Abstract– We urge that He is the best case for a meaningful estimation of solar composition without measurement of solar wind (SW) composition; the value of such an estimation is that it may then be compared to the actual measurements, thereby leading to an empirical constraint on the degree of isotopic fractionation arising in SW and thence to how much fractionation may have affected the SW composition of other elements. We take primordial 3He/4He to be as identified in the so-called Q component identified in meteoritic materials. In the Sun, however, 3He/4He is higher because of the augmentation of 3He by D-burning, the nuclear conversion of primordial deuterium. After accounting for the D-converted 3He, we estimate 3He/4He in the present Sun (post-D burning He), and then, from the difference between this and the 3He/4He found in Genesis SW, we estimate the isotopic fractionation between them. Then, from noble gas systematics, we show that Genesis SW noble gases may be related to Q-noble gases by a mass-dependent Rayleigh-type fractionation. We develop a kinetic description of isotopic fractionation of minor components in SW relative to the solar atmosphere, which is consistent with the Rayleigh-type fractionation. This predicts fractionation in the O mass range, which is significantly different from the value used by Heber et al. (2011). The latter value corresponds to the premise that Ca-Al-rich inclusion O is the same as solar O, whence this work does not support that premise.
In different classes of planetary materials there are well-known isotopic compositional variations (“anomalies”) in several elements, typically modest but analytically unambiguous. These are informative in illuminating diverse stellar nucleosynthetic processes and in constraining the provenance and formation processes of the various kinds of planetary bodies. Particularly to the latter end, there is keen interest in comparing planetary body compositions with the average bulk composition of the material from which the solar system formed, i.e., in the Sun.
In comparison with other kinds of solar system materials, however, knowledge of isotopic compositions in the Sun is limited. Although rapidly developing, optical observations are still of little value for determining isotopic compositions in the present context, and we have no physical samples of bulk solar material, but rather only of the solar wind. The distinction between “solar” and “solar wind” (hereafter SW) is significant: Although SW is directly ejected from the solar atmosphere, so that its elemental and isotopic compositions are generally regarded as good proxies for the Sun (see, e.g., Marti and Bochsler  for a recent review), SW is a chemically and isotopically biased sampling, as fractionations arise in acceleration of bulk solar material into the SW. The SW can be sampled and analyzed in direct real-time spacecraft measurements, in artificial targets exposed to SW in space and then returned to Earth in the Genesis mission, and in natural solid planetary materials exposed on airless bodies over geologic time. Short time variations in both elemental and isotopic compositions in SW are considerable, but their long-time averages are thought to be fairly uniform, whence it is commonly taken that there is a reasonably well-defined SW component, especially for the naturally exposed (over long times) materials. In practice, SW elements identified and usefully analyzed in the natural materials comprise mostly H, N, and the noble gases, volatile elements which are intrinsically very scarce in many kinds of planetary materials.
Distinct from SW, it is long and well known that there is another fundamental noble gas component in planetary materials: trapped/primordial gases, now commonly called the Q component (reviews by Ott 2002; Wieler 2002; Pepin 2003, Wieler et al. 2006). Both SW and Q are characterized by wide occurrence and by homogeneous isotopic compositions (except for Ne in Q; see Fig. 3). The origin of SW is straightforward; Q is commonly taken to be a sample of a large reservoir, which is most reasonably taken to be the presolar nebula, but there is yet no consensus regarding mechanism. Relative to presumed nebular gases, Q-noble gases show large elemental fractionation, which is widely thought to reflect the trapping process for Q, but, we hold, perhaps little or no significant isotopic fractionation. For example, in the case of surface trapping such as adsorption, a currently prominently considered process for acquisition of Q-noble gases (e.g., Wieler et al. 2006), polarizability, atomic size, and other factors are more important than mass difference (cf. Ozima and Podosek 2002) in elemental fractionation. In the case of isotopic fractionation, however, these physical parameters are essentially identical, and fractionation corresponding to mass difference becomes relatively unimportant.
In this view, solar He inherited from the presolar nebula should have had the same initial composition as Q-He. However, the 2H (deuterium, or “D”) also inherited from the nebula was quickly reacted to 3He in pre-main-sequence nuclear transformation in the bulk sun (“D-burning”; see, e.g., Geiss and Gloeckler 2009), thereby increasing solar 3He/4He. The effect is substantial, i.e., we can expect that solar (and SW) 3He/4He is much higher than Q-3He/4He.
