming unbiased sampling of the parent body) based on the Fo-P relationship proposed in the pressure-controlled smelting model of Wilson et al. (2008; P values shown in lighter font are my own (Fig. 2) interpolations/extrapolations) and a pressure-controlled smelting model that is analogous (including assumption that = 100 km) except has the Fo-P relationship constrained by Figs. 1a and 3.

In terms of any P-controlled smelting model, the low end of the Fo distribution must be the high end for PE. A clustering of compositions toward the high end for PE is the opposite of what might be expected based on unbiased sampling of the interior volume of the parent body. The relationship between depth and volume in a sphere is such that most of the volume is concentrated toward shallow depths and low pressures; e.g., half of the volume is shallower than depth = 0.21 × radius R. Clearly, the pressure-controlled smelting model requires that ureilites sample the parent body’s interior in a highly depth-selective way. (The possibility of a gross bias in the depth-sampling of the parent body is addressed in the Constraints on the Depth-Sampling Bias Hypothesis section).

The depth-pressure relationship is worth constraining in more detail. For a uniform-density sphere, it is well known that

image(4)

where G is the universal gravitational constant, ρ is the density, R is the full radius of the body, and r is the radius below the depth. A handful of measured ureilites have room-temperature average grain density of 3300 kg m−3 (Britt et al. 2010); translation to approximately 1200 °C would imply 3200 kg m−3. However, mainly for consistency with Wilson et al. (2008), I assume a density of 3300 kg m−3. The ureilite parent body probably had a small (nascent) metallic core before the body was catastrophically disrupted (e.g., Goodrich et al. 2004; Warren et al. 2006a). However, as indicated by equation (2–65) of Turcotte and Schubert (1982), the effect on pressure is, for all but the deepest mantle and core, only slight. For example, compared with the pressures calculated by Equation 4, adding a 10 vol% core of density 8000 kg m−3 would have the effect of increasing pressures in the upper 60 vol% of the mantle (54 vol% of the body) by a factor of less than 1.01, pressures in the next-deepest 26 vol% of the mantle by factors of 1.01–1.02, and the P at the very bottom of the mantle by a factor of 1.06. These mild effects are approximately offset by assuming 3300 instead of 3200 kg m−3 for the relevant bulk density.

From Equation 4, the depth z to a given pressure is:

image(5)

Also from Equation 4, an expression for the pressure PF, at which a given fraction F of a body with radius R is at lower pressures (i.e., shallower depths), can be derived:

image(6)

Again from Equation 4, an expression for F as a function of R and PF is:

image(7)

Selected depth–pressure–volume relationships implied by Equations 4–7 are shown in Figs. 6–9.

Figure 6.

 Pressures within an asteroid calculated as a function of body radius R and volume (at lower P) fraction F using Equation 6, assuming density ≡ 3300 kg m−3. To scale to a different density, multiply the indicated P times (density/3300) squared.

Figure 7.

 The depth within a spherical, uniform-density body at which olivine evolving in a pressure-controlled smelting scenario would assume three different Fo values; calculated using Equation 5. The pressure PF implicit in the y-axis is the pressure, calculated using Equation 6, at which a given fraction F of a body with radius R is at lower pressures (i.e., shallower depths). Fo76-81 is a key range because ureilite Fo shows a strong mode (approximately 58% of all ureilites) in this range (Downes et al. 2008). Two variants of the P-controlled smelting model are shown: the model of Wilson et al. (2008), with the Fo76–81 pressure range extrapolating to 100–86 bar; and a variant constrained to be consistent with Figs. 1a and 3, and thus with the Fo76-81 pressure range extrapolating to 79.7–75.4 bar.

Figure 8.

 The same results as in Fig. 7, but here with the depth translated into volume percent of the body shallower than the given level; calculated using Equation 7.

Figure 9.

 The fraction of a spherical, uniform-density body with pressure in the range that, in a P-controlled smelting scenario, would yield Fo76–81 olivine. Here, the Fo-P relationship is derived by extrapolation from three variants of the P-controlled smelting model: the model of Wilson et al. (2008), with the Fo76–81 pressure range extrapolating to 100–86 bar; an amalgamation of that model and those of Goodrich et al. (2004, 2007) (see Fig. 2), with the Fo76–81 pressure range extrapolating to 100–83 bar; and a variant constrained to be consistent with Figs. 1a and 3, and thus with the Fo76–81 pressure range extrapolating to 79.7–75.4 bar. At small body diameter (DB), the pressure even at the center of the body is insufficient to stabilize Fo76 olivine in the presence of hot graphite.

