# Chondritic models of 4 Vesta: Implications for geochemical and geophysical properties

M. Toplis, H. Mizzon, M. Monnereau, O. Forni, H. Mcsween, D. Mittlefehldt, T. Mccoy, T. Prettyman, M. C de Sanctis, C. Raymond, et al.

► To cite this version:

M. Toplis, H. Mizzon, M. Monnereau, O. Forni, H. Mcsween, et al., Chondritic models of 4 Vesta: Implications for geochemical and geophysical properties. Meteoritics and Planetary Science, 2013, 48 (11), pp.2300-2315. 10.1111/maps.12195. hal-02566115

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# Chondritic models of 4 Vesta: Implications for geochemical and geophysical properties

M. J. TOPLIS<fnref n="1" />*, H. MIZZON<fnref n="1" />, M. MONNEREAU<fnref n="1" />, O. FORNI<fnref n="1" />, H. Y. MCSWEEN<fnref n="2" />, D. W. MITTLEFEHLDT<fnref n="3" />, T. J. MCCOY<fnref n="4" />, T. H. PRETTYMAN<fnref n="5" />, M. C. DE SANCTIS<fnref n="6" />, C. A. RAYMOND<fnref n="7" />, and C. T. RUSSELL<fnref n="8" />

*(Received 17 February 2013; revision accepted 04 August 2013)*

**Abstract**—Simple mass-balance and thermodynamic constraints are used to illustrate the potential geochemical and geophysical diversity of a fully differentiated Vesta-sized parent body with a eucrite crust (e.g., core size and density, crustal thickness). The results of this analysis are then combined with data from the howardite–eucrite–diogenite (HED) meteorites and the Dawn mission to constrain Vesta’s bulk composition. Twelve chondritic compositions are considered, comprising seven carbonaceous, three ordinary, and two enstatite chondrite groups. Our analysis excludes CI and LL compositions as plausible Vesta analogs, as these are predicted to have a negative metal fraction. Second, the MELTS thermodynamic calculator is used to show that the enstatite chondrites, the CV, CK and L-groups cannot produce Juvinas-like liquids, and that even for the other groups, depletion in sodium is necessary to produce liquids of appropriate silica content. This conclusion is consistent with the documented volatile-poor nature of eucrites. Furthermore, carbonaceous chondrites are predicted to have a mantle too rich in olivine to produce typical howardites and to have Fe/Mn ratios generally well in excess of those of the HEDs. On the other hand, an Na-depleted H-chondrite bulk composition is capable of producing Juvinas-like liquids, has a mantle rich enough in pyroxene to produce abundant howardite/diogenite, and has a Fe/Mn ratio compatible with eucrites. In addition, its predicted bulk-silicate density is within 100 kg m⁻<fnref n="3" /> of solutions constrained by data of the Dawn mission. However, oxidation state and oxygen isotopes are not perfectly reproduced and it is deduced that bulk Vesta may contain approximately 25% of a CM-like component. Values for the bulk-silicate composition of Vesta and a preliminary phase diagram are proposed.

## INTRODUCTION

The vast majority of rocky and metallic objects delivered to Earth as meteorites are samples of protoplanetary bodies that escaped accretion into larger planets, providing a unique window into the history of the early solar system (e.g., McSween 1999). One of the

principal findings of the meteorite record is that short-lived radioisotopes, in particular ²⁶Al, may have been abundant in the earliest solar system (e.g., MacPherson et al. 1995) providing a potent heat source capable of fueling internal differentiation of early-accreted bodies (e.g., Ghosh and McSween 1998; Hevey and Sanders 2006; Neumann et al. 2012).

<footnote n="1">¹IRAP (CNRS - UMR 5277), Observatoire Midi-Pyrénées, University of Toulouse, 14 Ave. E. Belin, Toulouse F-31400, France</footnote>

<footnote n="2">²Department of Earth and Planetary Sciences, University of Tennessee, Knoxville, Tennessee 37996-1410, USA</footnote>

<footnote n="3">³Astromaterials Research Office, NASA Johnson Space Center, Houston, Texas 77058, USA</footnote>

<footnote n="4">⁴Department of Mineral Sciences, Smithsonian Institution, Washington, District of Columbia 20013-7012, USA</footnote>

<footnote n="5">⁵Planetary Science Institute, Tucson, Arizona 85719-2395, USA</footnote>

<footnote n="6">⁶Istituto di Astrofisica e Planetologia Spaziali INAF, Roma 00133, Italy</footnote>

<footnote n="7">⁷Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA</footnote>

<footnote n="8">⁸Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095, USA</footnote>

<footnote>*Corresponding author: E-mail: mtoplis@irap.omp.eu</footnote>
Understanding the extent and nature of differentiation in such small bodies is of critical importance, as those bodies are in turn the building blocks of larger planets such as the Earth or Mars.

However, even within the simple conceptual framework of radiogenic heating, once temperature rises above the solidus of the silicate and/or metal fractions, physical, chemical, and thermal interactions are sufficiently complex that it is difficult to predict exactly how differentiation will proceed as a function of space and time within the body. For example, there is debate concerning the critical melt fraction necessary for efficient metal segregation, some authors arguing for the need for silicate melt fractions as high as 50% (e.g., Taylor 1992), others suggesting that even a negligible silicate melt fraction will suffice (e.g., McCoy et al. 1997; Terasaki et al. 2008). At the other end of the density spectrum, there is also debate concerning how silicate melt can rise to form a primitive crust, some authors believing that the time scales of melt extraction are low enough that protoplanetary interiors may retain large local melt fractions (e.g., Righter and Drake 1997; Moskovitz and Gaidos 2011; Neumann et al. 2012), others suggesting that pathways for rapid extraction to the surface may exist such that protoplanetary interiors never contained more than a few percent of interstitial liquid (e.g., Wilson and Keil 2012).

The study of achondrite and metallic meteorites confirms that internal differentiation occurred within the first few million years of the solar system and that ²⁶Al is a plausible heat source (e.g., Bizzarro et al. 2005; Kleine et al. 2005; Qin et al. 2008). However, despite important mineralogical and petrologic constraints, meteorite samples lack geological context (i.e., at the outcrop scale) and much of the information concerning their spatial distribution at the surface or within their original parent body must be inferred indirectly, complicating the use of these samples for unraveling the details of the differentiation process.

A viable alternative is to study remnant parent bodies in regions such as the main asteroid belt between Mars and Jupiter, where the planet-forming process is thought to have been arrested due to the presence of Jupiter. Of the objects in the Main Belt, the asteroid Vesta is of particular interest as it is large enough to have experienced internal differentiation (520 km diameter), and it is known to have a basaltic surface dominated by FeO-bearing pyroxenes as demonstrated by visible-IR spectra obtained by ground and space-based telescopes (e.g., McCord et al. 1970; Drake 2001). Furthermore, such spectra of Vesta and associated Vestoids are remarkably similar to laboratory spectra measured on meteorites of the howardite-eucrite-diogenite clan (HED), leading to the paradigm that the

HEDs ultimately came from Vesta (e.g., Binzel and Xu 1993; Drake 2001). Geochemical and petrological studies of the HEDs confirm the differentiated nature of the near-surface region of their parent body, and imply that crust extraction occurred well within the first 10 Ma of solar system history (e.g., Nyquist et al. 2003; Trinquier et al. 2008; Kleine et al. 2009).

