Cosmogenic production rates and recoil loss effects in micrometeorites and interplanetary dust particles

Authors

  • Reto Trappitsch,

    1. Space Research and Planetary Sciences, University of Bern, Bern, Switzerland
    Current affiliation:
    1. Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois, USA
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  • Ingo Leya

    Corresponding author
    • Space Research and Planetary Sciences, University of Bern, Bern, Switzerland
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Corresponding author. E-mail: ingo.leya@space.unibe.ch

Abstract

We present a purely physical model to determine cosmogenic production rates for noble gases and radionuclides in micrometeorites (MMs) and interplanetary dust particles (IDPs) by solar cosmic-rays (SCR) and galactic cosmic-rays (GCR) fully considering recoil loss effects. Our model is based on various nuclear model codes to calculate recoil cross sections, recoil ranges, and finally the percentages of the cosmogenic nuclides that are lost as a function of grain size, chemical composition of the grain, and the spectral distribution of the projectiles. The main advantage of our new model compared with earlier approaches is that we consider the entire SCR particle spectrum up to 240 MeV and not only single energy points. Recoil losses for GCR-produced nuclides are assumed to be equal to recoil losses for SCR-produced nuclides. Combining the model predictions with Poynting-Robertson orbital lifetimes, we calculate cosmic-ray exposure ages for recently studied MMs, cosmic spherules, and IDPs. The ages for MMs and the cosmic-spherule are in the range <2.2–233 Ma, which corresponds, according to the Poynting-Robertson drag, to orbital distances in the range 4.0–34 AU. For two IDPs, we determine exposure ages of longer than 900 Ma, which corresponds to orbital distances larger than 150 AU. The orbital distance in the range 4–6 AU for one MM and the cosmic spherule indicate an origin either in the asteroid belt or release from comets coming either from the Kuiper Belt or the Oort Cloud. Three of the studied MMs have orbital distances in the range 23–34 AU, clearly indicating a cometary origin, either from short-period comets from the Kuiper Belt or from the Oort Cloud. The two IDPs have orbital distances of more than 150 AU, indicating an origin from Oort Cloud comets.

Introduction

The study of cosmogenic nuclides enables one, among other things, to determine for how long meteoroids traveled through the solar system after parent body break-up. While bodies are traveling through the solar system, they are irradiated by two kinds of high energetic particles: galactic cosmic-rays (GCRs) and solar cosmic-rays (SCRs). As the abundance of SCR particles is highest in the energy range up to approximately 200 MeV, any SCR-induced effects are limited to the upper few g cm−2 of the irradiated matter. In contrast, the majority of the GCR particles are in the energy range of a few hundred MeV up to a few GeV. Therefore, GCR particles penetrate much deeper into the irradiated object. As the upper layers of meteoroids are usually ablated when entering the Earth's atmosphere, SCR-induced effects are usually lost, and for most of the meteoroids, only production by GCR needs to be considered.

There already exist physical model predictions for GCR production rates in different types of meteorites (e.g., Ammon et al. 2009; Leya and Masarik 2009). However, there are also some meteorites in which SCR-produced cosmogenic nuclides have been measured, e.g., Salem (Evans et al. 1987). This meteorite, however, is somewhat special because it probably resembled before being attracted by the Earth's gravity field, allowing the SCR record to be preserved. In addition, samples from the Moon returned to Earth by the Apollo missions also have high concentrations of SCR-produced cosmogenic nuclides. Models have been published (e.g., Hohenberg et al. 1978; Reedy 1999) and used to calculate exposure histories of lunar surface samples.

In addition to the well-known and well-studied meteorites that are in the size range cm to meter, the bulk of the extraterrestrial material falling on Earth is less than 400 μm in diameter with an annual influx of 40,000 ± 20,000 tons year−1 (Love and Brownlee 1993). The Earth has accumulated nearly 1020 kg of dust since its formation. Cosmic dust accumulates in oceanic sediments (e.g., Brownlee 1985) and areas with slow sedimentation rates such as Greenland or Antarctica. While such micrometeorites (MMs) might have been important for delivering volatile elements to Earth, only little is known about their origin and cosmic-ray exposure. For more details, see, e.g., Maurette et al. (1991) and Taylor and Lever (2001). Besides the MMs the Earth also captures so-called interplanetary dust particles (IDPs), which are even smaller than MMs and which can pass through the Earth's atmosphere almost without being altered. Consequently, IDPs are often less altered than MMs. Some of the IDPs available for laboratory studies have been collected by high flying aircrafts in the Earth's stratosphere (e.g., Brownlee 1985; Bradley et al. 1988; Rietmeijer 1998). For a recent review on IDPs, see Bradley (2003).

As MMs and IDPs are both small particles, most of them reach the Earth's surface almost intact or only slightly altered (Love and Brownlee 1993). Therefore, they very often retain, besides the GCR-produced nuclides, also the SCR-produced nuclides together with the trapped solar wind (see below), which permits us to study their cosmic-ray exposure histories. By combining the cosmic-ray exposure ages with travel times according to the Poynting–Robertson drag, it is also possible to determine the place of the origin, i.e., the distance from the Sun, which helps to decide whether the particles are asteroidal, i.e., whether they have been produced in asteroid break-up events, or whether they are of cometary origin.

To apply cosmogenic production rate models to MMs and IDPs, not only production but also loss of cosmogenic nuclides must be considered due to the typically small size of the studied objects (several μm in diameter). When a high-energy particle induces a nuclear reaction, the product nuclide has a specific energy due to momentum conservation, which is called the recoil energy. To dissipate this energy, the produced cosmogenic nuclide travels a short distance within the target (the MM and/or IDP) until it fully stops. There is now a competition between the stopping range and the size of the target and some of the cosmogenic nuclides might get lost from the grain and escape into space (recoil loss). This effect therefore reduces the cosmogenic nuclide concentration and, if not corrected for, results in apparently too low exposure ages. To correct for recoil losses, we developed a model based on various nuclear model codes. Our model is able to calculate the SCR-induced production rates for all relevant cosmogenic nuclides as a function of grain size for MMs and/or IDPs with variable chemical composition. To extend the applicability of the model, also the shape of the projectile spectrum can be varied. However, the maximum energy is currently limited to 240 MeV. To allow the reader to calculate SCR-induced production rates for specific samples, we provide an Excel file at http://noblegas.unibe.ch. Using this file, which is also available upon request from the authors, the reader can calculate elemental and total cosmogenic production rates as a function of target size.

