Thermal constraints on the early history of the H-chondrite parent body reconsidered

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Geochimica et Cosmochimica Acta 74 (2010) 5410–5423 www.elsevier.com/locate/gca

Thermal constraints on the early history of the H-chondrite parent body reconsidered Keith P. Harrison *, Robert E. Grimm Southwest Research Institute, 1050 Walnut St., Ste 300, Boulder, CO 80302, USA Received 16 March 2010; accepted in revised form 26 May 2010; available online 25 June 2010

Abstract Reconstructions of the early thermal history of the H-chondrite parent body have focused on two competing hypotheses. The first posits an undisturbed thermal evolution in which the degree of metamorphism increases with depth, yielding an “onion-shell” structure. The second posits an early fragmentation–reassembly event that interrupted this orderly cooling process. Here, we test these hypotheses by collecting a large number of previously published closure age and cooling rate data and comparing them to a suite of numerical models of thermal evolution in an idealized parent body. We find that the onion-shell hypothesis, when applied to a parent body of radius 75–130 km with a thermally insulating regolith, is able to explain 20 of the 21 closure age data and 62 of the 71 cooling rates. Furthermore, six of the eight meteorites for which multiple data (at different temperatures) are available, can be accounted for by onion-shell thermal histories. We therefore conclude that no catastrophic disruption of the H-chondrite parent body occurred during its early thermal history. The relatively small number of data not explained by the onion-shell hypothesis may indicate the formation of impact craters on the parent body which, while large enough to excavate all petrologic types, were small enough to leave the parent body largely intact. Impact events fulfilling these requirements would likely have produced transient crater diameters at least 30% of the parent body diameter. Ó 2010 Elsevier Ltd. All rights reserved.

1. INTRODUCTION The H-chondrite meteorites are thought to have originated in a single, undifferentiated parent body (e.g., Wasson, 1972). The parent body underwent varying degrees of metamorphism as a result of heat released internally, probably by the radioactive decay of 26Al (Minster and Alle´gre, 1979). The degree of metamorphism is inferred from petrologic type, which ranges from type 3 (least metamorphosed) to 6 (most metamorphosed; Van Schmus and Wood, 1967). Petrologic type has thus been used as a proxy for peak metamorphic temperatures (Dodd, 1969, 1981). The peak temperatures of Dodd (1981) were derived for types 3 and 6 only (the respective ranges are 400–600 and 750–950 °C), with peak temperatures for types 4 and 5 calculated by interpolation. Newer thermometric techniques have yielded temperature ranges of 865–926 °C for type 6 *

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meteorites (Slater-Reynolds and McSween, 2005), 675– 750 °C for the lower bound on peak temperatures for types 4–6 (Wlotzka, 2005; Kessel et al., 2007), and temperatures anywhere from 260 to 600 °C for the different subclasses of type 3 (Huss et al., 2006, and references therein). The relationship between peak temperature and petrologic type has allowed broad constraints to be placed on the early thermal history of the H-chondrite parent body. The most straightforward approach, arising from a simple thermal model of internal heating in a sphere, is the “onion-shell” model. Peak temperatures decrease monotonically away from the center of the body, producing layers of progressively lower petrologic type (Wood, 1967; Minster and Alle´gre, 1979; Pellas and Storzer, 1981). The lower the peak temperature, the shorter the cooling time, and a range of methods (described in further detail below) have been employed in recent years to infer such times (Trieloff et al., 2003; Amelin et al., 2005; Bouvier et al., 2007). Additional constraints are available in the form of cooling rates: samples that originated near the center of the

History of the H-chondrite parent body

parent body, where temperature gradients were low, likely cooled slowly, while samples from shallow depths, where temperature gradients were steeper, likely cooled rapidly. The onion-shell model might thus be confirmed if petrologic type (i.e., peak temperature) were observed to correlate inversely with cooling rate. Some of the first cooling rate measurements made on Hchondrites (Pellas and Storzer, 1981; Lipschutz et al., 1989) seemed to confirm the onion-shell hypothesis, while others did not (Scott and Rajan, 1981). The analysis of a large number of samples by Taylor et al. (1987) again appeared to contradict the onion-shell model, leading these workers to invoke the hypothesis, first suggested by Grimm (1985), that the early hot parent body was shattered by a large impact, followed by the haphazard reassembly of fragments of various temperatures. Subsequent cooling of such a body would be expected to record no correlation between petrologic type and cooling rate. There are, however, problems with some of the cooling rate data collected by Scott and Rajan (1981) and Taylor et al. (1987). The highest H-chondrite cooling rates recorded by these workers are for metals in the fine-grained matrices of regolith breccias. These matrices appear to have formed by the comminution of larger clasts as a result of shallow regolith development on the surface of the parent body (Bischoff et al., 1983). If this process occurred during the early metamorphic heating of the parent body, the comminution of hot clasts into finer grains would have accelerated cooling rates in the material, explaining the very wide range of values up to a few thousand °C/Ma (Scott and Rajan, 1981; Taylor et al., 1987; Williams et al., 2000). Alternatively, these materials may have been reheated following early metamorphism (e.g., Kessel et al., 2007). These cooling rates may therefore have little relevance to global-scale parent body thermal history. While this does not necessarily put to rest the fragmentation–reassembly hypothesis, there are additional concerns about the Taylor et al. (1987) data that raise significant doubts, and these are addressed later. Some cooling rate data published after those of Taylor et al. (1987) appear to support an onion-shell model once again (Go¨pel et al., 1994; Trieloff et al., 2003), leaving a somewhat conflicting picture of the early H-chondrite parent body thermal history. We attempt to address this problem here by bringing together a large sample of the available data and comparing them to numerical models of onion-shell thermal development in an idealized parent body. 2. METHODOLOGY Our methodology, which is similar to that of Bennett and McSween (1996), consists of the following steps: (1) Initialize a numerical model of parent body thermal history with thermal parameter values drawn from a plausible range (Section 2.2). (2) Run the model iteratively, each time adjusting the heat source (via the initial 26Al/27Al ratio) until the peak temperature attained at the center of the body is approximately 1000 °C (Section 2.2). (3) Rerun the model with different parent body radii until an optimal fit is found to closure time and cooling rate data from the literature (Section 2.1).