Vesta is therefore a prime target for studies that aim to constrain the earliest stages of planet building, and it is within this context that the NASA Dawn spacecraft (Russell and Raymond 2011) orbited Vesta from July 2011 to September 2012. The results of the Dawn mission so far have significantly reinforced the HED-Vesta connection, confirming a significant degree of internal differentiation of the asteroid (Russell et al. 2012), a surface mineralogy perfectly compatible with that of the HEDs (De Sanctis et al. 2012a; Reddy et al. 2012), and near-surface concentration ratios Fe/O and Fe/Si consistent with HED lithologies (Prettyman et al. 2012).

The combination of data from the HED meteorites and the Dawn mission thus presents an unprecedented opportunity to use Vesta as a natural laboratory of early differentiation processes in the early solar system. However, the bulk composition of Vesta remains a significant unknown parameter, but one that plays a key role on the physical and chemical properties of the internal and surface reservoirs (core, mantle, crust). Several attempts have been made over the years to constrain the bulk composition of the eucrite parent body, early endeavors relying on petrological or cosmochemical constraints (e.g., Consolmagno and Drake 1977; Dreibus et al. 1977; Morgan et al. 1978). More recently, individual chondrite-class compositions, or mixtures thereof, have been considered, constrained by considerations such as O-isotopes, trace element ratios and siderophile element concentrations of the eucrites (Boesenberg and Delaney 1997; Righter and Drake 1997; Ruzicka et al. 1997).

The work presented here builds upon these latter studies, with the primary aims of (1) illustrating the potential diversity of the geochemical and geophysical properties of a fully differentiated Vesta-sized parent body, and (2) assessing which, if any, of the known chondritic bulk compositions are plausible analogs for proto-Vesta.

## METHODS

### General Approach: Compositions and Chemical Elements Considered

There is consensus that the primitive building blocks of the solar system were “chondritic” in bulk
composition. However, diverse classes of chondrite exist, from the volatile-rich Ivuna-class (CI), to metal-poor varieties such as the LL ordinary chondrites (Wasson and Kallmeyn 1990). While there is no guarantee that Vesta accreted from known chondritic precursors, these compositions provide a convenient reference frame for exploring possible compositional variations of early solar system materials.

Twelve chondritic compositions are considered here, comprising seven carbonaceous groups (CI, CV, CO, CM, CK, CR, CH), the three ordinary chondrite groups (H, L, LL), and the two enstatite chondrite groups (EH, EL). Compositions of the CK, CR, and CH groups are taken from Lodders and Fegley (1998), all other compositions being taken from Wasson and Kallmeyn (1990). Significant differences in composition exist, in terms of Mg/Si, sulfur, and iron content, volatile depletion, oxidation state of iron, and the concentration of incompatible lithophiles such as the REE. The role of these factors on the mineralogy and internal structure of a fully differentiated parent body will be explored here.

The basis of our analysis consists of distributing each chemical element between one or more of the principal solid differentiated geochemical reservoirs (core, mantle, crust), assuming a distribution that is consistent with the thermodynamics of element partitioning at magmatic temperature, as detailed below. Because our aim is to quantify the first-order effects of differentiation, we focus on those chemical elements that dominate the mass of the bulk object (Si, Al, Mg, Ca, Ti, Na, Fe, Ni, S, O), minor or trace elements (e.g., Mn, REE) being considered only where they provide complementary constraints. The volatile elements (H, C, N, etc) are expected to be strongly partitioning into a vapor phase at magmatic temperature in the low-pressure and low-gravity conditions at Vesta. Traces of volatiles such as hydrogen exist both at the surface of Vesta and in certain HEDs (e.g., Treiman et al. 2004; Barrat et al. 2011; De Sanctis et al. 2012b; Prettyman et al. 2012), but an internal origin is generally considered unlikely. While we cannot exclude the survival of a fraction of the original volatile inventory, residual concentrations are not expected to be volumetrically or petrologically significant after magmatic processing, so these elements will not be considered further for the purposes of this study.

## Core Materials and the Link to Bulk-Silicate Composition

The core of a fully differentiated protoplanet is expected to be dominated by Fe, S, and Ni. Of these

three elements, the silicate-metal partition coefficients of S and Ni are very strongly in favor of the metallic melt phase at oxygen fugacities ($fO_2$) near the iron-wüstite buffer (e.g., O'Neill and Mavrogenes 2002; Holzheid and Palme 2007). We will therefore make the simplifying assumption that all available Ni and S are sequestered in the core. On the other hand, the case of iron is more complex, as the silicate-metal partition coefficient is close to 1 at relevant $fO_2$ (e.g., Holzheid and Palme 2007). In other words, the available iron in the bulk composition will be more or less evenly distributed between the core (where it occurs in reduced metallic form) and in the bulk silicate (where it occurs in oxidized form). As such, the mass of the core is not uniquely constrained by bulk composition, and a wide range of core mass is possible. A lower bound is provided by the mass of S and Ni, and an upper bound is provided by the case in which all available iron is in the core (i.e., the bulk silicate contains no iron). Despite the wide range of possible solutions, it is of note that there is a quantitative link between calculated core size and the Mg# (100 × molar Mg/(Mg + Fe)) of the bulk-silicate fraction of the body, as illustrated in Fig. 1a. For example, the minimum mass fraction of the core for a differentiated parent body of H-chondrite composition is on the order of 5%, in which case, the corresponding bulk silicate has a low Mg# of approximately 55, while the upper bound on core mass is approximately 30%, when the Mg# of the silicate fraction is 100. In detail, maximum core size and Mg# are also functions of assumed bulk composition, as illustrated in Fig. 1a where results for the H and L groups are compared. The question then becomes how to distinguish between these potential solutions and constrain the core size and composition of a given bulk composition, a step that requires consideration of the crustal rocks as detailed below.

## Composition of the Crust and Its Implications

The crustal region of Vesta (as sampled by the HED meteorite suite) would appear to be a complex mixture of ultramafic Opx-rich cumulates (diogenite), gabbroic cumulates (cumulate eucrites), and various basaltic lithologies of diverse geochemistry (i.e., main-group eucrites, Stannern trend eucrites). Significant uncertainty surrounds the details of the petrogenesis of many of the HED lithologies, in particular, the diogenites and the Stannern-trend eucrites (e.g., Stolper 1977; Mittlefehldt 1994; Mittlefehldt and Lindstrom 2003; Barrat et al. 2007, 2008; Mittlefehldt et al. 2011). On the other hand, there is broad consensus that the main-group basaltic eucrites are samples of the magmatic crust of the parent asteroid (e.g., Stolper
<figure><img src="image_2.png" /><figcaption>Fig. 1. a) Variation of the Mg# of the bulk mantle (defined as 100 × molar Mg/(Fe + Mg)) as a function of the mass of the core calculated for bulk compositions corresponding to H chondrite (continuous line) and L chondrite (dashed line). b) Variation of $K_{d\text{mantle}-\text{Juvinas}}^{\text{Mg-Fe}}$ (defined as molar $(\text{Mg/Fe}^{2+})_{\text{Juvinas}}/(\text{Mg/Fe}^{2+})_{\text{mantle}}$) as a function of the mass of the core calculated for bulk compositions corresponding to H chondrite (continuous line) and L chondrite (dashed line). Values of $K_d$ corresponding to pure olivine and pure pyroxene are shown for reference.</figcaption></figure>

1977; Takeda 1997; McSween et al. 2011), as these samples show simple geochemical variations compatible with fractional crystallization of liquid in a near-surface environment. More importantly, as demonstrated by Stolper (1977), the most Mg-rich members of the main group are compatible with production by direct equilibrium melting of the primitive (i.e., chondritic) mantle (and/or equilibrium crystallization of a magma ocean; Righter and Drake 1997), a result that has far-reaching implications. For example, it implies that at

least some preserved eucritic liquids were in chemical equilibrium with the Vestan interior, providing indirect constraints on the latter, as described below. Second, as samples of putative primary magma composition, the primitive main-group (PMG) eucrites may be used as a proxy for the composition of an average “geochemical” crust.