From Figs. 1a and 3, the most ferroan (Fo75) ureilites might, in principle, have formed under conditions of TE≈ 1209 °C and smelting pressure  78 bar. The most magnesian (Fo95) ureilites might, in principle, have formed under conditions of TE≈ 1305 °C and  31 bar. For the Fo range of the spike in the ureilite compositional spectrum, Fo76–81 (encompassing approximately 58% of all ureilites), the TE range (Fig. 1) is ≈ 1215–1240 °C and the smelting P range is (in principle; Fig. 3) ≈ 80–75 bar. The depths (z) and vol% shallower (F) implied by these pressures are shown as a function of parent body size (diameter) in Figs. 7 and 8. These results indicate that if the pressure-controlled smelting model is to be reconciled with Fig. 1a, most ureilites have to be derived from a remarkably narrow band of depths within the parent body. A parent body with diameter DB <140 km is inconsistent (and not just in terms of the pressure-controlled smelting model) with the existence of olivine-core Fo75 ureilites with TE approximately 1200 °C. For intermediate assumptions regarding the body size, i.e., DB of about 145–400 km, the provenance of the approximately 58% of ureilites associated with the compositional (Fo76–81; Fig. 5) spike is implied to be a peculiarly narrow band deep within the parent body’s interior. Figure 9 indicates that the volume fraction of the body within the spike’s required 75–80 bar P range is never more than 3.2% (and even that only applies if the body diameter DB is very close to 180 km). Even at this optimal diameter, the fraction of the body with Fo76–81 olivine is too low by a factor of 18 compared with the volume fraction suggested by the observed compositional (Fig. 5) spike, assuming that depth bias was close to neutral during the sampling of the body by ureilite meteorites.

Figures 7–9 also show analogous results from modeling of the Fo76, Fo81, and Fo95 olivine pressures, not based on Figs. 1a and 3, but by extrapolation from three Fo-P combinations (one of which is Fo76, = 100 bar) suggested in fig. 1 of Wilson et al. (2008). The extrapolation technique is shown in Fig. 2. Overlooking for the sake of argument the problem of inconsistency (under the assumption of P-controlled smelting) with Figs. 1a and 3, and the inconsistency with any Fo76 olivine unless DB is at least 162 km, the Wilson et al. (2008) Fo-P relationship is slightly less improbable in its volume-sampling implications. For the Fo76–81 spike, the volume fraction of the body in the controlled-smelting-appropriate P range (Fig. 9) is far greater, reaching, at DB approximately 192 km, 8.6 vol%. Still, it is lower by a factor of 7 than the volume fraction suggested by the observed compositional spike (Fig. 5), assuming that depth bias was neutral during the sampling of the body by ureilite meteorites.

Figure 9 also includes results from analogous modeling of the Fo76-81 pressures, based on extrapolation (Fig. 2) from the total of seven Fo-P combinations (three of which are Fo76, = 100 bar) suggested in Wilson et al. (2008) and Goodrich et al. (2004, 2007). These results are only slightly less problematic than the results based on extrapolation from the Wilson et al. (2008) Fo-P combinations alone.

Figure 9 alone does not convey the full extent of the problem with this general class of models. The highest results for the Fo-peak linkable volume, where Fo76–81 olivine would form, occur in models in which the Fo76–81 olivine is located deep within the body, where such a strong sampling bias seems unlikely. For example, in the models consistent with Figs. 1a and 3, the Fo76–81 zone cannot constitute >2% of the body unless at least 38 vol% of the mantle is shallower than the top of the Fo76–81 zone (Fig. 8).

Discussion

Terminology

As Warren and Huber (2006) have previously noted, the term smelting, as applied in ureilite petrology to denote the late-stage and abortive redox processing that led to the characteristic reduced (low-FeO, Fe-metal-sprinkled) rims on ureilite olivines, is arguably a misnomer. The ureilite redox processing was short-lived because its onset coincided with a sudden shift from near-steady temperature to a regime of high –dT/dt (Miyamoto et al. 1985), so that in most ureilites, no significant melting accompanied the reduction. (Warren and Rubin [2010] note a few exceptional instances where impact melting, concentrated within pigeonite, accompanied the onset of the redox processing, i.e., where the term smelting seems entirely appropriate.) Semantically proper or not, the notion that the terminal redox episode was in general a case of “smelting” is entrenched in the literature (e.g., Sinha et al. 1997; Hutchison 2007; Janots et al. 2011). Confusion results, because to reject the related but thoroughly distinct hypothesis of pressure-controlled smelting during the main stage of ureilite anatexis can be seen as denying an obvious truth about ureilite evolution.

To alleviate confusion, it may be helpful to give a short yet descriptive name to the alternative hypothesis. I propose to call it gasless anatexis. As will be discussed below, possibly not quite all ureilite anatexis took place in total absence of CO gas (smelting). But I infer that it generally did, as may have occurred simply because the original parent body was big (high-pressure) enough to forestall anatectic smelting.

As an aside, controversy about igneous graphite-CO equilibria is not limited to the field of ureilite studies. Sato (1979) envisaged that the source regions of mare basalts deep in the lunar mantle contained traces of COx gas, and had fO2 constrained by the C-CO buffer. COx gas may have helped drive the ascent of the mare magmas even from an early stage, Sato (1979) suggested (cf. Wilson et al. 2008). Sato’s model implies a high fO2 for the original (pregraphite-oxidation) mare source region. He even speculated that as much as 0.80 wt% Fe2O3 may have been present. Longhi (1992) expressed skepticism about Sato’s model, noting that reactions involving graphite can only reduce silicate minerals in the presence of a C-rich gas phase, “and a free-gas phase in the Moon’s mantle seems unlikely.”Fogel and Rutherford (1995) agreed with Longhi, finding “no compelling reason to believe that the mere presence of graphite buffers the oxygen fugacity of the lunar interior.”