The Physical Model

Production Rates by Solar Cosmic-Rays

Most of the cosmogenic nuclides in MMs (and IDPs) are produced by irradiation with SCRs (see also below). The projectile spectrum needed for calculating production rates is assumed to be a rigidity spectrum as proposed by, e.g., McGuire and von Rosenvinge (1984):

display math(1)

with JSCR(E, J0, R0) the projectile flux density (cm−2 s−1 MeV−1) at proton energy E. The rest mass of the proton is E0, Z is the charge number (= 1 for protons), and e is the proton electric charge. The parameter k depends on the total fluence of the primary particles J0, the proton rigidity R10 for protons at 10 MeV, and the characteristic rigidity R0 of the spectrum and can be calculated via:

display math(2)

Equation (1) gives the flux densities for particles with energies greater than 10 MeV. As this is lower than the threshold energies for almost all reactions considered by us, describing the SCR spectrum via equation (1) is sufficient for our model. As SCRs consist of up to 98% protons (e.g., Goswami et al. 1988), nuclide production from heavier incident particles can be neglected. The production rate P(J0, R0) in (atoms/g/s) for a certain nuclide is given by:

display math(3)

Here, N is the total number of relevant target elements, ci is the concentration of target element i (g g−1), and Ai is its atomic mass number (g mol−1). Avogadros number is NA (mol−1), the cross section for the production of the considered nuclide from target element i at energy E is σi(E) (cm2), and J(E, J0, R0) is the particle flux at energy E (cm−2 s−1 MeV−1). For the cross sections, we use the same database as Leya and Masarik (2009). As MMs and IDPs are small particles, we assume: (1) homogeneous production within a given grain, i.e., we do not consider depth dependencies of the production rates (for limitations of this approximation, see below) and (2) we can neglect production of cosmogenic nuclides by secondary particles.

Production Rates by Galactic Cosmic Rays

For some MMs and IDPs and/or for some cosmogenic nuclides, e.g., 10Be, production by GCRs might well contribute to or even dominate (see below) the overall cosmogenic nuclide abundance. We therefore also include production by GCR in our model. Doing so, we use the same formalism (equation (3)), but instead of a SCR spectrum, we use a GCR spectrum in the form given by Castagnoli and Lal (1980) using a solar modulation parameter = 550 MeV:

display math(4)

Here, JGCR is the total flux of protons at energy E, cp = 1.244 × 106 cm−2 s−1 MeV−1 is the particle flux per unit area and energy, mp is the mass of the proton, and c is the speed of light. The factor x is given by:

display math(5)

For modeling the production rates due to galactic protons, we use the same cross section database as Leya and Masarik (2009). As GCR consist of 87% protons, 12% α-particles, and 1% heavier nuclei (e.g., Simpson 1983), production due to galactic α-particles needs to be considered. As most of the cross sections needed for proper modeling are not yet available, we calculated the required data using the nuclear model codes TALYS for energies below 240 MeV (Koning et al. 2008; see also below) and INCL4/ABLA (Boudard et al. 2002) for higher energies. For modeling, we assume that the shape of the spectra for primary galactic α-particles is similar to the spectral shape for primary galactic protons if the energy is given in energy per nucleon (e.g., Webber et al. 1987). Note that we explicitly consider production by primary galactic α-particles and protons, but we assume that the recoil losses for the GCR-produced nuclides are similar to the recoil loss for SCR-produced nuclides, i.e., we assume that the recoil losses for nuclides produced via GCR protons are the same as for the nuclides produced via GCR α-particles and that both are similar (in percent) to the recoil loss due to SCR particles. On the basis of the data by Leya and Masarik (2009), we use J0,p = 2.88 cm−2 s−1 for the integral number of primary galactic protons and J0,α = 0.4 cm−2 s−1 for the integral number of primary galactic α-particles.

The Recoil Loss Model

In the current version of the model, we consider production and recoil of the cosmogenic nuclides 3,4He, 10Be, 14C, 21,22Ne, 26Al, 36Cl, 36,38Ar, 41Ca, 44Ti, 53Mn, 60Fe, 78,80,82–84,86Kr, 129I, and 124,126,128–132,134Xe from the target elements C, N, O, Na, Mg, Al, Si, Cl, K, Ca, Ti, Fe, Co, Ni, Rb, Sr, Y Zr, Nb, Te, Ba, and La. The list of considered target-product combinations can easily be extended. For all relevant target-product combinations, the production cross sections and energy distributions of the products, i.e., the recoil spectra, were calculated using the TALYS-1.2 code (Koning et al. 2008). For the TALYS modeling, we consider protons in the energy range 1–240 MeV as projectiles, which is the upper limit of applicability of the code. The calculations were done in energy steps of 1 MeV for incident proton energies from 1 to 50 MeV, of 5 MeV for 50–100 MeV, and of 10 MeV for 100–240 MeV. Due to the limitation of the TALYS code to energies below 240 MeV, our current version of the model can only quantify recoil losses for SCR-produced nuclides. For GCR-produced nuclides, we simply assume that their recoil losses are on average similar to those for SCR-produced nuclides. By way of example, if our model predicts a recoil loss of 10% for the production of 21Ne from SCR particles, we simply assume for the same grain that also 10% of GCR-produced 21Ne is lost due to recoil. Note that this approximation is most likely not entirely correct due to the different spectra of the projectiles and the dependence of the recoil spectra on the projectile energy (see below). However, as the differences in recoil losses are not expected to be large and, even more important, the recoil losses for most of the MMs and IDPs discussed below are relatively low, this approximation should not be crucial for the final results, especially if one considers all the other uncertainties involved.

As the energy resolution of the recoil spectra calculated using TALYS-1.2 is not sufficient for our purpose, we used a linear interpolation between the given energy steps to increase the energy resolution. Especially important was thereby the extrapolation toward zero energy. This has been done by using the first two data (lowest and second lowest in energy), fitting a linear regression through both of them, and extrapolating this linear equation back toward zero energy. In case the thus calculated y-value is negative, the value was set to zero. This adjustment significantly improves the performance of the model for low recoil energies and therefore for modeling recoil losses in very small grains. For the interpolation/extrapolation procedure, we chose a step-size in energy of 0.1 MeV. Figure 1 shows for the proton-induced production of 21Ne from 26Mg the calculated recoil spectra, i.e., mb/MeV as a function of recoil energy, for three different incident proton energies, 30 MeV, 100 MeV, 200 MeV (upper panel). The lower panel of Fig. 1 depicts recoil spectra for the production of 21Ne from 23Na, 26Mg, 27Al, and 28Si, all at 100 MeV incident proton energy. In such a plot, the area under the curve, i.e., the integral over the recoil spectrum, is the production cross section at the given incident energy. However, the main information of the data is what percentage of the residual nuclide, here 21Ne, is produced with certain recoil energy.