In light of these considerations, the “crust” of our differentiated parent bodies is assumed to have the composition of the primitive main-group eucrite Juvinas (Kitts and Lodders 1998). The link between this geochemical crust and the petrologically diverse near-surface region of the HED parent body will be discussed below, but, for the moment, we will consider what may be learned from the chemistry of Juvinas, assuming that it was in equilibrium with the vestan mantle. First of all, the REE content of Juvinas may be used to provide a direct estimate of the fraction of basaltic crust relative to the bulk silicate, assuming that the REE are perfectly incompatible during melting/ crystallization. Given this relative mass fraction of basaltic crust and knowing its composition (i.e., Juvinas), the composition of the residual mantle may thus be calculated by mass balance if the bulk-silicate composition is known. For example, in this way, the FeO and MgO content of the residual mantle may be calculated. This is of significant interest, as the thermodynamics of Fe-Mg partitioning between olivine, pyroxene, and coexisting basaltic liquid are relatively simple and well known (e.g., Roeder and Emslie 1970; Beattie et al. 1991; Toplis 2005). In other words, the Mg/Fe ratio of the basaltic crust and that of the coexisting mantle are not independent, but are thermodynamically related through the Ol-liq and Px-liq exchange coefficients, $K_{d\text{Ol}-\text{Liq}}^{\text{Mg-Fe}}$ and $K_{d\text{Px}-\text{Liq}}^{\text{Mg-Fe}}$, defined as molar $(\text{Mg/Fe}^{2+})_{\text{liq}}/(\text{Mg/Fe}^{2+})_{\text{φ}}$ where $\phi$ is olivine or pyroxene. For example, the model of Toplis (2005) may be used to calculate that $K_{d\text{Ol}-\text{Liq}}^{\text{Mg-Fe}}$ has a value of approximately 0.35 for a liquid of Juvinas composition at 1170 °C (the liquidus temperature constrained experimentally by Stolper 1977), while experimental data in ferro-basaltic systems (e.g., Grove and Bryan 1983; Toplis and Carroll 1995) can be used to constrain the relevant $K_{d\text{Px}-\text{Liq}}^{\text{Mg-Fe}}$ to be approximately 0.24.

A combined consideration of the distribution of iron between core, mantle, and crust may then be undertaken to constrain thermodynamically plausible solutions. For example, a given mass fraction of iron in the core results in an apparent $K_{d\text{mantle}-\text{crust}}^{\text{Mg-Fe}}$, as illustrated in Fig. 1b. A cursory glance at this figure shows that of all the possible core mass fractions, only a restricted range is compatible with plausible Fe-Mg exchange coefficients. An even more stringent constraint
<figure><img src="image_3.png" /><figcaption>Fig. 2. Schematic section used to model fully differentiated chondritic parent bodies. The crust is assumed to have the composition of the primitive main-group eucrite Juvinas, the mantle is treated as a mixture of olivine and pyroxene, while both a metal component and sulfide component are considered for the core (see text for more details).</figcaption></figure>

on core size can be made if the relative proportions of olivine and pyroxene in the mantle can be predicted. This is possible if the mantle contains negligible plagioclase (as suggested by a flat REE pattern and phase equilibria arguments: Stolper 1977). In this case, the molar ((Ca + Mg + Fe)/Si) ratio of the calculated mantle residue may be used as a crude indicator of the relative proportions of olivine and pyroxene, because ((Ca + Mg + Fe)/Si)<sub>Px</sub> = 1, while ((Ca + Mg + Fe)/Si)<sub>Oi</sub> = 2).

In summary, consideration of Fe-Mg partitioning constitutes the fundamental basis of our approach. An iterative process is applied to find the iron content of the core for a given bulk composition that results in a bulk $K_d^{Mg-Fe}$ that is the mean of the values for olivine and pyroxene weighted by their calculated relative fractions in the mantle.

## Relative Masses, Volumes, and Thicknesses

The method described above provides estimates of the relative masses of the core (Fe-Ni-S), the mantle, and the basaltic crust, as shown schematically in Fig. 2. In detail, the core is divided into a sulfide component and a metal component of identical Fe/Ni ratio. While the latter assumption may not be correct in detail, available experimental data suggest that this is a reasonable first-order approximation at high temperature (Chabot et al. 2007). Relative masses are then converted into absolute masses using the mass of Vesta constrained by the Dawn mission (Russell et al. 2012). Masses are subsequently converted into volumes, using mineral densities. The values used are 1-bar room-temperature densities, as follows: Fe, 7874 kg m⁻³; Ni, 8900 kg m⁻³; FeS, 4840 kg m⁻³; NiS, 5300 kg m⁻³;

mantle olivine, 3690 kg m⁻³ (employing the grain density of Chassigny—a dunite sample of equivalent Mg#—as an analog); mantle pyroxene, 3420 kg m⁻³ (employing the grain density of diogenite as an analog); crust (Juvinas), 3180 kg m⁻³ (Consolmagno et al. 2008). The total volume is calculated for each bulk composition and compared with the measured volume of Vesta (Russell et al. 2012). In all cases, the Dawn-derived volume is larger than that predicted by summing individual units. This difference may be related to uncertainties in the density values used, or may be the result of porosity on Vesta, caused either by thermal contraction from a high-temperature state and/or the role of impacts, some of which may have been large enough to cause body-wide disruption (e.g., Buczkowski et al. 2012; Schenk et al. 2012). Assigning this volume difference to porosity and assuming uniform distribution throughout the silicate portion of the theoretical parent bodies, the thickness of the core, mantle, and crust is calculated assuming spherical geometry (Fig. 2), and the average densities of each unit are calculated.

## RESULTS

A summary of the calculated masses, thicknesses, densities, and other relevant compositions/mineralogies for each of the different bulk compositions can be found in Table 1. The principal differences concern the size and density of the core on the one hand, and the thickness of the crust and the mineralogy of the mantle on the other.