Constraints on the Depth-Sampling Bias Hypothesis

The “Largest Offspring” Model

In defense of the anatectic smelting model, Hartmann et al. (2011) conjectured that the depth-sampling represented by the ureilites may be grossly biased. They cite the modeling of Michel et al. (2002) to claim that the “few largest offspring” from disruptive collisions “tend to consist of materials derived from well-defined, restricted regions within the parent.” The disruption simulations of Michel et al. (2002) generally leave one exceptionally large fragment: e.g., 60 vol% of the parent. However, the modeling of Michel et al. was ill-suited to the ureilite problem. The target was modeled as a “monolith,” whereas in the ureilite break-up, the target was a weak mass of partially molten mush, with disintegrative tendency further enhanced by the vast jetting of CO gas that occurred (as by-product of the redox that formed the ureilites’ reduced rims: Warren and Rubin 2010). Most importantly, application of this model to ureilites would be inconsistent with the evidence for uniformly abrupt cooling of these materials (Miyamoto et al. 1985).

In the words of Goodrich et al. (2004, p. 291): “All monomict ureilites show evidence of extremely rapid cooling (on the order of 10 °C h−1 through the range 1100–650 °C) accompanied by a sudden drop in pressure. … This common PT history suggests that they are all derived from a single UPB [parent body], and were excavated, while still hot, by a single, major impact, possibly involving catastrophic disruption of the whole body (Takeda 1987; Warren and Kallemeyn 1992).”Herrin et al. (2010) have noted that the cooling became so rapid that the bodies in which the ureilites reposed in the short-term aftermath of the disruptive impact must have been “tens of meters in size or smaller.”

For comparison, to account for the wide diversity of ureilite composition (Fo), the P-controlled smelting model (Goodrich et al. 2007; Wilson et al. 2008) postulates that the ureilites sample most of the mantle depth range of an original ureilite body that was approximately 100 km in radius. This size is roughly a factor of 1010–1012 times more voluminous than the sizes inferred (Herrin et al. 2010) for the early postdisruptive phase. Thus, for ureilites, any “largest offspring” model is irrelevant. If there ever was a conspicuously large daughter body, none of the known ureilites came from it. They came from a second-generation large body (with a nearly pure-ureilitic megaregolith: e.g., Warren and Kallemeyn 1992; Goodrich et al. 2004), which in turn assembled from billions of small bits of the original body; and those bits probably underwent considerable jumbling, in part due to vast jetting of CO gas (Warren and Rubin 2010), before the reassembly. Given this evidence for disruption into relatively tiny bodies, a strong sampling bias toward origin deep in the original parent body, i.e., efficient depletion of shallow-origin material from the population of reassembly bodies, would require some additional complex process not yet conjectured.

Constraints on the depth-sampling bias hypothesis also include:

Putatively Shallow Ureilites

The putative avoidance of shallow-origin material would have to be strong yet far from total; i.e., the final ureilite population includes highly magnesian pieces that, according to the P-controlled smelting model, must have originated at shallow locations within the original body.

Undersampling of the Thermal “Skin”

Confirming that the depth-sampling represented by our samples is not completely free of bias, samples from the thermal “skin” of the original parent body are rare or absent. Within the skin layer (and possibly even a short distance further down), T never becomes hot enough for anatexis. Wilson et al. (2008) estimated that a solid-rock diffusivity will result in a skin thickness of about 8 km. As discussed by Warren (2011a; e.g., his fig. 20) in detail, the skin’s base position depends on a somewhat arbitrary choice for θ, i.e., the ratio (TbaseTsurface)/(TdeepTsurface); on the duration of the thermal evolution; and especially on the material’s thermal conductivity. A skin consisting of porous, poorly conductive megaregolith would not be nearly so thick. Much of the skin layer would undergo compressive sintering, and that process would be sensitive to the pressure near the base of the skin (Warren 2011a), which in the context of the P-controlled smelting model (e.g., Wilson et al. 2008) is only about 20 bars (Figs. 3 and 5). In short, zskin is difficult to constrain and somewhat model-dependent. The best we can say is that skin thickness, equating “skin” with material that avoids anatexis, was probably within a factor of two of 5 km. For the body size stipulated by Wilson et al. (2008), DB=200 km, a zskin of 5 km implies that the skin constitutes 7 vol% of the body.

However, much of the skin layer (the upper half or more; particularly at the low P implied by Wilson et al. 2008) may never have sintered enough to become dense and coherent; and the scarcity of such fragile material among our meteorites might stem from some late-stage physical differentiation processes, such as a tendency to not survive passage through Earth’s atmosphere. On the other hand, the deeper, more sintered half of the skin layer lacked the interstitial melt that probably remained within, and weakened, the anatectic (ureilitic) mantle; so the deeper skin would have been relatively resistant to disintegration during the disruptive impact. Another difference: the skin matter would not (in general, unless strongly impact-heated) have jetted large proportions of CO gas in the aftermath of the disruption. These different disruption-response characteristics may have caused the skin matter to generally reassemble faster, and thus possibly systematically deeper within the 2nd-generation large body, or even within a separate 2nd-generation body.