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We proceed first with a detailed description of the literature data used, followed by a full characterization of our thermal model. 2.1. Data analysis Our study integrates two types of data from the literature that are often reported separately. The first is the closure time corresponding to a particular radiometric dating technique, namely the time elapsed before a meteorite passes through a given temperature during metamorphic cooling of the parent body. The second type of data gives the rate at which the sample is thought to have cooled through a particular closure temperature. Critical to the comparison between these data and numerical results is the choice of peak temperatures used to distinguish each petrologic type: data from the literature are also used to motivate this choice. We discuss our various data sources below. 2.1.1. Closure times Closure time is defined as the difference between calcium–aluminum-rich inclusion (CAI) age and the closure age of the sample under consideration. We use a recently calculated CAI age of 4568.5 ± 0.5 Ma (Bouvier et al., 2007) for all data except those of Kleine et al. (2008), whose closure times use the statistically indistinguishable CAI age of 4568.3 ± 0.7 Ma (Lugmair and Shukolyukov, 1998). 40 Ar–39Ar closure times: 40Ar produced by the radiogenic decay of K is retained in oligoclase feldspar below about 280 °C (Turner et al., 1978). The amount of 40Ar and, therefore, the time taken for the sample to reach the closure temperature, is measured relative to artificially produced 39Ar. Trieloff et al. (2003) performed Ar–Ar measurements on several samples (Table 1), and we include their results in our analysis. We have followed the recommendation of Trieloff et al. (2003) and subtracted 30 Ma from their closure times to account for recent recalibrations of the Ar–Ar age scale (Renne, 2000; Begemann et al., 2001; Trieloff et al., 2001). (2) Pb–Pb closure times: Production of 207Pb by the decay of 235U early in the solar system allows age measurements of very old samples to be made through measurements of the lead ratio 207Pb/206Pb. The reliability of this method for a particular sample can be gauged by comparing its results against those of the 238U–206Pb system. Pb–Pb closure times, which have a closure temperature in the range 430–530 °C, were used by Go¨pel et al. (1994) to date phosphates in ordinary chondrites. Their results are widely cited (e.g., Ganguly and Tirone, 2001; Trieloff et al., 2003; Bouvier et al., 2007), and we include them in our analysis. We also include related Pb–Pb measurements, made by Bouvier et al. (2007) and Amelin et al. (2005), that have closure temperatures of 680– 880 °C. (A 480 °C Pb–Pb closure age of 77 ± 16 Ma for the Estacado meteorite is also available; Blinova et al., 2007. We acquired knowledge of this datum too late for it to be fully integrated into our analysis,

(1)

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Table 1 Closure time and cooling rate data. Meteorite

Type

Closure timea (Ma)

Temperature (°C)

Method

Reference

Closure times Forest Vale

H4

7.6 ± 0.7 16.5 ± 8.5

480 ± 50 280 ± 20

Pb–Pb Ar–Ar

Go¨pel et al. (1994) Trieloff et al. (2003)

Ste. Marguerite

H4

ALH 84069

H5

5.8 ± 1.1 6.8 ± 1.7 6.5 ± 16.5 5.9 ± 1.4

480 ± 50 730 ± 50 280 ± 20 825 ± 75

Pb–Pb Pb–Pb Ar–Ar Hf–W

Go¨pel et al. (1994) Bouvier et al. (2007) Trieloff et al. (2003) Kleine et al. (2008)

Allegan

H5

18.3 ± 0.8 27.5 ± 11.5

480 ± 50 280 ± 20

Pb–Pb Ar–Ar

Go¨pel et al. (1994) Trieloff et al. (2003)

Nadiabondi

H5

12.9 ± 3.9 9.6 ± 2.8 33.5 ± 10.5

480 ± 50 730 ± 50 280 ± 20

Pb–Pb Pb–Pb Ar–Ar

Go¨pel et al. (1994) Bouvier et al. (2007) Trieloff et al. (2003)

Richardton

H5

Estacado

H6

5.6 ± 1.1 17.8 ± 3.1 43.5 ± 11.5 10.0 ± 1.7 103.5 ± 5.5

825 ± 75 480 ± 50 280 ± 20 825 ± 75 280 ± 20

Hf–W Pb–Pb Ar–Ar Hf–W Ar–Ar

Kleine et al. (2008) Amelin et al. (2005) Trieloff et al. (2003) Kleine et al. (2008) Trieloff et al. (2003)

Guaren˜a

H6

64.1 ± 0.5 84.5 ± 6.5

480 ± 50 280 ± 20

Pb–Pb Ar–Ar

Go¨pel et al. (1994) Trieloff et al. (2003)

Kernouve

H6

9.4 ± 1.1 46.0 ± 2.0 69.5 ± 6.5

825 ± 75 480 ± 50 280 ± 20

Hf–W Pb–Pb Ar–Ar

Kleine et al. (2008) Go¨pel et al. (1994) Trieloff et al. (2003)

Meteorite

Type

Cooling rate

Temperatureb (°C)

Method

Reference

Cooling rates Dhajala

H3

50c

500

Met.d

Taylor et al. (1987)

Tieschitz Conquista

H3 H4

2c 25

500 500

Met. Met.

