4.1 Constraints to the Chemical Evolution of PPD
Following the quantitative analyses in configuring bulk chemistry of various types of chondrites (Section 3), we distinguish chondrites between three generation groups in accord with the order of events, CAI incorporation versus chondrule formation. G-1: CAIs were incorporated into chondrite-forming components ‘after’ the chondrule formation event, as represented by CV, CM and E chondrites. G-2: CAIs were incorporated ‘during’ the chondrule formation, like CO and LL. G-3: CAIs were incorporated ‘before’ the chondrule formation, like H and L. If the CAIs formation and their subsequent migration to the outer disk had occurred during a limited period in the PPD evolution, it can be used as a time pivot for whatever processes that are related to the CAIs. Thus the three generations of chondrites recognized above are interpreted as reflecting a formation sequence in the order, G-1 through G-3, as to their chondrule forming events, on condition that the chondrule forming location, viz. its radial distance from the protostar, is fixed.
In Sections 4.2 and 4.4.3, we propose the snowline in the disk as an ideal place for chondrule formation. Thus, if the snowline moved radially in a time scale comparable to or shorter than the CAI migration timescale, the order (G-1 through G-3) might not represent the formation sequence. Here, we continue our investigation by assuming that the snowline was relatively stationary in the radial direction during the period of CAI migration.
As indicated in Section 3.5, fs (a redox indicator of primordial dust or duston) ascends in the order, CV, CM, E, CO, LL, H and L chondrites. This is exactly the same order as G-1 →G-2 →G-3.
With these facts and the assumption, together with other observational information of chondrites and comets, we attempt to make a prediction about a possible evolutionary sequence of primordial PPD materials.
4.1.1 Evolution in redox state
The increase in fs with the order G-1 →G-2 →G-3 suggests that the redox state of primordial dust or dustons evolved towards oxidizing with time. We speculate when, where and how it happened.
In their chemical network model of PPD, Walsh et al. (2015) have indicated that gas phase reactions dominate in the inner disk (≤10 au) because of high temperatures and that the reaction of atomic O (produced by photodissociation of CO) with OH (produced by reaction O+H2) proceeds to form molecular oxygen,
$$ {\mathrm{O} + \text{OH} \to \text{\(\mathrm{O}_{2}\)} + \mathrm{H}}. $$
(2)
Furuya et al. (2013), in their reaction network model of PPD, have suggested that at 10 au (∼60 K) ultra-fine ice grains (∼0.1 µm) are continuously supplied to the disk surface by turbulent vertical mixing and destroyed to atoms by stellar UV photons and X-rays, which in turn come back to the disk midplane by turbulence. Atomic oxygen is then converted to molecular oxygen by reaction 2, which becomes a predominant O-bearing species in the disk, given enough time (>105 ys).
We propose that the molecular oxygen was radially transported by turbulent diffusion and made the disk gradually oxidized inward as well as outward. This picture qualitatively matches the chronological order of the generation groups of chondrites, G-1 through G-3.
As an alternative, the cometary O2 can be a source of oxidizer in PPD. The comet 67P/Churyumov-Gerasimenko is known to have kept producing a neutral gas coma with unusually abundant O2 molecules (O2/H2O= 0.01-0.1) (Bieler et al. 2015) during its period of observation. In their model calculations of the chemical evolution of material from the pre-stellar core to the midplane of PPD, Taquet et al. (2016) and Mousis et al. (2016) have investigated the yield of O2 ice in cometary ice inventories and concluded that the high abundance of O2 in 67P, if produced solely as O2 ice by radiolysis, is only adequately explained as having formed in the parent cloud. Eistrup and Walsh (2019) have found a sweet spot parameters for production of O2 ice in the pre-solar nebula midplane at a level matching those in 67P and 1P/Halley, but preferred a primordial origin in the parent cloud, having considered a sensitivity of such a result to the assumed chemical parameters.
If true, the O2-rich cometary materials such as 67P and 1P might be a source for dustons that formed the generation group G-3 (viz., H and L chondrites), while the O2-free or -poor cometary materials like most other comets could be a source for the generation group G-1 (viz., CV, CM and E chondrites) and perhaps G-2.