### Core Size, Composition, and Density

All bulk compositions have a significant core, but the relative proportions of metal and sulfide can be widely different. Of note is that solutions corresponding to the CI and LL groups have a negative calculated metal fraction, implying that no satisfactory thermodynamic solution is possible in these cases. For the other groups, the metal fraction (relative to sulfide) is predicted to be as little as approximately 20% (in the case of a CM bulk composition), to almost 100% (in the case of a CH bulk composition). These highly variable metal/sulfide ratios lead to a wide range of predicted average core density, spanning values from approximately 5000 to almost 8000 kg m⁻³ (Table 1; Fig. 3). Furthermore, total core mass is predicted to vary from a little less than 10% by mass of the parent body (in the case of CV, CK, and L chondrites), to as much as approximately 30% in the case of CH and EH bulk compositions. However, core size (radius) is typically predicted to be in the range 100–120 km. Total
<table><caption>Table 1. Predicted characteristics of fully differentiated Vesta-sized parent bodies of chondritic composition.</caption><thead><tr><th></th><th>CI</th><th>CM</th><th>CO</th><th>CV</th><th>CK</th><th>CR</th><th>CH</th><th>LL</th><th>L</th><th>H</th><th>EL</th><th>EH</th><th>¾H + ¼CM</th></tr></thead><tbody><tr><td>Mass (10<sup>19</sup> kg)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Mass FeNi</td><td>-1.03</td><td>0.63</td><td>1.26</td><td>0.46</td><td>0.82</td><td>1.65</td><td>7.31</td><td>-0.24</td><td>0.71</td><td>2.60</td><td>1.13</td><td>2.87</td><td>2.19</td></tr><tr><td>Mass FeNiS</td><td>5.84</td><td>2.85</td><td>1.45</td><td>1.60</td><td>1.26</td><td>1.47</td><td>0.26</td><td>1.66</td><td>1.56</td><td>1.41</td><td>2.37</td><td>4.22</td><td>1.71</td></tr><tr><td>Mass core</td><td>4.81</td><td>3.48</td><td>2.71</td><td>2.06</td><td>2.07</td><td>3.12</td><td>7.57</td><td>1.42</td><td>2.27</td><td>4.00</td><td>3.50</td><td>7.08</td><td>3.90</td></tr><tr><td>Mass mantle</td><td>17.77</td><td>18.49</td><td>19.17</td><td>18.96</td><td>19.92</td><td>19.85</td><td>15.75</td><td>21.12</td><td>20.18</td><td>18.68</td><td>21.14</td><td>16.38</td><td>18.63</td></tr><tr><td>Mass crust</td><td>3.33</td><td>3.94</td><td>4.02</td><td>4.89</td><td>3.92</td><td>2.94</td><td>2.59</td><td>3.37</td><td>3.46</td><td>3.22</td><td>1.27</td><td>2.45</td><td>3.38</td></tr><tr><td>%Mass core</td><td>18.6</td><td>13.4</td><td>10.5</td><td>8.0</td><td>8.0</td><td>12.0</td><td>29.2</td><td>5.5</td><td>8.8</td><td>15.5</td><td>13.5</td><td>27.3</td><td>15.1</td></tr><tr><td>%Mass mantle</td><td>68.6</td><td>71.4</td><td>74.0</td><td>73.2</td><td>76.9</td><td>76.6</td><td>60.8</td><td>81.5</td><td>77.9</td><td>72.1</td><td>81.6</td><td>63.2</td><td>71.9</td></tr><tr><td>%Mass crust</td><td>12.8</td><td>15.2</td><td>15.5</td><td>18.9</td><td>15.1</td><td>11.4</td><td>10.0</td><td>13.0</td><td>13.3</td><td>12.4</td><td>4.9</td><td>9.4</td><td>13.0</td></tr><tr><td>%Ni/(Ni + Fe)<sub>core</sub></td><td>14.4</td><td>15.5</td><td>16.9</td><td>24.0</td><td>21.8</td><td>14.3</td><td>9.2</td><td>32.8</td><td>18.2</td><td>11.7</td><td>12.9</td><td>8.4</td><td>12.3</td></tr><tr><td>%Fe/(Fe + FeS)<sub>core</sub></td><td>—</td><td>18</td><td>47</td><td>22</td><td>39</td><td>53</td><td>97</td><td>—</td><td>31</td><td>65</td><td>32</td><td>40</td><td>56</td></tr><tr><td>%Ol/(Ol + P<sub>x</sub>)<sub>mantle</sub></td><td>93.7</td><td>95.0</td><td>95.9</td><td>116.7</td><td>100.0</td><td>82.3</td><td>65.4</td><td>54.6</td><td>55.4</td><td>62.0</td><td>30.7</td><td>11.1</td><td>68.2</td></tr><tr><td>Bulk porosity (%)</td><td>7</td><td>8</td><td>8</td><td>7</td><td>7</td><td>8</td><td>18</td><td>3</td><td>5</td><td>9</td><td>6</td><td>10</td><td>8</td></tr><tr><td>Thickness (km)<sup>a</sup></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Crust</td><td>14.5</td><td>17.3</td><td>17.6</td><td>21.3</td><td>16.8</td><td>13.0</td><td>15.4</td><td>13.4</td><td>14.2</td><td>14.4</td><td>5.4</td><td>11.6</td><td>15.0</td></tr><tr><td>Mantle</td><td>110.6</td><td>128.0</td><td>141.5</td><td>143.5</td><td>150.1</td><td>142.2</td><td>113.8</td><td>158.4</td><td>148.5</td><td>133.7</td><td>142.0</td><td>107.0</td><td>132.4</td></tr><tr><td>Core</td><td>136.4</td><td>116.3</td><td>102.5</td><td>96.9</td><td>94.6</td><td>106.4</td><td>132.3</td><td>89.8</td><td>98.9</td><td>113.5</td><td>114.2</td><td>143.0</td><td>114.2</td></tr><tr><td>Density (kg m<sup>-3</sup>)<sup>a</sup></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Crust</td><td>2909</td><td>2915</td><td>2924</td><td>2952</td><td>2952</td><td>2901</td><td>2533</td><td>3089</td><td>3026</td><td>2877</td><td>2981</td><td>2798</td><td>2885</td></tr><tr><td>Mantle</td><td>3358</td><td>3370</td><td>3382</td><td>3471</td><td>3425</td><td>3320</td><td>2861</td><td>3460</td><td>3392</td><td>3241</td><td>3279</td><td>3034</td><td>3266</td></tr><tr><td>Core</td><td>4529</td><td>5281</td><td>6005</td><td>5425</td><td>5838</td><td>6175</td><td>7802</td><td>4684</td><td>5607</td><td>6540</td><td>5600</td><td>5786</td><td>6259</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>Fig. 3. Covariation of predicted core size (radius) and average core density. Open diamonds indicate the optimal solution calculated using the methods described in the text for each of the tested bulk chondrite compositions, as labeled. The open circle is a ¾ H: ¼ CM mixture, considered as a plausible analog of Vesta (see text for details). The solid lines around each point correspond to the range of acceptable solutions when the optimal value of $K_d$ is varied by ±0.03. Thin dashed lines correspond to solutions of core size/density that are compatible with fixed values of bulk-silicate density in a simple two-layer model of Vesta (values of silicate density, as labeled). The gray region is the family of solutions that are consistent with gravity constraints from the Dawn mission.</figcaption></figure>

core size (metal + sulfide) and average core densities nevertheless span a significant range, as illustrated in Fig. 3. This figure shows optimal values calculated using the methods described above (open symbols), as well as an indication of the range of possible solutions in each case (shown as solid lines), the latter calculated assuming a variation in $K_d^{Mg-Fe}$ of ±0.03 around the optimal value. The implications of these results in light of the geophysical/gravity data of the Dawn mission will be discussed below.