Willis and Goldstein (1981) Taylor et al. (1987)

Kesen

H4

20

500

Met.

Taylor et al. (1987)

Sete Lagoas

H4

15

500

Met.

Williams et al. (2000) Trieloff et al. (2003)

Ste. Marguerite

H4

84 ± 77

200

244

Wellman Allegan

H4 H5

8 3.25 ± 0.55 15

500 200 500

Met. 244 Pu Met.

Willis and Goldstein (1981) Trieloff et al. (2003) Taylor et al. (1987)

Ehole

H5

4

500

Met.

Willis and Goldstein (1981)

e

Pu

Fayetteville

H5

20 to >1000 (3)

500

Met.

Williams et al. (2000)

Ipiranga

H5

5–20 (3)

500

Met.

Williams et al. (2000)

Malotas

H5

8

500

Met.

Willis and Goldstein (1981)

Nuevo Mercurio

H5

15

500

Met.

Taylor et al. (1987)

Nulles

H5

25–140 (11)

500

Met.

Williams et al. (2000)

Richardton

H5

2.95 ± 0.45 20

200 500

244

Pu Met.

Trieloff et al. (2003) Taylor et al. (1987)

Sena

H5

2.45 ± 0.35

200

244

Trieloff et al. (2003)

Sete Lagoas

H5

5–25 (2)

500

Met.

Williams et al. (2000)

Sutton

H5

4

500

Met.

Willis and Goldstein (1981)

Cangas de Onis

H6

5–40 (12)

500

Met.

Williams et al. (2000)

200 500

244

Trieloff et al. (2003) Taylor et al. (1987)

Estacado

H6

2.55 ± 0.35 10

Pu

Pu Met.

History of the H-chondrite parent body

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Table 1 (continued) Meteorite

Type

Cooling rate

Temperatureb (°C)

Method

Reference

Guaren˜a

H6

75 ± 25 2.95 ± 0.45

775 200

Ol–Spf 244 Pu

Kessel et al. (2007) Trieloff et al. (2003)

Ipiranga

H6

5–25 (11)

500

Met.

Williams et al. (2000)

244

Kernouve

H6

2.65 ± 0.35 10

200 500

Pu Met.

Trieloff et al. (2003) Taylor et al. (1987)

Sete Lagoas

H6

5–75 (7)

500

Met.

Williams et al. (2000)

a

Closure times are relative to CAI formation. A CAI age of 4568.5 ± 0.5 Ma (Bouvier et al., 2007) is used to calculate closure times from ages when necessary. b Uncertainties for temperatures associated with cooling rates are not generally available; we use ±25 °C. c Cooling rates from Taylor et al. (1987) and Willis and Goldstein (1981) are, at the former authors’ suggestion, assumed to have an uncertainty of a factor of 2.5. d Met. = Metallographic cooling rate method. e Numbers in parentheses indicate the number of clasts for which independent cooling rate measurements were made by Williams et al. (2000). For brevity, we provide the only the range of cooling rates obtained, and refer the reader to Williams et al. (2000) for details. f Ol–Sp = Olivine–spinel cooling rate method.

but we have determined that it, and an associated cooling rate of about 6 °C/Ma from the same authors, are consistent with our conclusions). (3) Hf–W closure times: 182W produced by the decay of 182 Hf early in solar system history can, when compared to other W isotopes, be used to determine ages for the relatively high closure temperature range of 750–900 °C (e.g., Harper and Jacobsen, 1996). Kleine et al. (2008) applied this system to ordinary chondrites, and we include their results in our analysis. 2.1.2. Cooling rates (1) Metallographic cooling rates: As Fe–Ni alloys in the parent body began to cool from high temperatures (>700 °C), the phase diagram of the binary Fe–Ni system indicates that they consisted of pure taenite (Wood, 1967). As cooler temperatures were reached, however, precipitation of kamacite began, and the Ni content of the two phases changed via diffusion from taenite to kamacite. Because the rate of diffusion in both phases decreases with cooling, the system must eventually have moved out of equilibrium. Evidence for this is found in the heterogeneous distribution of Ni in the grains which, together with idealized models of Ni diffusion, can be used to infer the cooling rate experienced by the grains as they passed through about 500 °C. Most of the cooling rate data available in the literature are derived with the metallographic method. We use the rates listed in Taylor et al. (1987), which include data acquired by previous workers (e.g., Wood, 1967; Scott and Rajan, 1981) and later revised by Willis and Goldstein (1981). Interestingly, most of the measurements taken directly by Taylor et al. (1987) appear to be consistent with the onion-shell model, as pointed out by Go¨pel et al. (1994). Of the remaining data, we omit the following: (a) Bath meteorite: The cooling rate of 80 °C/Ma may be problematic due to scatter in the data, as discussed by Willis and Goldstein (1981). (b) A cooling rate of approximately 140 °C/Ma is reported for two meteorites (types 4 and 5) in the