Figure 1.

Recoil spectrum (mb/MeV) as a function of recoil energy (MeV) for the proton-induced production of 21Ne from 26Mg at three different proton energies (30 MeV, 100 MeV, and 200 MeV) (upper panel). Recoil spectrum for the proton-induced production of 21Ne from 26Mg, 27Al, 23Na, and 28Si at 100 MeV (lower panel).

At small incident energies, most of the nuclear reactions are so-called compound reactions, in which the target absorbs the projectile and a compound nucleus with a relatively long lifetime (10−16 s) is formed. In this compound state, the energy of the projectile (kinetic energy plus binding energy) is transferred to all or at least most of the protons and neutrons in the nucleus, which leads to a large number of excitations and re-arrangements. The decay of the compound nucleus is via γ-rays or nucleon emission (we can ignore fission here). Due to the statistical nature of the evaporation process, ejectiles are emitted in all directions, which ends in a net momentum of about zero. Consequently, the compound nucleus and therefore also the residual nucleus still has the momentum from the projectile, which yields a maximum ratio of recoil energy relative to incoming energy. By way of example, consider the production of 21Ne from 24Mg, which is the most abundant Mg isotope, by 30 MeV protons. The momentum of the incoming proton can be calculated via:

display math(6)

If no momentum is transferred to the ejectiles due their isotropic emission (which might not entirely be true), the total momentum is conserved, i.e., the momentum for the residual nucleus 21Ne can be calculated via:

display math(7)

Considering now that 21Ne is approximately 21 times heavier than a proton, we obtain an energy for 21Ne of about Eproton×mp/mNe-21 ≈ 30 × 1/21 = 1.4 MeV, which is in good agreement with the more precise TALYS predictions (e.g., Fig. 1a).

For higher projectile energies and/or very light target elements, nuclear reactions are no longer dominated by compound reactions, but by pre-equilibrium and/or spallation reactions. In both types of reactions, particles are emitted in forward direction before thermodynamic equilibrium is achieved. Consequently, some of the incoming momentum is transferred to the (forward-emitted) ejectiles, leaving the residual nuclide with less momentum, i.e., less recoil. The more momentum is carried away by the (forward-emitted) ejectiles, the lower is the momentum left for the residual nuclide and the lower is the recoil. Consequently, the usual assumption that higher projectile energies produce higher recoil energies and therefore larger recoil losses is not always true. In contrast, for proper quantifying of recoil losses, the reaction types for all relevant target-product-combinations must be considered.

The discussion above holds for all types of residual nuclides but not for 3He and 4He, which are both rather emitted ejectiles than residual nuclides. To also cover 3He and 4He, we calculated ejectile spectra using the TALYS code. Such spectra are handled by TALYS with a higher energy resolution than the recoil spectra, which enables a detailed calculation of recoil losses for both nuclides without improving the spectra by interpolation and extrapolation procedures.

For each recoil energy, we calculated a corresponding range, i.e., the distance the product nuclide travels before it completely stops, using the PRAL algorithm given by Biersack (1981). The ranges were calculated from zero recoil energy up to a threshold energy, which is defined as the value at which the cross section per energy is 100 times lower than its maximum value. Fig. 2 shows the recoil spectrum for the production of 21Ne from natMg at incident proton energy of 150 MeV. Also shown as a dashed line is the thus defined threshold. It can be seen that the area under the curve from zero MeV up to the energy at the threshold at about 10 MeV is much larger than the area under the curve from the energy at the threshold toward higher energies. In this special case is the (excluded) area over 10 MeV only 6.9‰ of the total area. Therefore, neglecting the high-energy part of the recoil spectrum adds only very little uncertainty to the model predictions because only very few nuclides are produced with such high recoil energies, but it significantly reduces calculation time.

Figure 2.

Recoil spectrum (mb MeV−1) as a function of recoil energy (MeV) for the production of 21Ne from natMg. The incident proton energy is 150 MeV. For quantifying recoil losses, we introduced a threshold, which is at 1% of the maximum value (dashed line). Below this threshold, i.e., above this energy, recoil losses are assumed to be negligible.

The nuclear and electronic stopping parameters needed for stopping range calculations have been calculated for each recoiling nuclide that is slowed down or stopped in the matrix of the surrounding grain using the SRMODULE of the SRIM-2008 package (e.g., Ziegler 2004). The stopping ranges of the recoiling nuclides are then calculated using the PRAL code and from this, the recoil loss is calculated using the projected range and the target dimensions. As a first approximation, we assume MMs and IDPs to be spherical objects, which enable one to reduce the problem of quantifying recoil losses into simple geometrical operations in two dimensions. A sketch of such a calculation is shown in Fig. 3. The solid circle illustrates the MM/IDP with radius r and center position M. The nuclide of interest is produced at position P with a recoil range pr. In this simple picture, the nuclide gets lost due to recoil if the trajectory leaves the grain. Of all possible trajectories, the ones ending in the dotted part of the circle outside the grain indicate recoil losses; all trajectories that end inside the grain (dash-dotted line) do not end in recoil losses. By using simple geometry, the recoil loss l, which is for one nuclide at one energy, i.e., range, can be calculated via:

display math(8)
Figure 3.

Schematic sketch illustrating the recoil loss calculations. For labels and description, see text.

Here, MP is the distance between the center M of the MM/IDP and the place of nuclide production P. As nuclide production within the MMs and/or IDPs is assumed to be homogeneous, total recoil losses for one nuclide and one recoil energy can be calculated by dividing the MM/IDP into concentric shells, calculating the expected recoil loss for each shell, and adding all recoil losses by also considering the masses of the respective shells. While most nuclide production is close to the surface, because the mass is highest in the outermost shell, also the recoil losses are obviously highest close to the surface. The calculation is done for all possible recoil energies and the results are added according to their occurrence in the recoil spectrum, which gives the total recoil loss for a given target-product-combination, e.g., 21Ne from natMg, at a given projectile energy in a MM/IDP with a given chemical composition. This procedure is repeated for all considered isobars, e.g., 21O, 21F, and 21Na, and the results are added according to their production cross sections along the isobar. As we consider the cross sections calculated by TALYS as relatively accurate relative to each other, i.e., we consider them as relatively consistent (e.g., Broeders et al. 2006), we use only TALYS predictions for the recoil loss modeling to avoid inconsistencies between different cross section databases. In the next step, the whole loop is repeated for all other target elements that are of importance and the results are combined according to the chemical composition of the target, i.e., the MM or the IDP. Note that while only target elements that can produce the cosmogenic nuclide of interest are considered for modeling production rates and recoil losses, the full chemical composition of the MM and/or IDP is considered for calculating stopping ranges. Finally, the total recoil loss is obtained by calculating the recoil losses for all energies of the considered projectile spectrum and adding all results (that are for one energy, see above) according to their fluence in the projectile spectrum.