## Mineralogy and Thickness of the Crust-Mantle System

The calculated mineralogy of the residual mantle is highly variable from one bulk composition to another, the mantle of carbonaceous chondrites being predicted to be almost pure olivine, while that of the enstatite chondrites is predicted to be dominated by pyroxene (Table 1). The ordinary chondrites are intermediate in this respect with 50–60% of the mantle being predicted to be olivine. An additional parameter of interest is the proportion of pyroxene relative to that of the eucrite crust, given that the howardites have a high proportion of diogenite mixed in with crustal eucrites (e.g., Warren 1985; Warren et al. 2009). As illustrated in Fig. 4, the mass of available pyroxene is typically well below that of the eucrite crust for the carbonaceous chondrites, but represents a mass at least equivalent to that of the crust for the ordinary and enstatite chondrites.

<footnote><sup>a</sup>For calculations of thickness and density, bulk porosity was distributed uniformly throughout the silicate portion of the parent body.</footnote>
<figure><img src="image_5.png" /><figcaption>Fig. 4. Calculated proportion of eucrite (crust)/(eucrite+ pyroxene) for each of the studied bulk compositions. Values of this parameter >50 (dashed line) make howardite formation unlikely due to a lack of pyroxene.</figcaption></figure>

The degrees of partial melting necessary to reproduce the REE concentrations in Juvinas are in the range 5–9%, corresponding to a crustal thickness typically on the order of approximately 15 km, the total range covering 5–21 km, being thinnest for the EL composition and thickest for the CV composition (Table 1).

DISCUSSION

The thermodynamically constrained mass-balance calculations presented above highlight the important role of bulk composition, illustrating the potential variability in internal structure, mineralogy, and local composition of fully differentiated Vesta-sized parent bodies, even for the seemingly restricted compositional range of chondrites. In light of this variability, we will now assess which, if any, of these compositions provides the most satisfactory fit to known geochemical/ geophysical properties of the HED meteorites/Vesta.

Making a Eucritic Crust

One of the principal limits of the approach employed above is that it arbitrarily assumes that the geochemical crust of each differentiated parent body has the major-element chemistry of Juvinas. While phase- equilibria constraints are consistent with the idea that Juvinas is a liquid in equilibrium with residual mantle (e.g., Stolper 1977), it is worth assessing to what extent partial melting of chondritic compositions really can produce Juvinas-like liquids or not.

Some experimental data relevant to this issue exist (e.g., Jurewicz et al. 1993, 1995a) and certain silicate

inclusions in iron meteorites have been interpreted as the melting products of chondritic precursors (e.g., Takeda et al. 2000, 2003), but data are not available for all of the chondritic groups modeled here. For this reason, the MELTS thermodynamic calculator (Ghiorso and Sack 1995) has been used. The bulk- silicate composition (mantle + crust) calculated for each chondrite using the methods described above was used as an input to the MELTS model. Calculations were performed at oxygen fugacity conditions corresponding to the Fe-FeO buffer at 1 bar, assuming equilibrium melting/crystallization. Liquid compositions were calculated from the liquidus to close to the solidus typically in temperature steps of 10° in the range 1250–1600 °C and steps of 1° in the range 1100– 1250 °C. The similarity of each liquid to Juvinas was quantified using the parameter:

$$
\xi = \sqrt{\frac{1}{n} \sum_i \left( \frac{c_i^{\text{Liq}} - c_i^{\text{Juv}}}{\sigma_i^{\text{Juv}}} \right)^2} \quad (1)
$$

where cᵢ is the concentration of oxide i (in the liquid, or Juvinas), σᵢ is the 2-sigma uncertainty in the concentration of oxide component i in Juvinas (derived from values given by Kitts and Lodders 1998), and n is the number of oxide components considered (seven in our case, SiO₂, Al₂O₃, TiO₂, MgO, FeO, CaO, Na₂O). If the calculated values for all oxide components are within the permitted bounds for Juvinas, then the value of ξ will be ≤1, increasing values of ξ indicating a calculated composition that is further and further away from that of Juvinas. For this exercise, the minimum value of ξ is not the only parameter of interest, as the temperature at which ξ reaches a minimum would ideally correspond to a degree of partial melting/ crystallization consistent with that derived from analysis of the REE. In addition, the fact that the REE spectrum of Juvinas shows no europium anomaly would indicate that feldspar is not a stable crystalline phase in the temperature range corresponding to generation of Juvinas-like liquids, and that constraint too will be considered when assessing the results of the MELTS modeling.

The results of the detailed thermodynamic modeling show that none of the bulk chondritic compositions are capable of producing Juvinas-like liquids, the minimum values of ξ, being typically >4. In particular, calculated silica contents are systematically well above that of Juvinas at relevant degrees of partial melting/ crystallization. Furthermore, calculated values of Na₂O are also well in excess of those of Juvinas, consistent with the well-known depletion in alkalis of the HED suite in general relative to typical chondrites (e.g.,
<table><caption>Table 2. Characteristics of predicted parent bodies and their agreement with constraints from the howardite-eucrite-diogenite meteorites and/or Vesta.</caption><thead><tr><th></th><th>CM</th><th>CO</th><th>CV</th><th>CK</th><th>CR</th><th>CH</th><th>L</th><th>H</th><th>EL</th><th>EH</th><th>¾H+¼CM</th></tr></thead><tbody><tr><td>Closest fit to Juvinas, ξ<sup>b</sup></td><td><strong>1.1</strong><sup>a</sup></td><td><strong>1.0</strong></td><td>3.7</td><td>1.8</td><td><strong>1.1</strong></td><td><strong>1.0</strong></td><td>1.2</td><td><strong>0.7</strong></td><td>2.5</td><td>3.4</td><td><strong>0.9</strong></td></tr><tr><td>Fe/Mn</td><td>68–85</td><td>87–109</td><td>107–133</td><td>101–127</td><td>76–96</td><td>99–123</td><td>50–63</td><td><strong>37–47</strong></td><td>64–81</td><td><strong>36–45</strong></td><td><strong>42–52</strong></td></tr><tr><td>Gravity data<sup>c</sup></td><td>&gt;–100</td><td>&gt;–100</td><td>&gt;–200</td><td>&gt;–200</td><td>&gt;–100</td><td>&gt;200</td><td>&gt;–200</td><td><strong>&lt;–100</strong></td><td>&gt;–100</td><td>&gt;100</td><td><strong>&lt;–100</strong></td></tr><tr><td>% eucrite/ (eucrite + Px)</td><td>81</td><td>84</td><td>100</td><td>100</td><td>46</td><td><strong>32</strong></td><td><strong>28</strong></td><td><strong>31</strong></td><td><strong>8</strong></td><td><strong>14</strong></td><td><strong>36</strong></td></tr><tr><td>Consistent with Righter</td><td>No</td><td><strong>Yes</strong></td><td><strong>Yes</strong></td><td>–</td><td>–</td><td>–</td><td>No</td><td><strong>Yes</strong></td><td>–</td><td>–</td><td>–</td></tr><tr><td>Δ<sup>17</sup>O</td><td>low</td><td>low</td><td>low</td><td>low</td><td>low</td><td>low</td><td>high</td><td>high</td><td>high</td><td>high</td><td><strong>OK</strong></td></tr><tr><td>Oxidation state</td><td>oxidized</td><td><strong>OK</strong></td><td><strong>OK</strong></td><td>–</td><td>reduced</td><td>reduced</td><td>reduced</td><td>reduced</td><td>reduced</td><td>reduced</td><td><strong>OK</strong></td></tr></tbody></table>

McSween et al. 2011). In light of this observation, and the fact that alkalis are known to strongly affect the silica content of olivine+pyroxene saturated liquids (e.g., Kushiro 1975; Jurewicz et al. 1995b; Hirschmann 2000), further simulations have been performed, modifying the initial Na₂O content of the bulk to a value of 0.43 × F<sub>Juv</sub> (where 0.43 corresponds to the wt% Na₂O in Juvinas, and F<sub>Juv</sub> is the degree of partial melting predicted from the REE for the bulk composition of interest).