Whichever mechanism of O2 enrichment in PPD is true, the O2 molecules must have reacted with metal and sulfide embedded in the primordial dust to form iron oxides.
4.1.2 Evolution in D/H ratio
Figure 10 shows D/H ratios in various substances in our solar system and extrasolar environments. CV and CM chondrites which have the lowest fs values and hence are the most reduced types in our study, show the lowest D/H ratios (<1×10−4) among the chondrites (Alexander et al. 2012). LL chondrites which have a higher fs value in our study, show a high D/H ratio (∼3×10−4) (Alexander et al. 2012). R chondrites, which are not included in our study due to the lack of composition data, is known as the most oxidized type and have the highest D/H ratio (7.26×10−4) (McCanta et al. 2008). The comet 67P/Churyumov-Gerasimenko, in spite of its being a J. F. Comet, have the highest D/H ratio (5.3×10−4) among the comets ever observed (Altwegg et al. 2015). This comet contains unusually abundant O2 molecules as described above. All these evidence points to a strong correlation between the high oxidation state and the high D/H ratio.
The water ice is mostly responsible for the D/H ratios of chondrites and comets except some contribution of the organic hydrogen (Alexander et al. 2012). Interstellar ices show the highest D/H ratio of ∼10−2 in the galaxy (Fig. 10). It is postulated that H2D+ is preferentially produced by ion-neutral reactions in a molecular cloud core and is subsequently turned into ices in the coldest (∼10 K) environment (Cleeves et al. 2014). All matters including gas, ice, silicate and organics in PPD come from a molecular cloud core (e.g., Williams and Cieza 2011). In fact, the D/H ratios of all the solar system materials lie between 10−2 and 2×10−5 (that of the Sun) as shown in Fig. 10. This implies that some amount of interstellar ice survived the formation of the solar system and was incorporated into planetesimal bodies (Cleeves et al. 2014).
Furuya et al. (2013) proposed a model that explains the decrease in D/H ratio of water ice in PPD. Depending on the temperature in the midplane (either <40 K or >60 K), atomic oxygen is either transformed into water ice (regeneration of water ice) by reaction with adsorbed hydrogen on the ice surface, or into molecular oxygen in the gas phase reaction such as reaction 2. Given enough time (>105 ys), the regeneration of water ice reduces the D/H ratio of water ice (Furuya et al. 2013). In the latter case, on the other hand, the initial D/H ratio of water ice tends to be maintained in exchange for depletion of the water ice, and the disk gas becomes gradually loaded with O2 as described above.
The role of atomic oxygen, however, is not one-sided since both ice-regeneration and O2-formation should concur (Furuya et al. 2013) and it is a matter of bias depending on the midplane disk temperature. We postulate that the disk conditions had changed with a timescale ∼ 105 years in such a way that the average midplane temperature increased.
The reason why the increase in the D/H ratio of chondrites and comets has a good correlation with the increase in their oxidation states is easily understood because both require the production of free oxygen in PPD.
4.1.3 Chronology of chondrules and CAIs
Here we examine whether the generation sequence of chondrites, G-1 →G-2 →G-3, is consistent with the chronological information of chondrules and CAIs, on condition that the chondrule forming location, viz., its radial distance from the protostar, is fixed as explained in Section 4.1.
CAIs typically have excess 26Mg, a trace of extinct radionuclide 26Al at the canonical level of initial 26Al/27Al ∼5×10−5, while CAIs with less or no excess 26Mg are also abundant (see review by MacPherson et al. 1995). Chondrules, on the other hand, generally have no excess 26Mg, while some have initial 26Al/27Al ∼8×10−6 (e.g., Hutcheon and Hutchison 1989; Russell et al. 1996). With the half-life of 26Al = 7.3×105 yr, it has been interpreted that there is an age difference between CAIs and chondrules of ∼2.5 Myr or more. It looks like an immediate contradiction because the chondrule formation of the generation group G-1 (viz., CV, CM and E) occurred before the invasion of CAIs. The generation group G-3, on the other hand, requires that it should have taken CAIs for >2.5 Myr to travel from its formation zone (perhaps the inner rim of the disk; e.g., Dullemond et al. 2007) to the zone of chondrule formation (∼3 au if it coincides with the asteroid belt) because the chondrule formation of the group G-3 (viz., H and L) occurred after CAI invasion. Considering the mass accretion rate of T-Tauri stars typically of ∼10−8 M ⊙ per year (Hartmann et al. 2016), such an age difference is comparable to or longer than the time scale for dissipation of the gas disk, and thus unlikely.