Here, it is worth emphasizing that besides the approach used by us to calculate recoil spectra and recoil losses, there is also a similar study by Wrobel (2008). For calculating recoil spectra, he developed the code DHORIN (detailed history of recoiling ions induced by nucleons), which provides the spectra of secondary particles emitted during a nuclear reaction. This code treats the shape elastic process of the nuclear reaction using the ECIS96 subroutine (Raynal 1994). For the nonelastic processes, pre-equilibrium and equilibrium reactions are considered. While the details are different, the DHORIN code used by Wrobel (2000) and the TALYS code used by us are based on the same physical approaches and, even more important, also on essentially the same input parameters for the optical model, the transmission coefficients, and the level densities. Even more important, also the angular distribution of the emitted particles during pre-equilibrium, which is the important information for recoil loss studies because such particles determine the momentum that is left for the residual nucleus, is treated similarly in both computer codes, i.e., both are based on the systematics given by Kalbach (1988). Consequently, it is of no surprise that the modeled recoil spectra are very similar for both approaches.

Recoil Losses and Production Rates

Below we (1) compare the SCR production rates modeled by us to results from an earlier approach (Reedy 1990, 1999) and to some experimental data (Nishiizumi and Arnold 1992; Nishiizumi et al. 1995, 2007, 2008); (2) briefly discuss the GCR production rates; and (3) discuss the recoil loss corrections, present the grain size-dependent production rates, and compare our results with the model predictions by Ott et al. (2009).

SCR Production Rates for MMs and IDPs

For 21Ne and 38Ar, we can compare our production rates with the model predictions by Reedy (1999). In his study, however, the production rates are given for L-chondrite composition and he used a different SCR spectrum from the one we use here. To nevertheless enable a comparison, we also calculated SCR production rates for L-chondrite composition (Jarosevich 1990) using the same spectral parameters as Reedy (1999), i.e., J0 = 70 cm−2s−1 and R0 = 100 MV. The modeled production rates reasonably agree, the differences between both approaches are below 15%.

For the radionuclide 26Al, our production rate of 595 dpm kg−1 agrees reasonably well with the model predictions by Reedy (1990). He predicts 26Al saturation activities in the range 450–920 dpm kg−1. Both theoretical approaches, however, predict much higher 26Al production rates than measured in cosmic-spherules that are all below 250 dpm kg−1 (Nishiizumi and Arnold 1992; Nishiizumi et al. 1995). Part of the discrepancy might be due to the fact that the cosmic spherules have terrestrial ages of about 0.5 Ma (Nishiizumi et al. 1995), which reduces their 26Al activity by about 60%. However, even after this adjustment, there is still a discrepancy between measured and modeled 26Al production rates, which is most likely due to the significant depth dependency of SCR-produced 26Al. By way of example, considering that the 26Al production rate drops by about a factor of 2 within the first 1 g cm−2 of shielding (e.g., Reedy 1990), even minor ablation losses significantly affect the average radionuclide budget of the MM and/or IDP.

For 10Be, the database is even more complicated. Reedy (1990) predicts a 10Be production rate in the range 3–4 dpm kg−1, which is much lower than our value of 15 dpm kg−1. Part of this discrepancy is due to the fact that Reedy (1990) used a different chemical composition for the mini-spherules than we use here for MMs and IDPs. For example, he ignored C as a target element, whereas we use a C concentration of 3.22%, which adds more than 2 dpm kg−1 to the total production rate. In addition, he used an O concentration of 40.7%, whereas we use an O concentration of 46.5%. Using the same chemical composition as he used, we calculate a 10Be production rate of about 10 dpm kg−1, i.e., much lower than before, but still a factor of 2 higher than the value given by Reedy (1990). However, on the basis of our model, we predict a maximum 10Be production rate (GCR + SCR) in MMs and IDPs of about 25 dpm kg−1, which is only slightly higher than the highest value of about 20 dpm kg−1 measured by Nishiizumi et al. (1995) for cosmic spherules. Note, however, that most of the 10Be concentrations measured in MMs and cosmic spherules are at about 10 dpm kg−1 (e.g., Nishiizumi and Arnold 1992; Nishiizumi et al. 1995, 2007, 2008), i.e., much lower than we predict using our model. Such low 10Be concentrations are only possible assuming irradiation exclusively by GCRs. In contrast to this, the 26Al/10Be production rate ratios measured in Antarctic spherules are in the range 2–24 dpm dpm−1, which is in between the ratio of 1.4 for pure GCR and about 39 for pure SCR production, clearly indicating a significant SCR contribution. Again, this apparent discrepancy can be due to the fact that some of the SCR-produced nuclides are lost during atmospheric entry. For example, the data measured by Nishiizumi and Arnold (1992) and Nishiizumi et al. (1995, 2007) can be explained assuming that most of the SCR-produced 10Be, but only some of the SCR-produced 26Al, had been lost while the outer layer of the MM or IDP got ablated during atmospheric entry.

Ignoring the depth dependency of the SCR production rates has (at least) two consequences. First, the average production rate of a MM/IDP is lower than the surface value. In experimental studies, the entire grain is dissolved/melted and therefore average nuclide concentrations are measured, which are then expected to be lower than our modeled surface production rates. Second, some of the MMs/IDPs suffered ablation losses during atmospheric entry. Such losses remove the outer layers with the highest nuclide concentrations, which correspond to our model predictions, leaving only inner parts with lower nuclide concentrations. Note that ignoring the depth dependency for the 21Ne production rate has only little effect on the discussion of cosmic ray exposure ages and travel distances (see below). Even assuming a SCR production rate for 21Ne, a factor of 2 lower than given in Table 2 increases the ages by not more than approximately 80% for the lowest age (To440081) and by less than 10% for most of the other ages.