The results obtained are significantly different from those obtained in the alkali-rich case (Fig. 5). Ten bulk compositions were considered (CI and LL were not modeled in light of the negative metal core fractions) and of these, both of the enstatite chondrites and the CV group provided very poor fits to Juvinas for all degrees of partial melting/crystallization (see Table 2). The CK group and, to a lesser extent, the L-group also show poor agreement. On the other hand, minimum values of ξ for the CM, CO, CR, and CH groups are marginally consistent with production of Juvinas, while the simulations for the H-chondrite provide the best match of all tested compositions (Fig. 5). For all cases for which ξ falls to values close to 1, the fraction of liquid is generally consistent with values derived from the REE and to within a few Kelvin; all liquids are predicted to be unsaturated in plagioclase (Fig. 6). Furthermore, predicted temperatures for these groups (CM, CO, CR, CH, and H) are perfectly consistent with those measured experimentally by Stolper (1977) for the liquidus of Juvinas. The data shown in Figs. 5 and 6 thus indicate that certain bulk compositions are unlikely to have produced Juvinas-like liquids at any point during magmatic evolution, while for others, an excellent self-consistent scenario emerges.

<figure><img src="image_6.png" /><figcaption>Fig. 5. Similarity of liquids predicted by MELTS to Juvinas, as a function of the fraction of liquid (see text for details), calculated for the silicate fraction of EL, H, CH, and CO groups. In all cases, the Na₂O content of the bulk composition was modified as described in the text. Values of ξ, less than 1 indicate models that are indistinguishable from the composition of Juvinas at the 2 sigma level. Vertical arrows indicate the fraction of liquid expected for the EL, H, CH, and CO groups based upon analysis of their REE concentrations (see Table 1).</figcaption></figure>

## Fe/Mn Ratios of the Crust

An additional geochemical constraint of potential interest is the Fe/Mn ratio of the bulk silicate. Indeed, as discussed by Boesenberg and Delaney (1997), the HED parent body is known to have rather constant Fe/Mn, in the range 30–45. Assuming that Mn is not partitioned into the core, the Mn concentration of different chondrite groups can be combined with the

<footnote><sup>a</sup>Values indicated in bold show a satisfactory fit to constraints from the HED/Vesta. Others do not.</footnote>

<footnote><sup>b</sup>See text for details concerning the definition of ξ.</footnote>

<footnote><sup>c</sup>The values indicated are the minimum offset between the predicted density of the bulk-silicate mantle derived from the core size and density calculated here, and that constrained by the gravity data of the Dawn mission (in kg m⁻³).</footnote>
<figure><img src="image_7.png" /></figure>

Fig. 6. Summary of MELTS results concerning the compositional similarity of predicted liquids and Juvinas. For each bulk composition, the small horizontal bars represent the temperature at which plagioclase is no longer a stable phase; the cross represents the temperature at which ξ is a minimum, while the open circle represents the temperature at which melt fraction is that derived from consideration of the REE. In addition, the temperature range over which ξ is ≤1 is shown by a solid bar, where applicable. Ideally, the cross and circle should be concordant, for a value of ξ ≤ 1, at a temperature above the liquidus of plagioclase (see text for more details).

bulk-silicate Fe content calculated above to constrain bulk-silicate Fe/Mn. These values provide an upper bound as olivine and/or pyroxene crystallization may act to decrease the Fe/Mn of the liquid. A lower bound has thus been estimated using a value for $K_{dol/px-liquid}^{Mn-Fe}$ of approximately 1.3 (e.g., Snyder and Carmichael 1992), as illustrated in Fig. 7. This comparison shows that with the exception of the H and EH chondrites, the calculated values of Fe/Mn are typically well above the range observed in the HEDs.

## Geophysical and Geochemical Properties of the Core

The calculated variations in core size/density (e.g., Fig. 3) also provide a potential means of constraining relevant bulk composition. For example, the measured bulk density of Vesta and its J2 gravity coefficient determined by the Dawn mission may be used to constrain internal mass concentration (Russell et al. 2012). Using simple 2-layer models, it may be shown that for reasonable values of oblateness, the density of the upper silicate layer is well constrained by J2 to have a value in the range 3050–3140 kg m⁻³ (Russell et al. 2012). This range of silicate density provides a stringent constraint on the size and density of the core, as illustrated in Fig. 3. Interestingly, none of the predicted cores provide a perfect match to the geophysically constrained range of

<figure><img src="image_8.png" /></figure>

Fig. 7. Predicted Fe/Mn for the silicate portion of each bulk composition considered. In each case, the upper bound is calculated directly from mass balance calculations once Fe had been partitioned into the core, while the lower bound takes into account a possible effect of olivine/pyroxene crystallization (see text for more details). The range described for the howardite-eucrite-diogenite parent body is indicated in gray.

acceptable values, although the closest approach is for the H-chondrite composition (Fig. 3).

On a related note, the concentrations of siderophile elements in eucrite basalts have been used to constrain estimates of core mass assuming a number of different bulk compositions (Righter and Drake 1997). Although not all chondrite groups were tested, it is of interest to compare the estimates of Righter and Drake (1997) with the values derived here, to assess to what extent the results of these two independent approaches are concordant. This comparison shows that for the CI, CV, CO, and H groups, the mass of the core predicted here and that predicted by Righter and Drake (1997) are in excellent first-order agreement, while values for the L, LL, and CM groups are not concordant (Fig. 8).

## Oxidation State and Oxygen Isotopes

In the mass-balance calculations described above, the element oxygen was left unconstrained, its final concentration being ultimately fixed by the core-mantle redox equilibrium. As such, the final oxidation state of our differentiated chondrite parent bodies is not necessarily the same as that of bulk chondrite materials as they are found today. Indeed, with the exception of the EH-composition, all the other compositions studied here had a final calculated $Fe^{2+}/(Fe^{2+} + Fe^{0})$ ratio of 0.6–0.8, whereas the starting materials have $Fe^{2+}/(Fe^{2+} + Fe^{0})$ varying from 0 to 1, as illustrated in Fig. 9. Comparing the bulk oxidation state of natural chondrites with those predicted to be in equilibrium
<figure><img src="image_9.png" /><figcaption>Fig. 8. Values of the % of parent body as core derived from this work, compared with values predicted by Righter and Drake (1997) from the concentrations of siderophile elements (Ni, Co) in eucrite basalts.</figcaption></figure>

with eucrite basalts, it is found that CV and CO groups require the least change in oxidation state, that EH, EL, H, L, CR, and CH groups require various amounts of oxidation, while the CM group requires reduction (Fig. 9). It is also of note that in light of the extremely reducing conditions recorded by the natural enstatite chondrite groups (e.g., McCoy et al. 1999; Berthet et al. 2009), the amount of oxidation required to reach the values of $Fe^{2+}/(Fe^{2+} + Fe^{0})$ modeled here makes such a scenario unlikely.