Our result implies an irrefutable possibility that the 26Al ages for chondrules (Davis and McKeegan 2014, references therein) are not real. In our investigation, chondrites except for CV, CM and E types contain ghost CAIs, indicating that chondrules formed from silicate liquids made from a mixture of primordial CI-like dust and invading CAIs. Even if the primordial dust contains no 26Al, chondrules should have 26Al as a result of mixed CAIs in the silicate liquid. In fact, CO and LL chondrites for which the invasion of abundant ghost CAIs are implied from the present analysis contain many chondrules having excess 26Mg, and this is particularly so for their unmetamorphosed types (3.0 or 3.1) (Kita et al. 2000; Mostefaoui et al. 2002; Kunihiro et al. 2004; Kurahashi et al. 2008). Chondrules with high Al contents are preferentially analyzed because of their high precision in determination of 26Al/27Al (e.g., Kita and Ushikubo 2012). As a matter of fact, the high-Al chondrules exhibit highest 26Al/27Al values, ∼1/5 of the canonical CAI value (Davis and McKeegan 2014), reinforcing our prediction. We presume that chondrules with high concentrations of live 26Al simply represent jet-droplets from portions of the silicate liquid in MLB, that is inhomogeneously mixed with large CAIs. We conclude that the 26Al chronology for chondrules is subject to a serious problem in that their real ages are indeterminable because of the pre-mixing of CAIs which are high in Al and 26Al.
Connelly et al. (2012) and Bollard et al. (2017) have shown that the ages of six among twenty-two chondrules measured with the U-corrected Pb-Pb dating method agree with the average age of four CAIs (4567.30 ±0.16 Myr) within errors. With this result they claim that chondrules and CAIs are coeval, and that the assumption of the uniform distribution of 26Al in PPD is wrong. If they are coeval, the time interval for chondrule formation between the group G-1, G-2 and G-3 could be as short as 0.16 Myr, although only six chondrules show such a sign and only four data are available for CAIs ages. Their results, however, appear contradictory because the ages of thirteen chondrules from NWA 5697 (L3) span between 4563.64 and 4567.61 (±0.50) Myr, viz., ∼4 Myr interval. It seems improbable that a single chondrite could reserve chondrules that had been continuously produced in PPD for as long as 4 Myr.
The Pb-Pb chronology for chondrules appears to be free of the problem of CAI mixing unlike 26Al, but the wide age span of chondrules in a single chondrite cast a doubt on using it as a constraint on the timing of chondrule formation. We explore a little more about the age data. The four CAIs used for determination of their Pb-Pb ages (Bollard et al. 2017) are limited to those in CV chondrites (three from Efremovka and one from Allende). In our study, CV in the generation group G-1 is actually Efremovka itself. The U-corrected Pb-Pb method analyzed only two chondrules that belong to CV chondrites (Connelly et al. 2012). They are Allende chondrules, one of which shows 4567.32 ±0.42 Myr in good agreement with the CAI age although another is a Myr younger. Thus the chondrules and CAIs in CV chondrites (viz., Efremovka and Allende), as far as the existing data concerned, agree in their ages within analytical errors except one chondrule. This is consistent with our observation of the generation G-1 in which chondrules formed prior to the invasion of CAIs, as long as the time needed for CAIs to migrate to the zone of chondrule formation is short. We therefore suggest that a comparative chronology should be made on chondrules and CAIs that belong to the same chondrite or at least to the same chemical type of chondrites.
4.2 Completion of the Chemical Fractionations
Chemical fractionations in chondrites are not completed until the leftover refractory residue of MLB and the leftover volatile vapor (or condensates) are separated from the chondrite-forming ingredients, viz., chondrules and matrix.