Table 1 compiles the elemental production rates for the cosmogenic nuclides 3,4He, 10Be, 21,22Ne, 26Al, 36Cl, 36,38Ar, 41Ca, 53Mn, and 60Fe for the relevant target elements. For modeling, we assume a SCR spectrum with spectral parameters J0 = 100 cm−2 s−1 and R0 = 125 MV, which has been proposed by Bodemann (1993) to describe exposure ages of lunar rocks. Note that for some target product combinations, e.g., 21Ne from Ti, we do not give elemental production rates because the cross sections are missing. However, such contributions are usually only very small and can be neglected. The table is also available online at http://noblegas.unibe.ch/ or from the authors. In the online version, we also give elemental production rates for SCR spectra with different characteristic rigidities.

Table 1. Elemental SCR production rates for relevant target elements
Cosmogenic nuclideElemental production rates for noble gases (10−8 cm3STP g−1 Ma−1) and radionuclides (dpm kg−1)
BCNONaMgAlSiSKCaTiFeNi
  1. The SCR production rates have been calculated using a rigidity spectrum with J0 = 100 cm−2 s−1 and R0 = 125 MV. For target-product combinations where no production rates are given, there is either no production or no cross sections are available. An electronic version of this table (also with results for different R0-values) is available at http://noblegas.unibe.ch and/or from the authors.

3He1.81.51.41.40.510.51
4He616044261311
10Be1.6 × 1037730264.02.91.10.710.210.21
21Ne227.52.21.00.195.3 × 10−34.5 × 10−43.7 × 10−4
22Ne659.94.51.30.236.7 × 10−34.9 × 10−43.8 × 10−4
26Al1.7 × 1031.1 × 1042.9 × 1034.7 × 1028.01.50.0820.035
36Cl1.5 × 1035.8 × 102352.01.2
36Ar161.1 × 10−38.4 × 10−4
38Ar171.2 × 10−25.9 × 10−3
41Ca8.33.8
53Mn5.2 × 1031.2 × 103
60Fe0.51

GCR Production Rates for MMs and IDPs

In Table 2, we compare GCR- and SCR-induced production rates for 3He, 10Be, 21,22Ne, 26Al, and 36,38Ar for MMs and IDPs having CI-chondritic composition. As for the SCR production rates, we also neglect for the GCR production rates depth dependencies and the production of cosmogenic nuclides by secondary particles. For the GCR and SCR spectra used by us and the assumed chemical composition of the MM/IDP, the SCR production rates are in all cases higher than the GCR production rates, the differences are between factors 1.4 for 10Be (see also above) and more than 40 for 26Al. This difference is mainly due to the fact that the flux density for SCR particles in the energy range between 10 MeV and about 100 MeV, i.e., in the energy range where a significant part of the production occurs, is significantly higher than for GCR particles, which directly translates into higher production rates.

Table 2. SCR and GCR production rates for micrometeorites and IDPs with CI-chondritic composition and for a 4π irradiation
Cosmogenic nuclideElemental production rates (10−8 cmSTP g−1Ma−1) for noble gases and in (dpm kg−1) for radionuclides
SCRGCR
  1. For the SCR spectrum, we us a rigidity spectrum with J0 = 100 cm−2 s−1 and R0 = 125 MV. The GCR production rates have been calculated using a solar modulation parameter M = 550 MV.

3He1.240.614
10Be15.110.8
21Ne0.9580.0511
22Ne1.460.0674
26Al59514.7
36Ar0.1490.00516
38Ar0.1640.0134

Results of the Recoil Loss Calculations

To check the quality of our recoil loss calculations, we compare the results from our model with the predictions given by Ott et al. (2009) and with experimental data published by Ott and Begemann (2000). The authors of the latter study measured 21Ne recoil losses in industrial SiC powder that was packed in a paraffin matrix and irradiated with 1.6 GeV protons (Table 3). For interpreting the measured data, it turned out that assuming a constant recoil range of 2.5 μm gives sufficient results. The more advanced model by Ott et al. (2009) uses recoil spectra calculated using the approach given by Wrobel (2008) (see also above). For modeling, however, Ott et al. (2009) assumed that nuclide production is exclusively via 200 MeV protons. To directly compare our results with the results given by Ott et al. (2009), we also calculated retention rates in SiC grains assuming that 21Ne production is only due to 200 MeV protons.

Table 3. Cosmic-ray exposure ages and orbital distances for MMs and IDPs
SampleTypeWeight (μg)Size (μm)Cosmogenic 21Ne (cm3 STP g−1)Recoil loss (%)ReferenceCRE, 1 AUa (Ma)CRE, 1AUb (Ma)CRE, real (Ma)Distance (AU)
  1. a

    Cosmic-ray exposure age calculated assuming 4π irradiation of the MM or IDPs with GCR and SCR.

  2. b

    Cosmic-ray exposure age calculated assuming 2π irradiation on a regolith (only GCR).

F97AC001AMM2.0110(1.3 ± 0.1)×10−73.4Osawa and Nagao (2002)1312223333
F97AC003AMM0.5100(2.2 ± 0.9)×10−83.7Osawa and Nagao (2002)2.320.73723
F97AC013AMM0.570(8.6 ± 0.2)×10−85.4Osawa and Nagao (2002)9.082.515934
T0440081Spherule0.795 × 805.7 × 10−94.3Osawa et al. (2003)0.555.43.75.5
F96DK036AMM0.9100 × 80<4.9 × 10−94.2Osawa et al. (2000)<0.5<4.6<2.1<3.9
L2036 I8IDP0.01622 × 284.46 × 10−78.6Kehm et al. (2006)48440>900>150
L2021 B19IDP0.02525 × 324.46 × 10−77.6Kehm et al. (2006)47435>900>150

In Fig. 4, we compare the predictions of the three different approaches, i.e., (1) constant recoil range of 2.5 μm (Ott and Begemann 2000), (2) Ott et al. (2009), (3) our study, with each other and with experimental data (Ott and Begemann 2000). For the latter, the open and closed symbols refer to different sample recovery methods; a full description is given by Ott and Begemann (2000). It can be seen that all three models give very similar results for large grains (>20 μm), i.e., for grains where recoil is lower than about 20%. The models also agree, in that they predict almost complete loss for very small grains, i.e., grains with a diameter of less than about 0.5 μm. The approach by Ott and Begemann (2000) predicts complete recoil loss already for grains in the size range 2–3 μm, which is seen neither in the other two models nor in the experimental data. This shortcoming is due to the fact that Ott and Begemann (2000) assumed a constant recoil range of 2.5 μm. Consequently, grains smaller than 2–3 μm cannot retain any cosmogenic nuclide. In reality, the situation is different as some of the residual nuclides have no or only very little kinetic energy and therefore a very small recoil range (see discussion of the recoil spectra above). As a consequence, also very small grains can retain some cosmogenic nuclides. This is clearly seen in our model, where the recoil loss never reaches 100%. In contrast, also the model by Ott et al. (2009) predicts total losses for small grains. However, this is most likely due to the rather coarse energy resolution of the recoil spectra given by Wrobel (2008). Note that our model would also predict recoil losses of 100% if we would not have carefully extrapolated the recoil spectra toward zero energy (see above). Anyway, due to the high energy resolution used for our recoil spectra and due to the fact that we considered the full SCR particle spectrum, we consider our recoil loss calculations as superior to the earlier approaches by Ott and Begemann (2000) and Ott et al. (2009).