## Overview of the Constraints on Bulk Composition

Based upon our analysis, each of the predicted properties can be considered to constrain likely bulk composition (Table 2). First of all, simple mass-balance arguments would seem to exclude CI and LL bulk compositions, as these are predicted to have a negative metal fraction. Second, modeling of the production of Juvinas-like liquids using MELTS would likewise seem to exclude the enstatite chondrites, the carbonaceous groups CV and CK, and to a lesser extent, the L-ordinary chondrites. Of the five remaining groups, the carbonaceous chondrites CO and CM have a mantle that is far too rich in olivine to produce the volumes of pyroxene seen in typical howardites. Furthermore, CO, CM, CR, and CH chondrites all have predicted Fe/Mn well in excess of that of the HED parent body. On the other hand, the H-chondrite composition provides the closest fit to a Juvinas-like crustal composition (Fig. 5); it

<figure><img src="image_10.png" /><figcaption>Fig. 9. Comparison of the bulk $Fe^{2+}/(Fe^{2+} + Fe^{0})$ ratio required to satisfy the geochemical constraints of a eucrite crust (this work) with values of bulk $Fe^{2+}/(Fe^{2+} + Fe^{0})$ for the different bulk chondrite groups as observed today.</figcaption></figure>

has a mantle relatively rich in pyroxene capable of producing abundant diogenite/howardite (Table 1; Fig. 4), and it is the only nonenstatite group with a Fe/Mn ratio compatible with eucrites (Fig. 7). In addition, the predicted bulk-silicate density (derived from predicted core size and density) is within $100 \text{ kg m}^{-3}$ of solutions constrained by gravity and density data of the Dawn mission (Fig. 3). Taken together, a surprisingly coherent picture thus emerges, with an Na-depleted H-chondrite composition fulfilling almost all of the necessary criteria. Interestingly, this conclusion is perfectly consistent with the trace element chemistry of the HED suite, as described by Morgan et al. (1978) over 30 years ago.

However, the match is not perfect, in particular in terms of oxidation state, but more importantly in terms of oxygen isotopes, the latter providing a well-defined “fingerprint” for many different groups of meteorite (e.g., Clayton 1993). In this respect, it is of note that none of the chondrite groups provide a perfect match to the oxygen isotopic composition of the HED suite (see Fig. 10), leading several authors to propose a mixed origin (e.g., Boesenberg and Delaney 1997; Righter and Drake 1997). While it is possible that a body with a bulk composition similar to that of the H-chondrite, but with a different isotopic signature, may have existed, we briefly explore which mixture of known chondrite parent bodies provides the best fit to the available data. In light of the excellent first-order success of H-chondrite, we assume that this composition forms the dominant component by mass. Indeed, of all the chondrite groups
<figure><img src="image_11.png" /><figcaption>Fig. 10. Summary of the stable oxygen isotope composition of various materials of relevance to Vesta. H, L, and LL correspond to the ordinary chondrite groups. TFL is the terrestrial fractionation line. Howardite-eucrite-diogenite is the eucrite parent body and the thick section of this line is where the majority of samples concentrate (Boesenberg and Delaney 1997). The dashed lines, corresponding to the labeled carbonaceous chondrite groups, were drawn after Clayton and Mayeda (1999).</figcaption></figure>

(with the exception of the enstatite chondrites), it is the H-chondrites that are closest to the HED in terms of O-isotopes. The choice of component to mix would appear to be limited to the carbonaceous groups, as these are the only ones with lower $\Delta^{17}O$ (e.g., Clayton and Mayeda 1999; see Fig. 10). However, to satisfy bulk oxygen isotopes, the calculated proportions of CR or CH material would be on the order of 50%, making such mixtures too rich in carbonaceous material. On the other hand, the relative proportion of CO, CV, CK, or CM would be approximately 25%. Of these possibilities, only addition of a CM component keeps Fe/Mn and core density relations within reasonable bounds of independently constrained values. Furthermore, addition of CM material would add a source of oxidized material, consistent with the bulk oxidation state calculated here that is intermediate between H and CM (Fig. 9). Detailed calculations have thus been performed for a ¾H:¼CM mixture (of reduced Na content), and this composition is found to satisfy all available constraints (see Tables 1 and 2, and Figs. 3, 4, 6, and 7).

## A Preliminary Phase Diagram and Olivine in the Mantle

The analysis presented above thus provides estimates of bulk composition that are consistent with many geochemical and geophysical characteristics of the HEDs and/or Vesta. Two of these (H-chondrite and ¾H:¼CM)

are summarized in Table 3. While the core composition is a little different in each case, the compositions of the silicate portions are very similar. Using this information, we have used MELTS to calculate a preliminary equilibrium phase diagram relevant to the high-temperature evolution of the vestan mantle (Fig. 11). The calculated differences between the two bulk compositions tested are negligible, both having olivine on the liquidus at a temperature close to 1600 °C. Pyroxene is the second phase to saturate upon cooling, at a temperature a little over 1350 °C for equilibrium crystallization, when the proportion of olivine is approximately 40% of the bulk silicate (and the fraction of melt approximately 60%). Pyroxene and olivine are then predicted to co-crystallize until saturation in plagioclase at 85% crystallization and a temperature a little below 1200 °C (Fig. 11). The solidus is predicted to be at approximately 1150 °C. Taken at face value, this phase diagram thus suggests that if the vestan mantle experienced perfect equilibrium crystallization of a magma ocean (e.g., Righter and Drake 1997) or direct equilibrium melting (e.g., Stolper 1977), then the rocks directly beneath the eucrite crust could contain on the order of approximately 65% olivine. On the other hand, if Vesta experienced a magma ocean, some fraction of the most refractory olivine may have sank to the bottom of the mantle, either because it never melted (due to insufficient $^{26}$Al) and/or through crystal settling during cooling. Indeed, Righter and Drake (1997) suggested 20-40% of residual olivine in their analysis of Ni and Co partitioning. In this case, the rocks just below the eucrite crust may contain significantly less olivine than the value expected for perfect equilibrium crystallization. The exact proportion will be a function of the degree of fractional crystallization, and we note that the phase diagram suggests that in the range 1250-1200 °C, the cotectic proportion of olivine is very low (i.e., its proportion is not increasing significantly with decreasing temperature). Indeed, consideration of Fig. 11 shows that a natural consequence of this phase diagram is the generation of rocks with pyroxene as the sole crystallizing phase just prior to feldspar saturation. Although the trace element characteristics of diogenites suggest that their petrogenesis is not simple (e.g., Fowler et al. 1994; Barrat et al. 2008; Mittlefehldt et al. 2011), our analysis therefore implies that precipitation of Opx-rich cumulates does not seem unreasonable from a major-element phase equilibrium perspective (see also Warren 1997; Beck and McSween 2010).