key figure (Fig. 5) of Taylor et al. (1987), but the source of these data is not clear. Candidates are the Weston, Fayetteville, and Leighton meteorites. Weston and Fayetteville are regolith breccias, and because the high cooling rates initially reported by Scott and Rajan (1981) were measured in the matrices of these breccias, we regard them as irrelevant to global-scale thermal history, as discussed in Section 1. The Leighton cooling rate of 200 °C/Ma, originally measured by Wood (1967) and modified upwards by Willis and Goldstein (1981), was derived from a relatively incoherent data plot. Wood (1967) suggests that “nothing can be said about [its] cooling rate”. We therefore discard this datum also. Finally, we include a large set of metallographic cooling rates estimated for equilibrated clasts in four H-chondrite regolith breccias (Williams et al., 2000). Once again, we omit widely variable cooling rates for matrix material also estimated by these authors. Williams et al. (2000) used the same methodology as Taylor et al. (1987) and we therefore assign to all metallographic cooling rates the uncertainty of a factor of 2.5 suggested by the earlier authors. There may also be a systematic error associated with the metallographic method: Taylor et al. (1987) suggest that the method may produce cooling rates up to a factor of 3 too small. A more recent revision to the method indicates that cooling rates may be up to an order of magnitude too small, but this analysis was applied to iron meteorites and mesosiderites only (Hopfe and Goldstein, 2001). Although these suggestions are worth noting, the lack of reliable data constraining systematic cooling rate errors for ordinary chondrites compels us to assume negligible values for the time being. (2) 244Pu cooling rates: Fission tracks produced by 244Pu fission will fail to anneal below a certain mineral-dependent temperature, thereby remaining in the rock indefinitely. Fission track density can thus be related to the time at which this temperature was reached (Pellas and Storzer, 1981; Pellas et al., 1997). Trieloff et al. (2003) analyzed fission tracks in two minerals (orthopyroxene and merrillite)

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in ordinary chondrites, yielding two closure times and therefore a cooling interval between the two closure temperatures (280 and 120 °C, respectively). We use this interval to infer an approximate cooling rate at the intermediate temperature (200 °C). To compute the uncertainty in these measurements, we use individual and systematic uncertainties in the cooling interval, and an uncertainty in closure temperature (Trieloff et al., 2003). (3) Olivine–spinel cooling rate: Fe–Mg exchange between olivine and spinel can be analyzed in a fashion similar to the metallographic method in order to obtain cooling rates at temperatures of about 700–850 °C (Kessel et al., 2007). Kessel et al. (2007) provide a single measurement only, which we include in our analysis. 2.1.3. Peak temperature A crucial part of the modeling effort is the delineation of predicted results according to petrologic type. This exercise relies on the assumption introduced earlier that peak temperature and petrologic type are correlated. Although this assumption is still thought valid, recent work suggests that it ought to be quantified somewhat differently. Early work by Dodd (1981) yielded peak temperature estimates of 400–600 °C for type 3 and 750–950 °C for type 6. Types 4 and 5 were assigned intermediate peak temperatures through interpolation. Further work on type 3 meteorites has revealed a wide range of peak temperatures from 260 to 600 °C (Huss et al., 2006, and references therein). Concerning type 6 meteorites, Kleine et al. (2008) refer to more recent work using two-pyroxene thermometry, which indicates peak temperatures of 865–926 °C (Slater-Reynolds and McSween, 2005), although a higher limit of 1000 °C is possible (this is where melting in the FeNi–FeS system be-

gins). Kleine et al. (2008) also note that olivine–spinel thermometry indicates a 675–750 °C lower bound on peak temperatures for types 4–6 (Wlotzka, 2005; Kessel et al., 2007), which dovetails reasonably well with the 600 °C upper limit for type 3. Thus, while types 3 and 6 appear to be easily distinguishable by peak temperature, types 4 and 5 do not. In our thermal modeling work we therefore consider types 4 and 5 to be part of one group with peak temperatures ranging from 675 to 865 °C. Subtypes within type 3s appear to be quite well correlated with peak temperature (e.g., Wlotzka, 2005), but there is little point in delineating these subtypes in thermal models since there are so few type 3 age and cooling rate data to compare against the predicted regions. Accordingly then, we delineate model parameter spaces into three regions corresponding to all type 3s (peak temperatures <675 °C), types 4 and 5 together (675–865 °C), and type 6s (865–1000 °C). 2.2. Numerical model As stated above, the purpose of the current work is to compare closure time and cooling rate data with predictions made from onion-shell numerical models. The numerical model allows us to estimate which parts of the temperature-vs.-time and cooling rate-vs.-temperature parameter spaces are expected to be occupied by meteorites of different petrologic types. It also allows us to determine if multiple data from a single meteorite are consistent with the cooling history of a single parcel of material in the parent body. Our thermal model, implemented with the COMSOL 3.5a finite-element code (www.comsol.com) is a 1D, spherically symmetric abstraction of a parent body with uniform internal heating due to 26Al decay, and a radiative

Table 2 Parameter values for our optimal model with parent body radius 100 km. Optimal results can be obtained for other radii by varying porosity or thermal diffusivity as indicated in Fig. 1. Thermal and geometric properties Thermal diffusivitya A B

A + B/T 1.56  107 m2 s1 8.88  105 m2 K s1

Thermal conductivityb

(A + B/T)q cP(T)(1  1.13/0.333) Interior

Megaregolithc

Regolithc

Bulk density (q, kg m3) Porosity (/, %) Initial temperature Parent body radius

3250 6 170 K 100 km

2500 25

1500 50

Internal heating Initial 26Al/27Al Mass fraction 27Al 26 Al decay constant

7.45  106 (2.2 Ma after CAIs) 0.0117 9.63  107 year1

Radiative boundary condition Semi-major axis Emissivity Albedo

3 AU 0.8 0.05

a b c

After Yomogida and Matsui (1983). After Akridge et al. (1998). Specific heat in this expression is modeled after Yomogida and Matsui (1983). Megaregolith and regolith are both 410 m thick. This value was obtained through the process of optimizing the model.