The physical separation is only possible through aerodynamic actions operating on objects with different sizes. The leftover evaporation residue is a few-mm thick, once-molten, surface layer of a large duston with the radius R>0.01 m. Bodies with R in the 0.01-10 m range lose their angular momentum per unit mass much faster compared to bodies of other sizes, due to their differential motions against the gas. According to Weidenschilling (1977), a body with R=1 m (solid ρ∼3 g cm −3, gas ρ∼10−9 g cm −3 and T ∼300 K) would migrate to the sun in ∼50 yr per au, while it takes ∼5000 yr per au for R= 0.01 or 10 m (for the same parameters). On the other hand, grains smaller than chondrules (R ≤0.001 m) take ≥105 yr per au (ibid) and should remain in the chondrule formation zone for a long time.
We propose that dustons were trapped in a large-scale vortex in the protoplanetary disk and that the chondrule formation took place inside the vortex immediately after their entrapment. There the Coriolis force is at work, which pushes dustons of appropriate size, 0.01-10 m in radius, to the center of the vortex in a few rotation periods (e.g., Tanga et al. 1996; Chavanis 2000). The result would be that small objects such as chondrules and finer dust are left near the outer edge of the vortex. Small grains with diameter <1 cm tend to bail out to the outside of the vortex due to turbulent diffusion (Chavanis 2000). Therefore chondrules must grow in size by attaching fine dust rather efficiently (Beitz et al. 2012). Once chondrule-cored nodules and their multiple clusters grow in size >1 cm, they would run after dustons but at a slower pace. In this way we expect three populations being separated from one another as a result of aerodynamic effects: (Pop-1) the chondrule-cored nodules and their clusters that follow the dustons much later in time, (Pop-2) the dustons with refractory residues that settle in the center of the vortex in a short time scale, and (Pop-3) the fine dust, a mixture of the volatile-rich condensate and the primordial CI-like dust, which escape from the vortex. The three populations correspond to the three components that are produced in the chemical fractionation process during the chondrule formation, (A-1), (A-2) and (A-3) as described in Section 3.6, except that Pop-2 consists of A-2 and a non-melted portion of dustons, and Pop-3 is a mixture of A-3 and the primordial dust.
We discuss the two populations that remain in the vortex. The dustons (Pop-2) are so effectively trapped into the center of vortex (e.g., Barge and Sommeria 1995; Fromang and Nelson 2005; Surville et al. 2016) that a gravitational instability is triggered to generate a large planetesimal (e.g., Tanga et al. 1996). A swarm of the late-arriving, chondrule-cored nodules, viz., Pop-1, would be gravitationally attracted by the planetesimal and accumulate onto its surface, forming a layer of ‘chondrite’. As a result the chemical fractionation is completed because the chondrite is spatially segregated from the dustons that form the core of the planetesimal and represent most of its mass. Vortices may not be only attractor of dustons. Any mechanism that attract dustons preferentially (e.g., a dust-loaded ring: Surville et al. 2016) could provide a place for forming planetesimals and late veneers of chondrites around them.
As a logical consequence we cast doubt on a hypothetical, meteorite (or chondrite) parent body. The petrologic types (from 3.0 to 7) of chondrites have long been believed as representing thermal metamorphic grades which reflected depths of the sources where the chondrites came from after destruction of the parent body. Rubin (2003, 2004) and Rubin and Wasson (2011) found that the common occurrence of shocked and annealed ordinary and enstatite chondrites is consistent with collisional heating being a major mechanism responsible for metamorphosing those chondrites. Friedrich et al. (2014) found that 26Al was too depleted to have caused high degrees of thermal metamorphism and partial melting of LL7 chondrites and that heating due to impact is the most likely heat source for the recrystallized chondrites. We’d like to point out that the outermost layers of planetesimals should have been most prone to shocks and disruption by impacts of other bodies. Disrupted pieces may have accumulated on their original planetesimal surface or formed independent rubble piles that were loosely tied with weak gravity, as seen in extant asteroid belts (Walsh 2018). The third population (Pop-3) may have been further mixed with a CI-like dust in the disk and diluted to an insignificant concentration. Recent rendezvous missions to comets, however, revealed high concentrations of crystalline silicates in cometary comas, which are highly enriched in Na and Si relative to Mg (Schulz et al. 2015; Engrand et al. 2016; Bardyn et al. 2017). The enrichment of volatile Na (and K), and Si relative to Mg is exactly a feature of the volatile condensates in the third population (Fig. 9). The third population may also give a hint to the origin of GEMS (Keller and Messenger 2011), UCAMMs (Dobrica̧ et al. 2012) and CPMMs (Noguchi et al. 2015), all of which are suspected to have genetic links to comets.