## Bulk Composition and Data from the Dawn Mission

One of the principal motivations for this study is to provide a framework for interpretation of data of the
<table><caption>Table 3. Bulk compositions of the silicate and metal fractions of plausible Vesta analogs.</caption><thead><tr><th rowspan="2"></th><th colspan="8">Bulk silicate<sup>a</sup></th><th colspan="3">Core<sup>a</sup></th></tr><tr><th>wt% SiO<sub>2</sub></th><th>wt% TiO<sub>2</sub></th><th>wt% Al<sub>2</sub>O<sub>3</sub></th><th>wt% FeO</th><th>wt% MgO</th><th>wt% CaO</th><th>wt% Na<sub>2</sub>O</th><th>wt% S</th><th>wt% Fe</th><th>wt% Ni</th></tr></thead><tbody><tr><td>H-chondrite</td><td>43.39</td><td>0.10</td><td>2.56</td><td>23.87</td><td>27.91</td><td>2.10</td><td>0.06</td><td>12.80</td><td>76.97</td><td>10.23</td></tr><tr><td>¾H+¼CM</td><td>42.59</td><td>0.10</td><td>2.70</td><td>24.42</td><td>27.92</td><td>2.20</td><td>0.07</td><td>16.01</td><td>73.67</td><td>10.32</td></tr></tbody></table>

<figure><img src="image_12.png" /><figcaption>Fig. 11. Phase proportions of liquid, olivine, pyroxene, and plagioclase as a function of temperature predicted by MELTS for equilibrium melting/crystallization of the silicate portion of an Na-depleted H-chondrite bulk composition capable of producing a Juvinas-like liquid.</figcaption></figure>

Dawn mission. For example, the results presented here may be used to predict that a pure eucrite crust on Vesta would have an average thickness on the order of 15 km (last column of Table 2), a value that could be larger if porosity is concentrated in the crust, but smaller if the Jovian Early Bombardment eroded the earliest crust (Turrini et al. 2012). This prediction would appear in first-order agreement with data from the Rheasilvia impact basin, where the depth to diogenite-rich lithologies was found to be on the order of 20 km (McSween et al. 2013). Furthermore, the predicted thickness and density of the principal geochemical reservoirs may also be a useful guide for interpretation of gravity data (e.g., Zuber et al. 2011). However, the stratigraphic section proposed here (e.g., Fig. 2) is clearly an oversimplification as it does not account for the petrologic complexity of the HED suite, nor does it necessarily represent the current configuration of the crust. For example, even if a simple interface between eucrite crust and underlying mafic lithologies once

existed (e.g., Takeda 1979, 1997), that interface may have been erased by 4 billion years of impact. In addition, the original crustal structure may have been significantly more complex, with the possible presence of diogenite plutons emplaced throughout the crust (Barrat et al. 2010). Both of these possibilities will add a significant diogenite fraction to the near-surface region (e.g., Jutzi et al. 2013), increasing the thickness of the “crust” and its density relative to values shown in Table 1, and attenuating a sharp density contrast at the base of an eventual eucrite layer, conclusions consistent with analysis of the Dawn gravity data (e.g., Raymond et al. 2013).

Knowledge of the bulk composition is also of interest from a chemical point of view, as, although the HEDs provide an extremely useful basis for interpreting data from the Dawn mission, there is no guarantee that they provide a complete vision of all possible crustal (and mantle) lithologies that are exposed at the surface of Vesta (e.g., Barrat et al. 2009, 2012a). In this respect, our approach has the potential to extend predictions to thermodynamically plausible rock types that are not necessarily present in the HED collection. However, the fact that Juvinas-like liquids cannot be produced from bulk compositions with chondritic concentrations of alkalis (consistent with the depletion in alkalis that characterizes the HED suite) raises the question of whether the HED parent body was assembled from Na-depleted building blocks, or whether Na was lost during differentiation. In the former case, it is possible that other volatile elements were depleted too. In light of the possible loss of sulfur in this case, we have performed additional calculations with reduced concentrations of S. It is found that calculated bulk-silicate compositions are comparable to the full-S case. The core size is predicted to be smaller, but denser, such that average core properties lie along lines of constant bulk-silicate density (i.e., dashed lines of Fig. 3). Alternatively, the high temperatures and low oxygen fugacities during radiogenic heating may have resulted in significant loss of the alkalis (e.g., Tsuchiyma et al. 1981), either during surface volcanism under near vacuum conditions and/or through impact processes at the surface (e.g., Ikeda and Takeda 1985; Nyquist et al. 2003). In this case, severe redistribution of Na and K may have occurred (e.g.,

<footnote><sup>a</sup>The relative mass fractions of bulk silicate and core can be found in Table 1.</footnote>
Mittlefehldt 1987), potentially explaining the existence of K-rich lithologies in certain howardite breccias (e.g., Barrat et al. 2009, 2012b). On the other hand, potassium isotopes do not show severe fractionations (Humayun and Clayton 1995), although the possibility of equilibration between gas and solid/liquid may act to attenuate isotopic fractionation (e.g., Yu et al. 2003; Alexander and Grossman 2005). Finally, it is also of note that many howardites contain a CM component (e.g., Herrin et al. 2011; McSween et al. 2011), and that certain regions of the Vestan surface are potentially rich in volatile-bearing carbonaceous chondrite material (De Sanctis et al. 2012b; Prettyman et al. 2012). In addition, simple models for the thermal evolution of radiogenically heated parent bodies predict the existence of a surface layer of primitive material that was never heated above the metal and/or silicate solidus (e.g., Neumann et al. 2012). In light of our results, the possibility thus arises that the observed CM material in howardites could be the remnants of primitive material. However, we consider this scenario highly unlikely because in that case, even greater fractions of H-chondrite material should be present, inconsistent with petrographic observations of the HED and inconsistent with the Fe/O ratio and neutron adsorption of the Vestan surface measured by GRAND, which would seem to exclude metal-rich materials (e.g., Mittlefehldt et al. 2012).

## CONCLUDING REMARKS

The simple mass-balance and thermodynamic constraints employed here illustrate the potential diversity of the geochemical and geophysical properties of a fully differentiated Vesta-sized parent body with a geochemical crust of eucrite composition. However, detailed consideration of the results shows that important constraints on the bulk composition of Vesta are provided, and that the latter would appear to be dominated by a component similar to H-chondrite. Indeed, an Na-depleted H-chondrite bulk composition is capable of producing Juvinas-like liquids, has a mantle relatively rich in pyroxene capable of producing abundant diogenite/howardite, with a Fe/Mn ratio compatible with eucrites. In addition, its predicted bulk-silicate density (derived from calculated average core size and density) is within 100 kg m⁻³ of solutions constrained by gravity and density data of the Dawn mission. However, oxidation state and oxygen isotopes are not perfectly reproduced by this composition and it is deduced that bulk Vesta may contain approximately 25% of a CM-like component.

Identification of an acceptable bulk composition is an important step forward, as it opens the possibility of predicting the mineralogy and composition of solid and

liquid products over wide ranges of partial melting and crystallization, provides a useful and self-consistent reference frame for interpretation of the Dawn data. Furthermore, knowledge of the bulk composition (core and bulk silicate) provides essential constraints for thermal and physical models of Vestan evolution at high temperature (e.g., Ghosh and McSween 1998; Gupta and Sahijpal 2010; Moskovitz and Gaidos 2011) that may ultimately lead to a better understanding of the differentiation process on protoplanetary bodies such as Vesta.

*Acknowledgments*—Enlightening discussions with J.-A. Barrat and formal reviews by H. Takeda and G. J. Taylor are gratefully acknowledged. MT thanks the Centre National d'Etudes Spatiales (CNES) for their financial support, which enabled participation in this work and the Dawn mission.

*Editorial Handling*—Dr. Carle Pieters

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