Estimation of solar He composition from Q-He and the cosmic D/H ratio leads to a prediction of solar 3He/4He, and comparison with SW 3He/4He thus leads to an estimation of the (mass-dependent) fractionation between solar and SW He. With a theory of SW fractionation, this can be extrapolated to other elements. For example, with the use of Ne isotopic fractionation as reference, measurement of SW O in Genesis materials (McKeegan et al. 2011) is widely interpreted to show that solar O is similar to O in Ca-Al-rich inclusions (CAIs in undifferentiated meteorites) and distinct from O in the Earth and bulk meteorites (also see Heber et al. 2009, 2011). We argue below, however, that SW He indicates a significantly different fractionation correction for these observations.
Primordial, Solar, and Solar-Wind He
By “primordial” He, we here mean the He which was inherited by both the Sun and the various planetary objects from the interstellar medium from which the (pre) solar nebula (PSN) was formed. In accordance with a common scenario for planetary origins, we adopt the assumption that primordial He is preserved and present in observable abundance in specific (and very minor) fractions of meteoritic materials. Along with the other noble gases, this is the “Q” component (see reviews by Ott 2002; and Wieler 2002). The isotopic composition of Q-He is observable only in very specialized fractions: Most phases of meteoritic materials have very low concentrations of He (and other volatiles), such that He composition is dominated or strongly influenced by radiogenic 4He (in practice, radiogenic 4He is generally accompanied by some coproduced 3He, but only in very low 3He/4He ratio, of order 10−7); in other materials, He composition is significantly affected by the addition of cosmic-ray-induced nuclear spallation He (with relatively high 3He/4He, of order 10−1).
Busemann et al. (2000) analyzed 3He/4He in the Q-phase of three different classes of chondrites, reporting (1.41 ± 0.01) × 10−4, (1.45 ± 0.01) × 10−4, and (1.23 ± 0.02) × 10−4. Here, we follow Ott (2002), who chose the last value of (1.23 ± 0.01) × 10−4 determined on the Isna meteorite, as the best representative composition of Q-He, as Isna has an extremely short cosmic ray exposure age and is essentially free from cosmogenic 3He, the most serious source of error in determining indigenous 3He/4He ratio.
In current understanding for formation of the giant planets, He in their atmospheres should also have been acquired by capture from the PSN, and, as both radiogenic and cosmic-ray-induced contributions will be negligible, their atmospheric He should also retain primordial isotopic composition. This view is supported by the value 3He/4He = (1.66 ± 0.05) × 10−4 for the atmosphere of Jupiter reported by Mahaffy et al. (2000), which, as for Q-He, is also much lower than SW-He (see below). This value is also significantly higher than in the meteoritic Q component; however, this issue deserves continued attention, but for present purposes we will continue to use the better established meteoritic value for Q-He.
Early observation of SW He in long-exposed natural materials indicated that SW 3He/4He ≈ 4 × 10−4 is unambiguously higher than in meteoritic trapped (Q) He. We adopt, as the best available value, SW 3He/4He = (4.64 ± 0.09) × 10−4, which Heber et al. (2009) determined by very careful analyses of SW samples collected on a Genesis bulk solar-wind collector. This averages SW over only 2.4 yr, the Genesis collection time, but Heber et al. show that this agrees well with results obtained on Apollo collector foils as well as the long-time averages in lunar soils.
Geiss and Reeves (1972) first pointed out that the high (relative to trapped meteoritic) 3He/4He in SW evidently reflects generation of 3He within the Sun by pre-main-sequence nuclear D-burning. This leads to the relation
Geiss and Reeves (1972) used this relation to estimate the D/H ratio in the proto-solar nebula, one of the most fundamental parameters in cosmology. Here, we apply the opposite logic: From available determinations of primordial D/H and He/H, we estimate the value of 3He/4He in the post-D-burning Sun. From the far-UV spectrum, Linsky et al. (2006) argued for D/H = (2.31 ± 0.01) × 10−5 as representative of the interstellar medium within 1 kpc of the Sun. For solar He/H, we adopt 0.084 ± 0.003, based on helioseismology (Basu and Antia 2004). Applying these values in Equation 1, we obtain (3He/4He)post-D = (3.98 ± 0.3) × 10−4, significantly smaller than the SW value. In the above calculation, we assume that the isotopic compositions of noble gases in the photosphere represent the values in the outer convective zone (OCZ) in the Sun, i.e., the solar isotopic ratio. We ignore any putative secular variation of 4He due to gravitational settling in the OCZ (estimated to be a few percent by Vauclair 1998; also see Turcotte and Wimmer-Schweingruber 2002) and further that main-sequence H-burning in the core has negligible isotopic effect in the OCZ. We attribute this difference primarily to isotopic fractionation between the Post-D He in the Sun and average SW-He, which is the main object of this article. Figure 1 illustrates a schematic view of the isotopic evolution of (3He/4He) in the early solar system.