History of the H-chondrite parent body

boundary (Table 2). We use the finite-element method instead of simpler finite-difference or analytical solutions because we were originally working toward a model of 3D fragmentation and reassembly (Grimm et al., 2005). Our model assumes that parent body accretion occurred on a time scale short enough to be thermally insignificant. Certainly, if accretion was relatively sedate (on the order of 1 Ma), thermal evolution during this time would be important (Ghosh et al., 2003), however recent transient-overdensity models suggest that accretion may have occurred much more rapidly (within several orbits, Johansen et al., 2007). We ran two types of model: homogeneous and insulated. The homogeneous model has spatially uniform thermal properties, while the insulated model has three distinct regions: interior, megaregolith, and regolith, modeled after Akridge et al. (1998). In all models, thermal diffusivity is temperature dependent. We use j(T) = A + B/T, where A and B are constants and T is temperature. This relationship, first put forward by Yomogida and Matsui (1983), is commonly used in other models of ordinary chondrite parent body thermal history (e.g., Bennett and McSween, 1996; Akridge et al., 1998). We ran models with three different sets of values for A and B, all from Yomogida and Matsui (1983) (Table 2). The first two are those considered by Bennett and McSween (1996) to be appropriate for uncompacted (A = 1.56  107, B = 8.88  105) and compacted (A = 3.66  107, B = 2.91  104) parent bodies, respectively. The third (A = 4.47  107, B = 1.32  104) is that used in the insulated model of Akridge et al. (1998). Thermal conductivity is given by k(T) = j(T)q cP(T), where q is bulk density and cP is specific heat. The model of Bennett and McSween (1996) uses a fixed thermal conductivity, implying that specific heat must vary with temperature so as to compensate for the temperaturedependence of the diffusivity. We found that this specific heat variation is in good agreement with the temperaturedependence suggested by Yomogida and Matsui (1983), which we use in our models. For our insulated model, we add a porosity term to the conductivity, in keeping with Akridge et al. (1998): kðT Þ ¼ jðT ÞqcP ðT Þð1  1:13/0:333 Þ

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with a unique combination of parent body size and thermal conductivity. Changes to parent body size require proportionate changes to conductivity, which can be made through modifications to either the thermal diffusivity or the porosity as indicated in Fig. 1. All models in the optimal suite accrete (instantaneously) at 2.2 Ma after CAI formation, corresponding to an initial 26Al/27Al of 7.45  106. We discuss in detail the 100 km radius parent body (Table 2), since this is the smallest body with a thermal diffusivity computed from parameters drawn from the chosen parameter space. However, we note that identical results can be obtained in even smaller bodies by increasing the porosity in Eq. (1) such that thermal conductivity decreases by the same factor as the parent body volume without changing the diffusivity. Such porosity increases are not unreasonable for bodies down to about 75 km radius (at this point, the interior porosity reaches that of the overlying megaregolith). We compare graphically the optimal model results with the collected literature data in Figs. 2 and 3. (In Fig. 3, the lateral spread of the data is made for clarity, and does not represent real temperature variations.) Our measure of model success has two components. First, we determine the number of data from our literature survey that fall within the region predicted (by our model) for their petrologic type. Second, we determine if there exist modeled thermal histories that can explain multiple datapoints available for a single meteorite. We begin with a discussion of the first, broader measure of model success, looking in turn at closure times, and then cooling rates.

ð1Þ

This approach models the lower bulk thermal conductivities associated with higher porosities in the megaregolith and regolith. We considered megaregolith and regolith thicknesses in the same range (0.5–3 km) as Akridge et al. (1998). Thicknesses were varied within this range so as to improve the fit between model and data. We ran models with the above variety of thermal parameters in combination with six alternative parent body radii: 55, 70, 85, 100, 125, and 150 km, which encompass the approximate range of values suggested by other authors (75–100 km; Grimm et al., 2005, and references therein).

3. RESULTS AND DISCUSSION We find a range of models that produce the same optimal fit to the literature data. These are insulated models

Fig. 1. Parameter space yielding optimal model results. The dashed line indicates the factor by which the interior porosity of the nominal model (0.06) must be multiplied in order to obtain optimal results for a different parent body radius. For radii below about 75 km, the interior porosity reaches that of the overlying megaregolith, and higher values are therefore unlikely. For radii above 120 km, porosity reaches zero and can no longer be used to optimize the model. Optimal results can alternatively be obtained by multiplying nominal thermal diffusivity parameters A and B by the factor indicated by the solid line. For parent body radii between 100 and 130 km, this adjustment yields diffusivities within the range considered in most studies.

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Fig. 2. (a) Closure times from the literature plotted against regions (shaded, with solid borders) for each petrologic type predicted by our optimal onion-shell numerical model. Numbered circles depict petrologic type. The five coolest types 4 and 5 data all correspond to a temperature of 280 °C, and have been spread vertically for clarity.