4.3 Comparison with the Equilibrium Condensation Model
Having discussed our new ideas on the origin of the chemical fractionations in chondrites, we come to a point where we could compare our model with those developed by Anders and his group. As described in Section 1, their model basis, viz., the equilibrium condensation of chondritic materials, has lost its reasoning. However, it might be beneficial for us and all to do this since essential points would be clarified. In addition to the chemical aspects which will be described below, there are several physical difficulties attached to their model. 1) The grain size of particles that condense from a gas of low density should be too small to be separated from the gas (Weidenschilling 1977), making the fractionation absolutely ineffective. 2) No reason is given for any particular temperatures at which they claim the fractionations should occur. 3) Chondrules, the most abundant constituent of chondrites, is not taken into consideration.
4.3.1 Lithophile element fractionation
We refer to the major element or refractory lithophile element fractionations in chondrites (Larimer and Anders 1970; Larimer 1979). Larimer and Anders (1970) have proposed that a partial loss of high-temperature-condensation minerals at appropriate temperatures and a subsequent condensation of minerals which followed from the remaining gas reservoir could explain major chemistry of ordinary and enstatite chondrites, starting from the CI-composition gas. They derived chemical compositions (for the five major elements, Si, Mg, Ca, Al and Ti) similar to those of bulk ordinary (and enstatite) chondrites, by subtracting 15 (25), 23 (45) and 40 (60) % of Si, Mg and Ca (same for Al and Ti), respectively, from the CI composition. Those minerals were identified as typical CAI minerals and forsterite. As they pointed out, these percentages are examples and other combinations are possible. Larimer (1979), based on his analysis on the condensation track of major elements and average compositions of ordinary and enstatite chondrites, have proposed that the bulk mineral chemistry to be subtracted from the CI composition was uniquely determined. His estimates of mass subtraction are not so different from those by Larimer and Anders (1970).
In order to explain the bulk chemical compositions of CII and CIII (now classified as CM for CII, and CO and CV subtypes for CIII), Larimer and Anders (1970) inexplicitly and Larimer (1979) explicitly suggested the addition of CAI minerals in appropriate proportions to the CI composition.
Larimer and Anders (1970) concluded that the chondrule formation had nothing to do with the lithophile element fractionations, and that chondrules were simply molten droplets of the existing solids.
An essential difference between our model and their model is that we consider the chondrule formation and the subsequent dynamical processes as a primary driving force for the lithophile element fractionation, while they do not. Let us recapitulate our model for the sake of comparison.
As shown in Fig. 9, the initial CI-like material, duston, is processed into three kinds of materials as a result of chondrule formation process in the vapor cloud that forms around it. The chondrule- and matrix-forming components, F1 through F4 in the calculation, when combined, are depleted in refractory elements such as Al, Ca and Ti relative to Mg and Si (Fig. 9; ‘Used’). As a result, not only enstatite and ordinary chondrites but also carbonaceous chondrites suffer from depletion in the refractory elements once. The difference among these chondrites is the amount of CAIs which invaded into a zone of chondrite formation. For carbonaceous chondrites, refractory elements (in the form of CAIs) invaded and mixed with chondritic components in amounts more than compensating the lost fraction during the chondrule formation. Enstatite chondrites incorporated Al-rich CAIs in quantity too small to compensate the largest depletion in the refractory elements caused during the chondrule formation. Ordinary chondrites (L and H types) incorporated no CAI except for a trace of ghost CAI, thus remained depleted in the refractory elements. Ordinary chondrites (LL type) incorporated both CAI and ghost CAI, but their combined mass was too small to compensate the depletion in the refractory elements. Such is a brief explanation in our model for the lithophile element fractionations in chondrites.