Isotopic Fractionation in the Solar Wind
Following Bodmer and Bochsler (2000), we define isotopic fractionation (i/j) of a minor element in SW as the isotopic flux ratio (φi/φj) observed at the Earth orbit (e.g., lunar or Genesis-SW sample) relative to the corresponding isotopic abundance ratio (ni/nj) at the base of the photosphere rb, where SW is taken to originate:
where ni denotes total density and vi the average radial velocity component of an isotope i, f(r) is a nonradial expansion factor of a magnetic flux tube, and φi(r) is the integral flux constant at heliocentric distance r. Combining Equation 3 with Equation 2, it is straightforward to deduce a simple expression for the isotopic fractionation factor:
Therefore, calculation of isotopic fractionation between SW and the Sun is reduced to estimation of the ratio of the radial velocity components of isotopomers at the basal level rb where SW starts to emerge.
The conservation law thus indicates that initial isotopic fractionation produced at the base of a SW magnetic flux tube must be retained within the tube, but the subsequent isotopic fractionation produced within the flux tube will be homogenized. Therefore, the noble gas isotopic composition in the Genesis bulk SW represents primarily the original isotopic signature inherited in the base of an SW magnetic flux tube.
In the following discussion, we follow a common view that SW stems from the lower chromosphere (e.g., Pucci et al. 2010), where the temperature is a few thousand degrees K, and species are essentially in a neutral state. We therefore assume that the isotopic fractionation in the chromosphere is a kinetic process rather than electromagnetic. This assumption is consistent with a recent theoretical study on a funnel-type flow geometry in the solar-wind source region by Pucci et al. (2010), who concluded that in the case of Ne, collisional interaction with neutral hydrogen is more important than that with H+ (SW main stream constituent).
A rigorous treatment to resolve the velocity of minor species in the main hydrogen flow is beyond the scope of the present article; here, we present a semiquantitative discussion. Schunk (1977) discussed the transport of minor species with respect to the average gas flow in relevance to aeronomy and space physics. Schunk (1977) showed that in many circumstances, including the solar atmosphere, the individual species velocity distributions were approximated by the Maxwellian velocity distribution, and thus concluded that if there were large drift velocity differences or temperature differences between the interacting species, the velocity distribution function of a given species was more likely to be Maxwellian about its own drift velocity rather than to be Maxwellian about the average gas velocity. Following Schunk, we assume that the velocity (vi,j in Equation 4) distribution of minor species in hydrogen flow in the lower chromosphere is approximately Maxwellian, being proportional to (kT/m)1/2 (k is the Boltzmann constant), and hence we can express an isotopic fractionation factor (Equation 4) in terms of a square-root-of-mass ratio, namely
We illustrate SW ejection of minor species in Fig. 2. Next, we show that the above relation is supported by empirical data.
Noble Gas Systematics in Sw/q
In Fig. 3, we show isotopic ratios of SW-noble gas (Genesis-bulk SW, Heber et al. 2009) to Q-noble gas (Busemann et al. 2000; quoted by Wieler  and Ott ) against 1/(mi/mj)1/2, where for He we take the post-D value in the Sun estimated above instead of Q-He. The numerical data are given in Table 1. As shown in this figure, the 1/(mi/mj)1/2 dependence of noble gas isotopic fractionation fits fairly well the empirical data, suggesting that our scenario is viable. Such fractionation trends are common in nature (Rayleigh fractionation). In spite of the highly complicated isotopic fractionation in SW, involving a variety of interactions (thermal, gravitational, and electromagnetic), it is surprising that the empirical data fit well the trend of the Rayleigh fractionation. Here, we emphasize that the above postulated theoretical model on the isotopic fractionation of minor components in SW flow is well consistent with the Rayleigh-type fractionation.
dTheoretical isotopic fractionation factor in Rayleigh-type isotopic fractionation is proportional to the mass ratio of isotopes i. j, namely 1/(mi/mj)1/2.