Figure 4.

Comparison of the model predictions for 21Ne recoil losses in SiC grains assuming that all 21Ne is produced via 200 MeV protons. The experimental data are from Ott and Begemann (2000). The retention curve given by Ott and Begemann (2000) has been calculated assuming a constant recoil range of 2.5 μm. The curve given by Ott et al. (2009) uses recoil ranges calculated by the model of Wrobel (2008).

For calculating recoil losses for MMs and IDPs, we assume that the objects have CI-chondritic composition (e.g., Jeffery and Anders 1970; Kehm et al. 2006) and we use a complete SCR proton spectrum (see above). The modeling has been done for grains with diameters between 0.2 and 2048 μm in steps of 0.2 μm for grain sizes less than 1 μm, and in step sizes of 0.5 μm for grain diameters between 1 and 2 μm. Subsequent grain diameters were calculated by doubling the previous value. The largest diameter considered by us is 2048 μm. Here, we report grain size-dependent production rates for 3He, 10Be, 21,22Ne, 26Al, and 36,38Ar. Calculations for other cosmogenic nuclides can also be performed and are available upon request.

Figure 5 depicts the production rates as a function of grain radius in a double logarithmic plot. The dashed lines are only for guiding the eye; they do not represent a fit through or interpolation between the modeled data. While recoil losses are always substantial for grain sizes below a few microns, they are, at least for most of the here considered nuclides, relatively low for grains larger than about 10 μm. One exception is 3He, for which recoil losses are significant already for grains in the size range of a hundred microns. This clearly demonstrates that the light cosmogenic nuclide 3He is lost more easily than the heavier ones, e.g., 38Ar, and that recoil losses for 3He (and 4He) are therefore always substantial.

Figure 5.

Production rates of 3He, 21Ne, 22Ne, 36Ar, and 38Ar (upper panel) and 10Be and 26Al (lower panel) as a function of the grain radius. For the incident particle spectrum, we use an SCR spectrum with rigidity R0 = 125 MV and J0 = 100 cm−2 s−1. We assume the MM and/or IDP to have a composition similar to CI meteorites (Bradley 2003) and a density of 2 g cm3 (Kehm et al. 2006).

Figure 6 shows the production rate ratios 3He/10Be, 3He/21Ne, 10Be/26Al, 21Ne/26Al, and 21Ne/38Ar (all noble gases in 10−8 cm3STP/g/Ma and all radionuclides in dpm/kg) as a function of grain radius. It can be seen that some of the production rate ratios vary as a function of grain size, which might help get some information about the size of the MM and/or IDP before alteration in the Earth's atmosphere. By way of example, if one measures a 10Be/26Al production rate ratio of about 2 × 10−3, we can conclude that the grain size during exposure was most likely in the range 0.4–1.0 μm. Combining such information for various production rate ratios might give some additional information about the irradiation history of MMs and/or IDPs.

Figure 6.

Production rate ratios as a function of the grain radius. The production rates for noble gases are in 10−8 cm3 STP g−1Ma−1 and for the radionuclides in dpm kg−1. For the incident particle spectrum, we use an SCR spectrum with rigidity R0 = 125 MV and J0 = 100 cm−2s−1. We assume the MM and/or IDP to have a composition similar to CI meteorites (Bradley 2003) and a density of 2 g cm−3 (Kehm et al. 2006).

Figure 7 depicts the retention values for 3He, 21Ne, 22Ne, 36Ar, 38Ar (upper panel) and 10Be and 26Al (lower panel) as a function of the characteristic rigidity R0 of the SCR spectrum. For modeling, we assume a grain with a diameter of 2 μm, CI chondritic composition, and we varied the characteristic rigidity from 70 to 130 MV. It can be seen that some of the recoil losses indeed depend on the characteristic rigidity, i.e., on the shape of the projectile spectrum, which is due to the fact that smaller values of R0 correspond to a larger number of low energetic projectiles. The modeling clearly shows that the dependency is more pronounced for low-energy products, e.g., 21Ne and 26Al, than for the high-energy products 3He and 10Be, which is due to the fact that the high-energy part of the spectrum does not change much with increasing characteristic rigidity. The changes in retention rates are for all studied nuclides less than 10%, i.e., the dependence of the recoil loss on the shape of the projectile spectrum is only very little and can in most cases be neglected.

Figure 7.

Percentage of retained cosmogenic nuclide as a function of rigidity (a function of spectral shape). The model results are for grains with CI-chondrite composition and a diameter of 2 μm. Characteristic rigidities R0 are from 70 to 130 MV.

Cosmic-Ray Exposure Ages for MMs and IDPs

For determining cosmic-ray exposure ages for MMs (and IDPs), we focus on cosmogenic 21Ne because there are various facts indicating that Antarctic micrometeorites (AMMs) lost cosmogenic 3He and 4He during atmospheric entry and/or terrestrial residence. First, AMMs have in general relatively low 3He excesses compared with IDPs, indicating preferential loss of cosmogenic 3He by severe heating during atmospheric entry (e.g., Osawa and Nagao 2002). Second, loss of He during atmospheric entry is further supported by the finding that molten spherules usually have the lowest concentrations of noble gases (e.g., Osawa and Nagao 2002). Third, the 4He contents in AMM correlate with atmospheric heating temperatures deduced from mineral compositions (e.g., Osawa et al. 2003). Fourth, loss of He during atmospheric entry is further supported by the finding that SEP He-abundances vary by about three orders of magnitude and that solar He abundances are low compared with the Poynting–Robertson spiral-in times (e.g., Stuart et al. 1999). Fifth, Osawa et al. (2003) and Osawa and Nagao (2002) also found relatively low 4He concentrations in Jarosite-bearing AMMs, which indicates He loss by aqueous alteration during terrestrial residence. Cosmogenic 21Ne concentrations in AMM have been published by Osawa et al. (2000), Osawa and Nagao (2002), and Osawa et al. (2003). Note that Stuart et al. (1999) did not measure Ne isotopes and that Osawa et al. (2003) found no cosmogenic 21Ne in a systematic study of 35 unmelted AMM from Yamato Mountains and of 3 cosmic spherules. Cosmogenic 21Ne concentrations in IDPs have recently been reported by Kehm et al. (2006).