The skin matter might be better represented as a component in polymict ureilites, but distinguishing it among the polymict ureilites’ other chondritic debris components (Ikeda et al. 2000) must be difficult. The recent Almahata Sitta fall has surviving porous regions, although available isotopic data neither confirm nor counter-indicate that these porous materials are close relatives of “normal” ureilites (Rumble et al. 2010).

Undersampling of Unsmelted Deep Interior

Along with the putative bias against shallow origin, the anatectic smelting model also implies that the final ureilite population became very strongly biased against origin deeper than the level where P became great enough to prevent all oxidation of carbon (i.e., smelting). Goodrich et al. (2004) and Wilson et al. (2008) concede that such a level probably existed. They assume that it coincided with the most ferroan ureilites (Fo75), and that a large portion of the deeper mantle was never smelted and thus retained ferroan (Fo65) olivine. In the Wilson et al. (2008) model, the distance between the Fo65 deep interior and the supposedly oversampled compositional peak at Fo78 is only about 3 km (Fig. 5; cf. fig. 1 of Wilson et al.). Yet, that Fo65 portion of the original parent body’s mantle remains completely absent among the population of many hundreds of different ureilites (including clasts) that have been characterized to date. Goodrich et al. (2006) posited that NWA 1500 might conceivably be such a material, but they ultimately admitted that the low-δ18O, moderate-δ17O oxygen isotopic composition and normal (more gradual) cooling of NWA 1500 render such an interpretation unlikely.

Preanatexis: Δ17O Stratification, Fractionated Ca/Al, yet mg Uniformity?

A key premise of the pressure-controlled anatectic smelting hypothesis is that the starting material was a carbonaceous-chondritic material, uniform in many aspects of composition, most crucially in terms of oxide mg (Fo). However, among ureilites, the diverse core-silicate mg ratios that this hypothesis assumes formed in response to P-control show an anticorrelation with Δ17O (e.g., fig. 7 in Downes et al. 2008), a ratio upon which igneous differentiation processes have virtually no effect. Thus, the P-controlled smelting model implies that the parent body’s mantle began anatexis with an O-isotopic stratification: from deep, higher Δ17O material, to shallow, lower Δ17O material. A related postulate (Goodrich 1999; Goodrich et al. 2002, 2004, 2007) is that the putative uniform starting material had a highly fractionated Ca/Al ratio, about 2.5 times chondritic, in order for the anatectic-smelting process to yield a mainly olivine-pigeonite (rather than olivine-orthopyroxene) residue. A high Ca/Al for the starting material has also been inferred on the more direct basis of the observed average value for this ratio in ureilites (Singletary and Grove 2006), although this outcome is at least equally well explained as a simple result of the quantitative removal of plagioclase by the ureilite anatexis.

In an abstract, Goodrich et al. (2002) suggested that both O-isotopic layering and Ca/Al enhancement developed as a result of “radial flow of fluid” (also described as “water-rock mixing” in a brief recap within Goodrich et al. 2004) during preigneous aqueous alteration of a CV-like parent body. “Ca may have been mobilized and concentrated during preigneous, parent-body aqueous alteration and dehydration… . The range of O-isotopic compositions of ureilites … is consistent with this suggestion … . [as] stratification in Δ17O … may have been established … during alteration and dehydration/heating.” Consistent with such a model, various authors have inferred from studies of components within chondrites that planetesimal water tended to have high Δ17O compared with most chondritic silicates (e.g., Wasson 2000; Zolensky et al. 2008). However, as noted by reviewer Hilary Downes, it might be expected that the shallow mantle would undergo more extensive hydrothermal processing; i.e., would acquire higher Δ17O, in comparison with the deeper mantle (Young 2001). But the P-controlled smelting model has the shallowest ureilites undergo the most smelting, and thus end up most magnesian. This leads to another contradiction, because magnesian ureilites tend to have the lowest Δ17O (Downes et al. 2008; Fig. 7).

For constraining the nebular provenance of the ureilite starting materials, the remarkable Δ17O diversity is only one aspect and, in isolation, a potentially misleading aspect of the story. As reviewed by Warren (2011b), recent measurements for Cr, Ni and Ti isotopes in all kinds of planetary materials, when viewed in combination with one another and Δ17O, show unequivocally that the ureilites are fundamentally unrelated to carbonaceous chondrites. This overturns the decades-long consensus view (as just two examples, Warren and Kallemeyn 1992; Goodrich et al. 2004) that the starting matter was carbonaceous-chondritic. Among many important implications (Warren 2011b), one is that the amount of water originally accreted to the parent body, and thus its potential for hydrothermal alteration, may not have been as ample as analogy to carbonaceous (e.g., CI, CM) chondrites would suggest.

The putative need for a high Ca/Al ratio for the ureilite source matter to leave pigeonite-rich residues is sensitive to other assumptions about the detailed nature of the starting material. In a variation on the same forward modeling approach used by Goodrich (1999), Kita et al. (2004) showed that substituting CM for CI chondrites in the anatexis yields (despite chondritic initial Ca/Al) pigeonite-rich residues. Data of Kita et al. (2004; cf. Ikeda et al. 2000; Ikeda and Prinz 2001; Cohen et al. 2004) also indicate that feldspathic clasts in polymict ureilites generally do not have high but low Ca/Al, in comparison with other known achondrites.