To complete the chemical fractionation, however, the leftover residue which is enriched in the refractory elements (Fig. 9; ‘Residue’), must be removed from the chondrule-forming zone. This is automatic because the residue is a once-molten surface layer of a large duston which subsequently falls into the center of a large-scaled vortex by the aerodynamic process. The equilibrium condensation model, on the other hand, has no means to remove the high-temperature condensates from their formation zone since they are ultra-fine-grained particles that strongly couple with the gas.
The removal of excess volatiles that are not incorporated into chondrite-forming materials (Fig. 9; ‘Vapor’) is also automatic in our model because the vapor condensates, fine-grained in nature, would effectively move away from the vortex by turbulent diffusion. The removed volatiles in the form of low-temperature condensates must include not only Na and K but also highly volatile elements (e.g., Pb, Bi, In, Tl). Therefore, our model does not have to invoke any extra chemical fractionation process such as accretion-temperature-controlled fractionation of volatiles proposed by Keays et al. (1971) and Laul et al. (1973) (viz., Chem. fract. in meteorites-IV & -VI).
4.3.2 Redox state and metal-silicate fractionation
Different types of chondrites have different redox states of Fe and different total Fe contents (Urey and Craig 1953). Fe exists in meteorites typically with three different states: oxides (mostly as FeO) in silicates, metals and sulfides. In the latter two, Ni and Co are invariably included as minor elements, which under most redox conditions are not oxidized. Larimer and Anders (1970) examined concentrations of Fe and Ni in various chondrites and ascribed the depletion in total Fe in L and LL chondrites as opposed to H and C chondrites, to the metal-silicate fractionation that had occurred between ∼1050 K and 680 K (temperature for FeS formation) before accumulation of chondritic materials into large bodies.
Larimer and Anders regarded the redox state of minerals in chondrites as reflecting their final equilibration temperatures with the nebular gas. In the equilibrium condensation model of high temperature nebular gas with the solar elemental abundances, Fe metal condenses at ∼1450 K at 10 −3 bar in total pressure (Grossman 1972) and at ∼1280 K at 10 −5 bar (Wood and Hashimoto 1993). No other Fe-bearing phase appears down to ∼900 K where a trace of Fe metal is oxidized and accommodated into Mg-silicates (forsterite and enstatite), but it is not until 700 K (10 −3 bar) or 600 K (10 −5 bar) where olivine takes FeO/(MgO + FeO) = 0.05, which is close to the FeO concentration in enstatite in E-chondrites and in forsterite in a reduced type of CV chondrite, viz., Efremovka. In order to oxidize Fe to a level of FeO/(MgO + FeO) ∼0.2 in olivine typically in ordinary chondrites, temperatures as low as 520 K is required (Wood and Hashimoto 1993).
We point out a contradiction between the above two arguments. The Fe/Ni molar ratios of bulk chondrites are 16.6 for H, 18.6 for L and 19.3 for LL (Jarosewich 1990), while the Fe/Ni ratio in CI chondrites is 18.1 (Lodders 2003). Comparison of the temperature range for the metal-silicate fractionation with those for oxidation of Fe metal, however, implies that the metal-silicate fractionation occurred before the oxidation. If so, the Fe/Ni ratio of chondrites should keep 18.1 if CI was their starting composition. Hence their model with respect to the redox states and metal-silicate fractionation bears an internal inconsistency.
The Fe/Ni ratios of bulk chondrites higher than 18.1 indicates that the oxidation of Fe occurred before the metal-silicate fractionation. L and LL chondrites must have lost a significant mass of metal before their accretion to large bodies. The lower Fe/Ni ratio of H chondrites relative to CI, on the other hand, suggests a gain of excess metal or a loss of silicate before their accretion.
In contrast with Larimer and Anders (1970), the discussions made in Sections 3 and 4.1.1 strongly argue for the possibility that the redox state of Fe in the primordial dust was predetermined before the chondrule formation process and that it evolved with time from reducing to oxidizing, corresponding to the generation sequence of chondrites, G-1 through G-3. This is consistent with the order of the events indicated by the Fe/Ni ratios of chondrites, that the oxidation is followed by the metal-silicate fractionation, since the latter should have occurred during or after the chondrule formation in our model.