For the following discussion, we assume that MMs and IDPs travel their entire lifetime as small particles through the solar system, i.e., we do not consider that the MM or IDP were irradiated as part of a regolith. This assumption is in accord with the conclusions by Nishiizumi et al. (1995, 2007), which are based on 10Be and 26Al measurements. To calculate the cosmic-ray exposure ages, we have to combine the distance dependency of the SCR particle spectrum with the Poynting-Robertson effect. According to the latter, particles larger than a critical radius, where the radiation pressure balances gravitational attraction, spiral inward. For circular orbits, the time a particle needed to spiral from its starting position at a to 1 AU can be calculated via:

display math(9)

with s the radius of the particle (cm) and ρ its uniform density (g cm−3) (e.g., Wyatt and Whipple 1950; Flynn 1987). Consequently, MMs and IDPs do not spend most of their lifetime in one stable orbit; instead, they spiral inward from outer regions of the solar system to inner regions. It is therefore not correct using only one single production rate for determining their cosmic-ray exposure age. We have to consider that the flux density of the SCR decreases quadratically with distance from the Sun. If we would use the production rates given in our tables, which are only valid for 1 AU, we would significantly underestimate the real exposure age because we would use a much too high SCR fluence (and therefore production rate). Most of the time the particle spent further out in the solar system and therefore accumulated less cosmogenic nuclides per time. Consequently, for a given cosmogenic nuclide concentration, the total exposure time must be longer for a particle spiraling inward than for a particle sitting its entire lifetime at 1 AU. Note that this is only true for SCR-produced nuclides. As the dependency of the GCR on the distance from the Sun is only very minor, this effect can be neglected considering all the other uncertainties involved. Note that there is another consequence of this effect: the contribution of GCR particles relative to SCR particles to the total production rate becomes more and more important, the higher the measured gas concentration is, i.e., the longer the particle spent in the solar system. This is simply due to the fact that longer times correspond to larger distances, i.e., starting points farther out, and at larger distances, the production rates due to GCR become comparable to or even higher than the production rates due to SCR. For example, the GCR production rate for 21Ne at about 3.7 AU is similar to the 21Ne production rate by SCR; at large distances, production by GCR clearly dominates and at lower distances, 21Ne production is mainly by SCR particles.

A lower limit for the exposure ages can be calculated assuming that the cosmogenic nuclides have been produced exclusively by SCR and GCR at 1 AU, i.e., by ignoring the Poynting–Robertson drag. The thus obtained ages for the MMs F97AC001, F97AC003, and F97AC013 of approximately 13, 2.3, and 8.9 Ma, respectively, are in good agreement with the ages obtained by Osawa and Nagao (2002) using the same assumptions (model 3). For the MM F96DK036, the age is <0.5 Ma, and for the cosmic spherule To440080, we obtain an age of about 0.55 Ma. For the IDPs L2036 I8 and L2021 B19, we obtain ages of 47–48 Ma, in perfect agreement with the results given by Kehm et al. (2006).

Using equation (9), we can now give a closer limit for the place of origin of the MMs and IDPs. Note that this is strictly nonconsistent because the ages have been calculated assuming that the MMs and IDPs spent their entire lifetime at 1 AU. However, calculating a lower limit for the orbital distance at origin is nevertheless instructive. Using the sizes and weights given in Table 3, we can calculate the density of the studied objects and using equation (9), also lower limits for the travel distances. The thus obtained travel distances for the MMs F97AC001, F97AC003, and F97AC013 are approximately 8, 6, and 8 AU, respectively, i.e., between the orbits of Jupiter and Saturn in the region of the Centaur comets. For the MM F96DK036 and for the cosmic spherule To440080, the distances are about <2.1 AU and approximately 2.3 AU, i.e., consistent with an origin in the asteroid belt. The closer limit of origin of approximately 37 and 34 AU for the two IDPs L2036 I8 and L2021 B19, respectively, is very similar to typical orbits for Kuiper Belt objects (30–50 AU).

As discussed above, the so far obtained cosmic-ray exposure ages and travel distances cannot be correct if we consider that particles in the studied size range spiral inward according to the Poynting–Robertson effect (equation (9)). If we now combine the Poynting-Robertson effect with the 1/r2 distance dependency of the SCR, we can calculate cosmic-ray exposure ages of approximately 233, 37, and 159 Ma for the MMs F97AC001, F97AC003, and F97AC013, respectively, which is in good agreement with results given by Osawa and Nagao (2002) using a very similar approach (model 1). The ages correspond to distances of about 33, 23, and 34 AU for F97AC001, F97AC003, and F97AC013, respectively, which in turn corresponds to a place of origin either (1) close to the orbit of Neptune, (2) at the outer edge of the Centaur objects, or (3) at the inner edge of the Kuiper Belt objects. For the MM F96DK036, we obtain an age of <2.2 Ma, which is significantly lower than the age estimate of approximately 4.5 Ma given by Osawa et al. (2000). However, these authors assume that F96DK036 has exclusively been irradiated by SCR and GCR particles at about 3 AU, which cannot be correct. If we use the same (wrong) assumption, we can reproduce the result by Osawa et al. (2000). Anyway, the (correct) age of <2.2 Ma corresponds to a distance of <4.0 AU, i.e., within the asteroid belt. The cosmic-ray exposure age for the cosmic spherule To440081 of approximately 3.7 Ma corresponds to a distance of approximately 5.6 AU, i.e., within the asteroid belt. Finally, the cosmic-ray exposure ages for the two IDPs are more than approximately 900 Ma, which correspond to distances of approximately −150 AU, i.e., even farther out than most of the Kuiper Belt objects.

On the basis of the exposure ages and (thereby connected) travel distances, we can speculate about the origin of the MMs and IDPs. Doing so, we assume that the studied object (MM, IDP, spherule) cannot originate from regions closer in than given by the calculated travel distances, because this would necessarily result in too low exposure ages. In contrast, the studied objects can come from farther out because the calculated travel distances only give the distances the MM/IDP travels as a small particle. By way of example, considering that we determined distances in the range of 4.0–5.6 AU for the MM F96DK036 and the spherule To440081, this can indicate that both objects have either been produced in the asteroid belt possibly by asteroid collisions or they were released at that distance from, e.g., short period comets from the Kuiper Belt. As we cannot distinguish between both probabilities, a discussion on the origin of MMs and IDPs based on cosmic-ray exposure ages alone is highly speculative.