Like other aspects of the pressure-controlled smelting model (see Warren and Huber 2006; Warren et al. 2006a), the hypothesis of alteration engendering enhanced Ca/Al leads to a mass balance problem. As Goodrich et al. (2002) admit, “Significant fractionation of Ca from Al during condensation and accretion appears highly unlikely.” Thus, the bulk Ca/Al ratio of the parent body was presumably for practical purposes chondritic. The alteration hypothesis appeals to mobilization of Ca (“Ca may have been mobilized and concentrated …”). Al is far less prone to mobilization in aqueous fluids (Young et al. 2003); and moreover, if Ca/Al enhancement had arisen largely by depletion of Al, including 26Al, the source material might never have undergone the consistently high degree of anatexis characteristic of the ureilites. Also, an aqueous alteration so intense that it significantly mobilized Al would probably have engendered comparable if not greater heterogeneity in the preigneous distribution of a water-soluble oxide such as MgO; i.e., in the preigneous mg.

Assuming little mobilization of Al was involved, the enhanced Ca/Al could only arise by complementary depletion of Ca from a large volume of the approximately chondritic parent body. The volume of the Ca-depleted region must be by conservative estimation (allowing for the possibility of slight Al mobilization, and also recognizing that the Ca depletion would never be quantitative) at least twice that of the 2.5-times enriched region. A mass balance problem arises, because the P-controlled smelting model typically assumes that the ureilite source region constituted most of the interior of the body. For example, Wilson et al. (2008) postulate that the body’s diameter was 200 km, and the various smelting pressures they specify imply that the ureilite source region constituted more than 70 vol% of the body (Fig. 8). The <30 vol% of the body available to serve as the complementary Ca-depletion zone is too small by a factor of (70 × 2)/30, i.e., 5. In principle, this Ca mass balance problem might be reduced by appeal to a larger parent body, in which the pressure range (i.e., the volume) required for the range of putative ureilite smelting outcomes is small in comparison with the overall volume of the body. However, invoking a parent body much larger than 200 km in DB would have the drawback of implying that the Fo76–81 spike in ureilite compositions represents an even smaller fraction of the parent body’s interior (Fig. 9).

Melt Porosity During Anatexis

Another postulate championed by advocates of the anatectic smelting hypothesis is that in general the ureilite anatexis occurred as “from the point of view of geochemical modelling … perfect fractional melting” (Goodrich et al. 2007, p. 2888; cf. Wilson et al. 2008); i.e., melt was removed almost quantitatively, leaving minimal melt porosity, at all times during the melting process. According to Goodrich et al. (2007), the anatectic melt porosity was never more than 2%; and in the main stage of melting (after melt interconnectivity had “very quickly” been established) the porosity was “at most” approximately 0.3%. Efficient elimination of residual porosity during the anatexis would be consistent with the assumption that CO gas was forming by smelting, as the gas would tend to dilate the material and thus facilitate melt egress. However, in the model of Goodrich et al. (2007; their fig. 9), for typical (e.g., >65 bars) pressures, gas production (smelting, triggered by T reaching the intersection between the P-sensitive graphite-gas curve and the olivine-silica-metal buffer) does not begin until the anatexis is half complete.

Disequilibrium for Incompatible Elements?

Normally, a porosity as low as 0.3% during anatexis leads to depletions of incompatible elements, e.g., the rare-earth elements (REE), far more extreme than the observed ureilite depletions; and thus Warren and Kallemeyn (1992) and in more detail Warren et al. (2006a) inferred that the efficiency of melt extraction was probably moderate, with a melt porosity of not much less than 10 wt%. However, Goodrich et al. (2007) have argued that during the brief period of ureilite anatexis (which ended about 5 Ma after the formation of the solar system: Nyquist et al. 2009; Goodrich et al. 2010), the slow rate of diffusion of REE in pyroxene and plagioclase would not have allowed equilibrium between the grain interiors and the melt.

Goodrich et al. (2007) modeled diffusion based on simple Arrhenius-plot extrapolations from data (Van Orman and Shimizu 2001; Van Orman et al. 2002) obtained for solid diopside no hotter than about 200 K below its melting temperature. However, Dimanov and Ingrin (1995) found that diffusion in diopside (they studied Ca, but the effect for REE is presumably analogous) enters a different and much faster mode when T is within about 148 K of the melting temperature. They attribute this effect to premelting, a phenomenon of relaxation of the crystal lattice at near-melting temperature (cf. Richet et al. 1994; Bouhifd et al. 2002). As a result, the diffusion coefficient (Dd, m2 s−1) is faster by a factor of 100 (2.0 log units) than an Arrhenius-plot extrapolation from data outside the premelting regime (Van Orman et al. 2002) would imply. Whether premelting is quite the same, in the deep interiors of crystals whose melting T is affected (lowered) by cotectic interaction with surrounding materials, is admittedly not certain, but there is no reason to presume that such circumstances make a great difference.