3.1. Closure times For our optimal model suite, only 1 of the 21 datapoints lies outside the region predicted for its petrologic type (Fig. 2). This point (closure time = 5.8 Ma; temperature = 480 °C) is from the type 4 Ste. Marguerite meteorite (Go¨pel et al., 1994), and is statistically identical to closure times estimated for this meteorite for two other temperatures (280 and 730 °C, Trieloff et al., 2003; Bouvier et al., 2007). Since the meteorite cannot have cooled through multiple temperatures at the same time, one or more of these data must be erroneous. The uncertainties in the two latter temperatures are such that a coherent cooling history may be derived for Ste. Marguerite if the Go¨pel et al. (1994) datum is ignored (see Section 3.3). 3.2. Cooling rates Cooling rate fits are shown in Fig. 3. Most of the cooling rates in our dataset are metallographic, and therefore have relatively large uncertainties derived from the cooling rate curves used and from the scatter of the data plotted over these curves (Wood, 1967; Taylor et al., 1987; Williams et al., 2000). Thus few points can, with statistical confidence, be said to lie outside the appropriate predicted region. Of the 33 type 4 and 5 meteorites and the 36 type 6 meteorites, only 7 and 2 suffer this fate, respectively. Only two type 3 cooling rates are available, and both fall within their predicted region. In order to further investigate the influence of the assumed uncertainty in metallographic cooling rates, we re-evaluated the fit for a range of uncertainty factors from 1 (no uncertainty) to 5, which includes our nominal value of 2.5 (Taylor et al., 1987). We find that the proportion of data fitting model predictions remains relatively high (>70%) for uncertainty factors as low as 1.7 (Fig. 4). Even the assumption of no uncertainty yields a fit greater than 50%. We thus retain our nominal uncertainty factor of 2.5. As described above, there may be systematic errors in the metallographic method that artificially reduce cooling rates by about a factor of 3 (Taylor et al., 1987) or possibly even 10 (Hopfe and

Goldstein, 2001). We find that no uniform upward revision of the metallographic cooling rates in our study produces any improvement to their overall fit with the thermal model. It may be that adjustments to the model could preserve the fit if a systematic increase in cooling rates was found to be necessary, but until such revisions are better constrained, we omit them from our analysis. Including non-metallographic cooling rates, then, we find that 87% of all the cooling rate data collected (62 of 71) conform to the predictions of our optimal onion-shell model suite. The nine offending data do not originate from one particular study, they are not confined to a single meteorite, nor are they exclusively metallographic (Fig. 3). 3.3. Thermal constraints on individual meteorites Our second method of assessing the thermal model is to consider the meteorites in our study for which multiple data (at different closure temperatures) are available. We wish to determine if there exist model thermal histories that can explain all measurements within a single meteorite. To begin, we consider closure time and cooling rate data independently. Starting with closure times, we seek the set of computed thermal histories that pass within the error bars of the closure time measurements for a given meteorite. There are eight meteorites for which multiple closure time data are available (Allegan, Estacado, Forest Vale, Guaren˜a, Kernouve, Nadiabondi, Richardton, and Ste. Marguerite). There exist thermal histories that successfully connect the closure age data for all of these meteorites except Ste. Marguerite (H4; Fig. 4 and Table 3). As discussed above, one of the Ste. Marguerite data does not lie within the field predicted for type 4/5 meteorites (Fig. 2). If we eliminate this datum, thermal histories with peak temperatures of 704– 837 °C are observed to connect the remaining two points. Next, we consider meteorites with multiple cooling rate data (Allegan, Estacado, Guaren˜a, Kernouve, and Richardton). Cooling rate histories can be found (Fig. 6) that connect the available for all of these meteorites, although we emphasize that only two data are available in each case.

History of the H-chondrite parent body

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Fig. 3. Cooling rates at 200 °C for (a) types 4 and 5 and (b) type 6; at 500 °C for (c) type 3, (d) types 4 and 5, and (e) type 6; at 780 °C for (f) type 6 meteorites. The abscissa of each panel represents the single closure temperature indicated, with the data spread laterally for clarity. As in Fig. 1, the solid shaded area in each panel denotes the region predicted by our optimal thermal model for the petrologic type(s) indicated. Note the varying ordinate scales.

Plausible thermal histories connecting either closure times or cooling rates for a given meteorite are presented quantitatively in Table 3. The histories are denoted by their range of peak temperature and their corresponding radial positions in the parent body. In all cases except one, plausible thermal histories overlap with the range corresponding to the petrologic type of the meteorite. The exception is Guaren˜a (H6): the range of thermal histories derived from its two cooling rates have peak temperatures between 762 and 793 °C, below the minimum peak temperature chosen for type 6s (865 °C). Having found thermal histories for closure time and cooling rate data independently, we now seek thermal histo-

ries that satisfy both sets of data. In principle, the two sets of histories for each meteorite should overlap. This is what we observe for four of the six relevant meteorites (Allegan, Estacado, Kernouve, and Richardton). Guaren˜a and Ste. Marguerite are the two exceptions. As noted already, the Guaren˜a cooling rate histories do not fall in the type 6 range, making it impossible for these histories to coincide with the very narrow type 6 range derived from closure time data. For Ste. Marguerite, the lack of plausible histories connecting its closure time data makes moot the inclusion of the cooling rate datum. However if, once again, we omit the Ste. Marguerite closure time that does not fall within