Anyway, from our new model, some important conclusions can be drawn. First, considering that the place of origin for two of the studied objects is as close as 4–5 AU, we can argue that, depending on the size and density of the objects, MMs originating in the asteroid belt will most likely end with measurable cosmogenic noble gas concentrations. By way of example, considering an MM with a diameter of 100 μm, a weight of 1 μg, which corresponds to a density close to 2 g cm−3, and a place of origin at 3 AU results in a travel time of about 1 Ma and an accumulated cosmogenic 21Ne concentration of about 0.34 × 10−8 cm3 STP g−1, i.e., 3.4 × 10−15 cm3 STP. Although challenging, such low cosmogenic gas concentrations have been measured before (e.g., Osawa et al. 2000; Kehm et al. 2006) and can be measured with present-day analytical techniques. Consequently, in a careful high precision study of MMs, one should be able to determine the cosmic-ray exposure ages for all MMs that originate in the asteroid belt or farther out. Second, most of the ages obtained by us for the MMs indicate an origin either in the asteroid belt in the range 4–5 AU (for one MM and one spherule) or between 20 and 40 AU, i.e., close to the Kuiper Belt (for three MMs). However, as discussed above, we cannot exclude that all MMs discussed here have been produced by short period comets from the Kuiper Belt, but that some were released at about 20 AU, while others were released at about 4 AU. Anyway, for the three MMs with an origin in the range 20–40 AU, we can exclude CM chondrites as their parent bodies (e.g., Kurat et al. 1994; Genge et al. 1997). Third, the cosmic-ray exposure ages for the two IDPs of more than 900 Ma significantly exceed typical ages for stony meteorites and place their origin in the range 150 AU, i.e., far beyond the Kuiper Belt. This would indicate that (at least these two) IDPs started their journey in the Oort Cloud and not in the Kuiper Belt.

For completeness, we also calculate the cosmic-ray exposure ages for the MMs and IDPs assuming that they spent their entire lifetime in a well-mixed regolith and were irradiated only by galactic cosmic-rays. Using the model predictions for lunar surface samples (Leya et al. 2001), we can estimate the production rate for 21Ne to be about 0.11 × 10−8cm3STP g−1Ma−1. The thus obtained ages are between <4.6 Ma for the MM F96DK036 and about 440 Ma for the two IDPs (Table 3). Currently we cannot decide whether most of the cosmogenic 21Ne has been produced while the MM (and/or IDP) was part of a regolith or whether the cosmogenic gases have been acquired while the MM (and/or IDP) was a small particle. To put more stringent constraints, further data, such as, e.g., 38Ar concentrations, are needed.

Summary

We present a purely physical model to determine cosmogenic production rates for noble gases and radionuclides in MMs and IDPs by SCR and GCR fully considering recoil losses. Doing so, we rely on various nuclear model codes to calculate the recoil cross sections; the recoil ranges; and finally the percentages of cosmogenic nuclides lost as a function of grain size, chemical composition of the grain, and shape of the projectile spectra. Our new production rates for 26Al, 21Ne, and 38Ar are in good agreement with earlier predications (Reedy 1990, 1999). For 10Be and 26Al, our modeled production rates are higher than measured values (e.g., Nishiizumi and Arnold 1992; Nishiizumi et al. 1995), which can be explained by the significant depth dependency of SCR-produced nuclides.

The recoil losses calculated by us for special geometries, target chemistries, and projectile energies are in good agreement with results from earlier studies (Ott and Begemann 2000; Ott et al. 2009). However, whereas the earlier studies are limited to a fixed target chemistry and, even more important, to one single input energy, our approach has the main advantage that we can vary the chemical composition of the target (MM/IDP) and the shape of the SCR and GCR spectra. In addition, we consider the entire particle spectrum up to 240 MeV for calculating recoil losses, which is a major advantage compared with the earlier approaches. However, the current version suffers from one limitation: we cannot calculate recoil losses for GCR-induced reactions because of energy constraints in the underlying nuclear model codes (TALYS 1.2). To overcome this limitation, we simply assume equal recoil losses for SCR- and GCR-induced reactions, which is not entirely correct, but which is a reasonable approximation considering all the other uncertainties involved.

Combining the calculated production rates with Poynting–Robertson orbital lifetimes enables us to calculate cosmic-ray exposure ages for four MMs, one cosmic spherule, and two IDPs recently studied byOsawa and Nagao (2002), Osawa et al. (2000, 2003), and Kehm et al. (2006). The ages obtained for the MMs and the cosmic spherule are in the range <2.2–233 Ma, which corresponds, according to the Poynting–Robertson drag, to orbital distances in the range <4.0–34 AU. The orbital distance in the range 4–6 AU for the MM F96DK036 and the cosmic spherule To440081 either indicate an origin in the asteroid belt or release from comets coming either from the Kuiper Belt or the Oort Cloud. For three MMs studied by Osawa and Nagao (2002), we obtain ages in the range 37–233 Ma, which corresponds to orbital distances in the range 23–34 AU, i.e., far beyond the asteroid belt. For these MMs, an asteroidal origin is highly unlikely. Instead, the data indicate a cometary origin, either from short-period comets from the Kuiper Belt or from comets from the Oort Cloud. The two IDPs have cosmic-ray exposure ages of more than 900 Ma, which corresponds to orbital distances of >150 AU, indicating an origin from Oort Cloud comets.

With the current database, it is impossible to definitely prove or reject that the MMs and IDP acquired their cosmogenic 21Ne (and other cosmogenic nuclide) concentrations entirely as small bodies in the solar system. We cannot exclude that some of the cosmogenic 21Ne has been produced while the particles were part of a regolith. To put more stringent constraints, additional data, e.g., 38Ar concentrations, are needed.

Acknowledgments

We thank Rebecca A. Fischer for constructive comments on a first version of the manuscript and Andrew M. Davis, Philipp R. Heck, and Thomas Stephan for helpful discussions. The work was supported by the Swiss National Science Foundation. RT was partially supported by the NASA Cosmochemistry Program through grant NNX09AG39G (to A. M. Davis). We thank Jozef Masarik for his careful review, which helped us in improving the model predictions.

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