Another problem with the hypothesis of disequilibrium anatexis is that Goodrich et al. (2007) assumed too coarse a grain size. Ureilites are often said to be “coarse grained,” but actually their constituent grains are medium-sized (it is the characteristically equant shape of their grains, and not so much the grains’ sheer size, that, along with other traits, indicates initial crystallization in a low dT/dt environment). Berkley et al. (1980) found that among eight ureilites, the average grain’s long dimension is 1.1 mm. The true average dimension was not measured, but assuming 2:1:1 as a typical aspect ratio for pyroxene and plagioclase (REE are extremely incompatible with olivine), the average most diffusion-length-relevant (shortest) dimension is probably about 0.55 mm, equivalent to a radius a of about 0.3 mm (Van Orman and Shimizu [2001] infer no anisotrophy in the REE diffusion rate in pyroxene). Goodrich (1992), reviewing a data base of about 40 monomict ureilites, described the average grain size (maximum dimension) as “approximately 1 mm.” However, Goodrich et al. (2007) modeled the grains as circular and 1 mm in radius.

The diffusion length 2(Ddt)0.5 provides a measure of how far diffusion will be effective in a time t. In a realistic ureilite anatexis scenario, this length is approximately the (average) short grain dimension, i.e., about 1/3 as long as assumed by Goodrich et al. (2007); and also, if the true relevant Dd is 100 times greater, the diffusion length increases 10 times that faster assumed by Goodrich et al. (2007). Looked at another way, the time scale for a given extent of diffusion, under these changed assumptions, is about 100/(1/3)= 1000 times shorter than estimated by Goodrich et al. (2007). On fig. 17 of Goodrich et al. (2007), the 10 Ma curve might be thought of as representing 10 ka, and the 1 Ma curve as representing 1 ka.

This calculation of a factor of about 1000 shorter diffusive equilibration time assumes that the relevant grain dimensions were the final, observed dimensions. More realistically, the grains underwent growth as anatexis proceeded. Wilson et al. (2008, p. 6165) assumed that the “upper end” of the “expected range of grain lengths” during the main stage of anatexis was 0.3 mm. Experiments by Lo Casio et al. (2008) suggest that modeling of volume diffusion is an oversimplified way to constrain the issue of disequilibrium during anatexis, because continual dissolution and reprecipitation have the effect of greatly enhancing the rate of equilibration between solid phases and melt.

Thus, for various reasons, the Goodrich et al. (2007) model probably overestimates the potential for disequilibrium between grain interiors and melt. The ureilites’ typically moderate depletions of incompatible elements (Warren et al. 2006a) stand as significant evidence in favor of a moderate porosity during anatexis.

Other Evidence

Goodrich et al. (2004) suggested that some magnesian ureilites formed as paracumulates, i.e., as uncommonly “mushy, cumulate-like” restites. Downes et al. (2008) inferred that the “Hughes cluster” of several ureilites that combine magnesian silicates with relatively high Δ17O and Mn/Fe (the best-known examples, FRO 90054 and Hughes 009, are also distinctive for having melt inclusions: Goodrich 2001) formed when a “large volume” of percolating melt reacted with restitic mantle material. Goodrich (1999) suggested that the poikilitic/“bimodal” texture of the extremely ferroan (Fo75) Lewis Cliff (LEW) 88774 (and also, by implication, several other, ferroan-bimodal ureilites) reflects “reaction with pore liquids” in a cumulate-like fashion.

Melt Porosity at the End of Anatexis

The gasless anatexis model does predict extremely low final melt porosity. As discussed elsewhere (Warren and Huber 2006; Warren and Rubin 2010), the end of anatexis coincided with the onset of graphite-fueled redox processing (loosely, smelting), which generated voluminous and ubiquitous CO gas. That gas in turn caused ubiquitous dilation before it was squeezed and blown out of the interior. The dilation and explosive outflow of gas both amplified the disruption begun by the impact, and facilitated the final egress of interstitial melt. Any ureilite that underwent the postdisruption “smelting” process (i.e., all or virtually all of our samples) is a ureilite that ended its igneous evolution in a dilated state with effluent gas sweeping out all but tiny fractions of whatever melt was present immediately prior to the catastrophic disruption of the parent body. Thus, the extreme depletion of basaltic matter (Al, feldspar) observed in the final ureilites bears no relation to the melt-porosity that was retained during gradual anatexis prior to the catastrophic disruption.

The Alternative to Anatectic Smelting

The gasless anatexis model simply assumes that the ureilites’ solid elemental carbon, approximately 3 wt% on average, remained stable during anatexis, although in the immediate aftermath of the catastrophic disruption it did become fuel for the ureilites’ distinctive rim-reduction form of redox, which is often (e.g., Sinha et al. 1997; Janots et al. 2011), despite its occurrence at −dT/dt, considered a form of smelting. Of the two key prerequisites for the gasless anatexis scenario, one is a given: that 3 wt% of carbon survived against oxidation in the crescendo of thermal metamorphism that presumably preceded anatexis (it is not so obvious that such would be the case with a parent body small enough to be susceptible to widespread anatectic smelting). The only other key prerequisite is that the original parent body was big enough, i.e., had an interior P regime high enough, to continue preventing oxidation of the carbon as anatexis proceeded.