In the above discussion, we discarded Q-Ne because of its ambiguity in characterizing the primordial component in the early solar system. However, it is interesting to note that if the value of 20Ne/22Ne ∼ 13 observed in the Jupiter atmosphere were used in Fig. 3 instead of Q-Ne, SW/Q for Ne almost perfectly lies on a slope-one line. This agreement may be accidental, but may suggest that the Jupiter 20Ne/22Ne is better representative of the primordial value in the early solar system. The recent observations of 20Ne/22Ne in some deep-mantle-derived materials such as fluid inclusions in Devonian plutonic rocks (Yokochi and Marty 2004) and in an Icelandic OIB (Mukhopadhyay 2012) gave 20Ne/22Ne values close to 13.0 in accordance with the Jupiter value.
Oxygen Isotopic Fractionation in the Solar Wind
So far, we have focused the discussion on noble gas isotopic fractionation between SW and the Sun. Heber et al. (2009), assuming that Genesis bulk SW–Ne isotopic data can be used as a reference for isotopic fractionation of the Genesis bulk SW O, showed that the extension of mass-dependent isotopic fractionation trend in a δ17O–δ18O diagram (linear trend with slope 1/2) deduced from the observed Genesis-bulk SW-O data passed close to the CAI O isotopic composition. Taking for granted a common assumption that the CAI oxygen isotopic composition is the same as the solar oxygen (e.g., Clayton 2002), McKeegan et al. (2011) suggested that the magnitude of isotopic fractionation between SW and the Sun was the same as that between the Genesis concentrator and SW, but in an opposite direction. The fractionation factor thus deduced corresponds to 21‰/amu with positive slope approximately 1/2 (Heber et al. 2011). However, from the above noble gas systematics of SW/Q, we derive an isotopic fractionation factor of 30.3‰/amu (at mass number 16). The difference is significant and requires an explanation.
From statistical analyses of meteorite O isotopic data, Ozima et al. (2007) argued that the assumption on the identical O isotopic composition between CAI and the Sun, which underlies the above suggestion by McKeegan et al. (2011), was unlikely to hold. In this regard, we also point out that this identical CAI-Solar O assumption leads to an unexpected implication that the isotopic fractionation factor (i.e., 21‰/amu by Heber et al. ) in the Genesis concentrator, namely the instrumental isotopic fractionation factor for O, is the same (except for polarity) as the O isotopic fractionation between SW and the SUN, despite totally different environmental conditions in the concentrator and the solar atmosphere. In short, we infer that the Genesis SW data do not support the assertion that solar O is the same as CAI O.
Isotopic fractionation can occur in two basic styles, one mass dependent and the other mass independent. Apart from the relative importance, any isotopic fractionation process is subject to both styles. In this article, we have examined only the mass-dependent isotopic fractionation of noble gases. This is because mass-independent fractionation is generally associated with chemical processes acting on a molecule (e.g., photodissociation), whence noble gases are less susceptible to mass-independent fractionation because of their chemical inertness. However, as the existence of CO in the chromosphere is now well established (Scott et al. 2006; Asplund et al. 2009), and the CO/O ratio in the chromosphere where isotopic fractionation is likely to take place amounts to about 25% (Grevesse, written communication, 2010), we should pay close attention to the possibility of mass-independent isotopic fractionation in the case of O in the solar atmosphere. In this regard, we note that our preliminary quantum mechanical calculation (Yamada et al. 2012) suggests large mass-independent isotopic fractionation in the photodissociation of CO.
1. The isotopic composition of He in the solar photosphere can be taken to be that of Q-He, modified by the addition of 3He produced in “D-burning.”
2. Noble gas isotopes in SW are mass-dependently fractionated from Q-noble gas with a fractionation factor inversely proportional to a square root of mass ratio of isotope, i.e., Rayleigh-distillation-type fractionation.
3. The Rayleigh-type isotopic fractionation is consistent with our proposed model on the isotopic fractionation in SW. The isotopic fractionation takes place through the interaction between minor neutral species and the main hydrogen flow (SW) at the base of the chromosphere.
4. Rayleigh-type isotopic fractionation of He between SW and the Sun leads to a fractionation factor of 30.3‰/amu at mass number 16, which is significantly larger than the 20‰/amu suggested for O by McKeegan et al. (2011). The latter value is based on the assumption that CAI O is the same as solar O. Therefore, this work does not support this assumption.
Acknowledgments— We thank V. Heber, M. Thiemens, and J. Wasson for constructive reviews. M.O. is grateful to V. Heber and N. Grevesse for very helpful discussions.