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Fig. 4. The proportion of metallographic cooling rates that fit with model predictions, as a function of the uncertainty factor assigned to these rates. The dot marks the nominal factor of 2.5 used in our analysis.

the type 4/5 region, we find thermal histories that connect the remaining two closure times and the cooling rate. These histories are the same as those derived from the two closure times alone: 704–837 °C, equivalent to normalized radial positions of 0.952–0.975. 3.4. Additional constraints We briefly consider other available constraints on early H-chondrite parent body thermal evolution. First is the time of parent body accretion as measured from CAI for-

mation. This has been estimated in other modeling efforts to be approximately 2 Ma (Miyamoto et al., 1981; Grimm, 1985; Grimm and McSween, 1993), and has been constrained by the Pb–Pb chronology of Go¨pel et al. (1994) to be 3.0 ± 2.6 Ma. Our value of 2.2 Ma agrees well with these constraints. Second is the radius of the parent body, which has been estimated to be between 75 and 100 km (Grimm et al., 2005 and references therein). As shown in Fig. 1, reasonable adjustments to porosity or thermal diffusivity allow our optimal results to be repeated for an even wider range of parent body radii (75–130 km). Next, we consider the formation time interval, defined as the time taken for the center of the body to cool through the Rb–Sr blocking temperature of about 130 °C. Miyamoto et al. (1981) used a formation time interval of 100 Ma, although more recent work by Bennett and McSween (1996) argues for a smaller value of about 60 Ma. Our optimal models do not conform well to this constraint, producing formation time intervals on the order of 400 Ma (although the most shallow type 6 material takes only 70 Ma). This is because some closure time age data used in our analysis are in direct conflict with a short formation time interval. Specifically, Ar–Ar closure time data for type 6 meteorites (Trieloff et al., 2003) indicate that some samples were still at temperatures more than twice the Rb–Sr blocking temperature at times as late as 100 Ma (Table 1 and Fig. 2). Further analysis of both the Rb–Sr results used to determine formation time interval, and the Ar–Ar ages of Trieloff et al. (2003), must be carried out in order to resolve this problem, and is beyond the scope of the current work.

Table 3 Plausible thermal histories for those meteorites with multiple data available (see Figs. 4 and 5). Name

Range of peak temperatures (°C)

Normalized radial distancea

Thermal histories derived from closure time data Forest Vale H4 Ste. Marguerite H4 Allegan H5 Nadiabondi H5 Richardton H5 Estacado H6 Guaren˜a H6 Kernouve H6

553–707 No plausible histories 831–909 773–886 804–923 984–990 991–993 971–985

0.975–0.991 0.929–0.953 0.938–0.965 0.922–0.959 0.848–0.862 0.836–0.842 0.861–0.885

Thermal histories derived from cooling rate data Allegan H5 Richardton H5 Estacado H6 Guaren˜a H6 Kernouve H6

717–998 762–988 826–1000 762–793 815–1000

0.804–0.973 0.853–0.966 0–0.954 0.961–0.966 0–0.957

Thermal histories derived from data of both types Ste. Marguerite H4 Allegan H5 Richardton H5 Estacado H6 Guaren˜a H6 Kernouve H6

No plausible histories 831–909 804–923 984–990 No plausible histories 971–985

a

Type

Distances are normalized to a radius of 100 km.

0.929–0.953 0.922–0.959 0.848–0.862 0.861–0.885

History of the H-chondrite parent body

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Fig. 5. Onion-shell thermal histories (shaded) can be found that pass within the error bars of all available closure time data for the meteorites indicated. Error bars are replaced with boxes surrounding each data-point (“x”). The range of peak temperatures corresponding to each set of thermal histories is given in Table 3.

Finally, we consider the proportion (by volume) of each petrologic type thought to contribute to the parent body. Values for our nominal optimal model are 84%, 10%, and 6% for type 6, type 4/5, and type 3, respectively. Of the models run by Bennett and McSween (1996), the one with initial conditions most closely matching those of our own yields proportions of 70%, 10%, and 20%, respectively. The Akridge et al. (1998) model yields proportions of 88%, 6%, and 6%. That our proportions are closer to those

of Akridge et al. (1998) reflects our use of insulating megaregolith and regolith layers. Ultimately, though, such proportions have limited applicability: Akridge et al. (1998) and Bennett and McSween (1996) note that processes such as parent body ejection and atmospheric passage, compounded by likely changes in flux over time, have almost certainly introduced significant bias to the proportion of petrologic types in the meteorite collection, rendering these proportions unsuitable for constraining thermal modeling.

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Fig. 6. Onion-shell thermal histories (shaded) can be found that pass within the error bars of all available cooling rate data for the meteorites indicated. Error bars are replaced with boxes surrounding each data-point (“x”). The range of peak temperatures corresponding to each set of thermal histories is given in Table 3.