The constraint on the requisite size is a lower limit, from the requirement nearly all of the mantle below the thermal-conductive “skin” must have been at P high enough to prevent carbon-fueled redox in even the most susceptible (i.e., FeO-rich, Fo75) ureilites. Again, the skin bottom is assumed to correspond to the shallowest level that becomes hot enough for anatexis. Assuming TE=1205 °C (Fig. 1a), the redox equilibria (Fig. 3) imply P must be greater than about 80 bars. The ureilites, at least the ferroan ones, originated on a large parent body.

Above, the issue of the thermal skin’s thickness zskin was discussed in terms of the Wilson et al. (2008) model for P-controlled smelting in a body with DB = 200 km. If DB is larger than 200 km, a slightly thicker zskin is implied. The skin’s thickness will depend upon its thermal conductivity, which is extremely sensitive to porosity (Warren 2011a), and thus to the degree of compressive-sintering within the skin. Although lithostatic P, for a given depth and assuming similar density, simply scales linearly with DB, translation from P into sintering-compression (i.e., porosity and conductivity) and thence into zskin (at the time of disruption) would be complex and difficult (Warren 2011a). But given that the relevant P is of order 10–100 bars (a sensitive range for sintering-compression), zskin probably scales with DB raised to a power of approximately 0.5; i.e., for consistency with the above treatment of the Wilson et al. (2008) model,

image(8)

in units of km for both zskin and DB. As discussed above, the rarity or absence of “skin” matter among known ureilites implies a probable sampling bias. However, a bias against the peripheral “skin” of the body (with little propensity for gas-jetting, the upper half probably weakly compacted, and the lowest portion possibly exceptionally cohesive) is more plausible than the alternative, implied by P-controlled smelting, of a similar bias against shallow depths, along with strong bias against intermediate depths, and total or near-total bias against depths shortly below the sampling peak (see the Undersampling of Unsmelted Deep Interior section).

Assuming (for rough modeling purposes) that any skin would be slightly porous with a uniform density of 3000 kg m−3, Equation 4 implies that the pressure within the skin will be

image(9)

in units of bars and km. Substituting for zskin, the skin-bottom pressure Psb is

image(10)

in units of km for DB and bars for Psb. Ignoring slight increase in density with depth, the same pressure gradient can be used to solve for the depth at which the lithostatic P reaches 80 bar; i.e.,

image(11)

Finally, combining Equations 8 and 11 with trivial geometry, the volume fraction Vsus of the body that would be both anatectic (i.e., below zskin) and, if at the most extreme ferroan end of the ureilite compositional range, susceptible to smelting (i.e., above z80), can be calculated as a function of DB (Fig. 10).

Figure 10.

 Estimated pressure Psb at the bottom of the thermal “skin,” and volume fraction Vsus of the body that would (if extremely ferroan, Fo75) be susceptible to smelting, shown as functions of body diameter DB (see text).

According to Fig. 10, provided the original parent body size was large enough, the fraction of its interior susceptible to smelting Vsus may have been very small. There is essentially no other constraint on the size of that body, unless one attaches significance to the fact that the only body believed to supply achondrites in comparable (higher) abundance, Vesta, has DB of 530 km. A Vesta-sized original ureilite parent body would have a Vsus of roughly 4.1% (the superjacent “skin” volume would comprise a further 8.9%; so Vsus would be about 5% of the nonskin portion of the body). At DB approximately 690 km Vsus would be squeezed down to zero (Fig. 10). It might reach zero at considerably smaller DB if some of the parameter choices, e.g., the highly uncertain exponent in Equation 8, were slightly modified. Already at a diameter of 230 km, more than 50 vol% of the nonskin portion of the body would never (at the range of TE shown in Fig. 1a, or cooler) be susceptible to smelting.

If any anatectic smelting occurred, the most likely setting would be the shallowest anatectic portion of the mantle, and the result would be a few oddly magnesian (and either metal-rich or siderophile-depleted: Warren and Huber 2006) ureilites. However, the observed magnesian ureilites show systematically high equilibration temperatures (Fig. 1a), so to derive them from the shallow mantle would imply an inverted geotherm, a scenario (Wilson et al. 2008) that has been critiqued above. Another remote possibility is that the magnesian ureilites underwent anatectic smelting on a separate and smaller body. The compositional diversity and 100° range in TE (Fig. 1a) are arguably surprisingly large, for a sampling from simultaneous disruption of the deep interior of a single body (cf. the idealized geotherms depicted in fig. 4 of Wilson et al. 2008). However, if the possibility of multiple parent bodies is admitted, the magnesian ureilites might simply come from a body that had a more magnesian bulk composition. Moreover, the compositional similarity between clasts in polymict ureilites and whole ureilites tends to favor a single ultimate parent body (Downes et al. 2008). The large TE range conceivably arose in part because magnesian parcels of the mantle would probably have a more refractory solidus T, and refractory solidus behavior might retard removal of the main local heat source (26Al).

Gasless anatexis, in contrast to pressure-controlled anatectic smelting, also has profoundly different implications for the style of accretion of the ureilite parent body. The anatectic smelting model holds that the matter accreted to the ureilite parent body was originally quite uniform, and was later profoundly modified not only by early, low-T processing (leading to the observed oxygen-isotopic and putative Ca/Al diversity: Goodrich et al. 2002), but also by anatectic, P-controlled smelting, leading to the mg diversity. By postulating uniformity of the accreted material, this model also suggests a limited solar-nebular provenance for the accreted matter. In contrast, the gasless anatexis scenario implies origin of the observed diversity (including O-isotopes and mg) mainly by inheritance of primitive characteristics despite anatexis and melt loss. Gasless anatexis slightly, but consistently, increased mg in each region of residual material. Conceivably, the mg diversity stems in part from preigneous hydrothermal alteration of an originally more uniform material. However, as discussed above, the Δ17O diversity more plausibly traces back to accretion. Thus, already as matter accreted to the ureilite planetesimal, it was highly inhomogeneous. In short, the pressure-controlled smelting model invokes an unusual style of differentiation within a pure-bred parent body, while the gasless anatexis model assumes a relatively normal style of differentiation within a remarkably heterogeneous, hybrid-accreted parent body.

Conclusions

  • 1 In the context of a pressure-controlled smelting model for ureilites, any combination of olivine-core Fo and pressure implicitly fixes the oxygen fugacity as well as the temperature (TE) of final (precatastrophic-disruption) equilibration. Any combination of olivine-core Fo and TE implicitly fixes the oxygen fugacity as well as the equilibration pressure.
  • 2 The strong correlation between olivine-core Fo and TE (as constrained by the pigeonite-based method of Singletary and Grove 2003) thus implicitly fixes the evolutionary path that P-controlled smelting would have to have followed, in terms of fO2 and P as well as T and olivine Fo, as the ureilites formed.
  • 3 Postulated combinations of olivine-core Fo and P in published variants of the P-controlled smelting model imply evolutionary paths with Fo versus TE slopes that show poor agreement with the actual (constrained by Singletary-Grove pigeonite thermometry) ureilites.
  • 4 Assuming that our sampling of the mantle of the original parent body is not grossly biased, the diversity of ureilite composition (Fo) is a key constraint. The hypothesis that the ureilites derive from an atypical “largest offspring” disruption survivor body can be discarded, because cooling history evidence shows that after the disruption the known ureilites were components in a cloud of billions of small bodies. Those small bodies probably underwent considerable jumbling, in part due to jetting of CO gas before reassembly.
  • 5 The anatectic, pressure-controlled smelting model carries implausible implications of a severe depth bias in the sampling by the ureilites of the original parent body. The compositional spectrum of actual ureilites shows a bias toward low mg, and in particular a spike (58% of all ureilites) at Fo76-81 olivine (Downes et al. 2008). But only a small fraction of any body can possibly be within the pressure range that, in a smelting scenario, leads to Fo76-81 olivine. As constrained by thermodynamics, the pressure-Fo relationship implies that this fraction is never more than 3.2% (18 times too small; and that requires a body diameter very near 180 km). To make matters worse, this tiny fraction (if it is to be ≫1%) must be a thin layer centered at an intermediate depth within the body, where no straightforward model would predict a strong bias through impact-driven sampling.
  • 6 The postulated sets of combinations of olivine-core Fo and P in published variants of the P-controlled smelting model (combinations in poor agreement with the Fo-TE trend) imply less extremely biased sampling, but still extrapolate to no more than 11 vol% (5 times too little) of the body having Fo76–81 olivine.
  • 7 The Ca/Al ratio of the ureilite starting matter cannot be 2.5 times chondritic, as has been suggested, unless the whole ureilite parent body featured a grossly nonchondritic Ca/Al ratio, or else the ureilite source region was at most 50% of the whole body. But published variants of the anatectic smelting model have the ureilites coming from a region that is ≫50 vol% of the parent body; and a larger body would exacerbate the implication that the Fo76–81 spike in ureilite compositions represents but a tiny fraction of the body’s interior.
  • 8 The ureilites’ moderate depletions in incompatible elements are difficult to reconcile with a fractional (extreme low-porosity) partial melting model. It is not plausible that melt formed in gross disequilibrium with the generally medium-sized ureilite crystals.
  • 9 A model of purely gasless anatexis implies the original parent body must be very large: diameter DB greater than roughly 690 km, to yield internal pressures totally prohibitive of smelting in even the shallowest and most ferroan portion of its anatectic mantle. To the degree that a small, shallow fraction of the body is allowed to be susceptible to slight smelting, the body size constraint may be relaxed. For example, a DB of 400 km would leave 12 vol% of the body’s interior (or 13 vol% of the interior apart from the thermal “skin” that never undergoes anatexis) prone, if both extremely shallow and extremely ferroan, to mild smelting.
  • 10 Gasless (or near-gasless) anatexis also implies that this large parent body was compositionally, at least in terms of mg, grossly heterogeneous before anatexis; probably stemming from its accretion, although conceivably also from preigneous hydrothermal alteration.

Acknowledgments–– I thank Hilary Downes and Jason Herrin for very helpful, constructive reviews; A. E. Alex Ruzicka for additional helpful comments; the Meteorite Working Group for allocations of Antarctic samples; N. Gessler, D. Gregory, B. Reed, W. Sajkowicz, E. Thompson, and S. Tutorow for donations of NWA samples; and NASA for support through grant NNX09AE31G.

Editorial Handling–– Dr. Alex Ruzicka

Ancillary