3.5. A perturbed onion-shell model A broad assessment of the data presented above indicates that 95% of closure times and 87% of cooling rates are consistent with our optimal onion-shell interpretation of early H-chondrite parent body thermal history. Cooling rates derived by fitting theoretical cooling curves to closure time data (Ganguly and Tirone, 2001; Kleine et al., 2008), also support this interpretation. In reality, an onion-shell thermal history will not have produced a perfect set of closure times and cooling rates. Our thermal model is highly idealized, and the regions it predicts for the various petrologic types should not be regarded as having fixed, sharply defined boundaries. Also uncertain are the peak temperatures we have chosen to distinguish between petrologic types. However, alternative choices were found to yield no improvements to the fit. We therefore need to consider processes that can perturb the onion-shell thermal structure, thereby explaining the small group of ill-fitting data without requiring complete

disruption of the parent body (Grimm et al., 2005; Schwartz et al., 2006; Scott et al., 2010). The most likely process is impact cratering due to collisions between the parent body and smaller asteroids. Although it is not certain that all petrologic types need to be excavated (for instance, Scott et al., 2010, argue for excavation of type 4s only), we adopt the conservative endmember assumption that all types must be included. Such an impact would have to excavate to a depth of at least 5.6 km in our 100 km radius optimal model. We employ a commonly used scaling law for gravity-dominated impacts (Housen et al., 1983; Asphaug, 1997) to confirm that such an impact is plausible: rp ¼ 0:41D1:28 g0:28 v0:56 : i Here, rp is the projectile radius, D is the transient crater diameter, g is surface gravitational acceleration, and vi is impact velocity. We set D = 56 km, since the excavation depth (which must be 5.6 km) is thought to be about a tenth of the transient crater diameter (Melosh, 1989). For a 100 km diameter target with mean density of 3250 kg m3

History of the H-chondrite parent body

(equivalent to the interior density of our model, which dominates the mean), we have g = 0.091 m s2. Given D and g, we seek an impact with a constant value of the expression rpvi0.56 = 2.5  105. For a wide range of impact velocities (0.1–10 km s1, corresponding to projectile radii of 19 km down to 1.3 km), the impact energy per unit target mass varies from about 30 to 150 J kg1. This range is about an order of magnitude lower than the energy required to shatter the body (103 J kg1, defined as the energy which results in fragments that remain gravitationally bound, with the largest fragment equal to half the total mass of the body; Nolan et al., 2001). The range is also orders of magnitude less than the energy required to permanently disrupt the body (105 J kg1; Housen et al., 1991; Benz and Asphaug, 1999; Nolan et al., 2001). We can also obtain an upper bound on excavation depth by finding the most energetic impact that just avoids shattering the body (i.e., an impact with energy 103 J kg1). For the range of projectile velocities considered above, maximum excavation depths for such an impact are found to lie between 9.2 and 13.5 km, or about twice the minimum excavation depth. An impact that excavated 13.5 km of material would produce anomalous cooling rates in the following approximate volumetric proportions of material (not accounting for the three-dimensional shape of the excavation zone): 15%, 27%, and 58% for type 3, type 4/5, and type 6, respectively. An impact that excavated only the minimum 5.6 km of material required to reach type 6s would result in proportions of 36%, 64%, and 0%. The minimum required transient crater diameter of 56 km is significant compared to the target body diameter (200 km). However, even larger impacts have been observed to leave their target bodies intact (e.g., Moore et al., 2004). The largest crater on Vesta, for instance, is estimated to have had a transient diameter of 300 km (Asphaug, 1997), about 60% of the Vesta diameter (530 km). In our case, the transient diameter is only 30% of the body diameter. A brief look at other parent body radii in our optimal model suite (i.e., 75–130 km) indicates that the excavation of type 6 material would require minimum transient crater diameters ranging from about 40 to 70 km. In all cases, the energy produced by such impacts is too low to shatter the parent body. We note briefly that deep excavation by impacts is suggested by the observation of all petrologic types in regolith breccia clasts. However, cooling rates in these clasts (unlike in the matrix material) are generally consistent with the onion-shell model (as seen in the data from Williams et al., 2000, for example), suggesting that impacts excavated these particular samples after the body cooled. 4. CONCLUSIONS In order to discriminate between the traditional onionshell hypothesis for ordinary chondrite parent body thermal evolution, and the alternative fragmentation–reassembly hypothesis, we have synthesized available H-chondrite closure time and cooling rate data in order to compare them with predictions from a spherically symmetric thermal model of the parent body. Our approach is to vary model

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parameters such as parent body radius, thermal conductivity, and the effectiveness of an insulating regolith, in order to find an optimal fit between model and data. Our optimal fit suggests that the data can be explained well by a thermally insulated onion-shell thermal history in a parent body with reasonable thermal and physical properties. Not only do 20 of the 21 closure age data, and 62 of the 71 cooling rates fall within the predicted ranges for their petrologic types but, in 6 out of 8 cases, plausible thermal histories can be found that pass through multiple data from an individual meteorite. The characteristics of our nominal optimal thermal model include a parent body radius of 100 km, a thermal diffusivity of j(T) = 1.56  107 + 8.88  105 T, an interior porosity of 0.06, insulating regolith and megaregolith layers 410 m thick, and an initial 26Al/27Al of 7.5  106. However, the same optimal fit to the data can be achieved by scaling the parent body radius together with either porosity or thermal diffusivity. The range of parent body radii accessible via this scaling is 75–130 km. Those meteorite samples with closure times or cooling rates that do not conform to our model may have been moved by impact processes to different depths in the parent body during cooling. Impacts capable of excavating material of even the highest (i.e., deepest) petrologic types are not likely to have shattered the parent body, even though they would have produced transient crater diameters of at least 30% of the parent body diameter. Larger craters (relative to parent body diameter) have been observed to form on certain bodies (such as Vesta) without causing them to disrupt. ACKNOWLEDGMENTS Funding for this work was provided by the NASA Outer Solar System program. The authors thank Hap McSween and an anonymous reviewer for insightful and helpful reviews.

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