4.4 In Search of Possible Heat Sources
Our model assumes that the surface of duston was heated above their boiling temperature with some external source of heat. Let us scrutinize possible heating mechanisms in PPD suggested for chondrule formation. Rubin (2000) has considered ten constraints that are related with petrologic and geochemical features of chondrules and made a check list for sixteen heating mechanisms with these constraints (figure 5 in his paper). He has pointed out the three mechanisms being consistent with all the constraints: nebular lightning, magnetic reconnection flares, and gas dynamic shock waves.
We introduce two lines of evaluation procedures apart from his. The first line has to do with the coexistence of chondrules with a matrix. In chondrites the fine-grained matrix materials fill interstices between chondrules. Their abundance in volume ranges from 20 to 80%, depending on the type of chondrites. They are free of melting process and generally rich in volatiles including organic materials and water, being characteristic of low-temperature origin. It means that any heating mechanism which violates the presence and features of the matrix materials is not appropriate for chondrule formation. The second line is the consistency with our chondrule and chondrite formation model, and is considered after the first line.
We apply our evaluation procedures to the following heating mechanisms from Rubin (2000, table 5): nebular lightning, supernova shock waves, magnetic reconnection flares, gas dynamic (nebular) shock wave and planetesimal bow shocks. We also evaluate the following mechanisms, that were postulated since Rubin (2000): shocks in the envelopes of giant protoplanets (Nelson and Ruffert 2005) and current sheets in magnetically active nebula regions (Joung et al. 2004).
4.4.1 Constraints from the coexistence with the matrix, and scrutinization of various heat sources
The first line of evaluation considers the following five constraints. With them, we attempt to scrutinize the heating mechanisms. a) The matrix materials are characterized by their very fine-grained nature, typically subµm to µm in size. Such fine dust move with gas and are unable to be decoupled from the gas. b) The matrix contains abundant materials and elements that are stable at low temperatures. Although recondensation or regeneration (if such processes followed the destruction during chondrule formation events) might partially restore their low-T features, most indigenous materials such as IOMs (e.g., Alexander et al. 2007) which are suggested as having inherited their isotopic signatures from the low-T, outer disk environments or from the molecular cloud would not survive even a moderate temperature rise. c) The matrix contains presolar grains whose isotopic compositions (e.g., Zinner 1998) are very distinct from those of the common chondrite-forming minerals. Any event, thermal or shock, strong enough to destroy or alter the grains is prohibited. d) The most stringent of all the constraints comes from the D/H ratios of water and organic materials in matrices in various chondrites, which differ from those of the sun and the earth. As already described in Section 4.1.2, different chondrite types appear to possess characteristic ranges in the D/H ratio, which are most likely attributed to the ion-molecule reactions in the molecular cloud (e.g., Tielens 2013) followed by modification in the low-T outer disk (e.g., Alexander et al. 2012; Cleeves et al. 2014). The D/H ratio of water should be easily reset to that of the nebular gas, ∼2×10−5, if temperature exceeded 500 K (Lécluse and Robert 1994) in the presence of the nebular gas. e) Complementary nature of the matrix to the chondrules. Two kinds of complementarity may be identified. 1) Chondrules and matrix show similar isotopic compositions and redox states, as in the case of ordinary and enstatite chondrites. Carbonaceous chondrites, whose matrices are relatively H2O-rich, possess oxidized matrices and reduced chondrules, but the oxidation of the matrices are known to have resulted from later hydrothermal actions after accumulation onto a large parent body (e.g., DuFresne and Anders 1962; Clayton and Mayeda 1984). ‘Similarity’ rather than complementarity may be a better term, but it indicates that both come from the same source, not a chance mixture of different origins. 2) Excess or deficit in abundances of particular elements or isotopes in either of chondrules or matrix cancels out to normal values when chondrules and matrix are combined in their chondritic proportion, viz., the bulk chondrite. It is recognized that chondrules are depleted in metallic elements, as opposed to enrichment in these elements in the matrix, while the bulk chondrite have approximately CI abundances in these elements (Bland et al. 2005). This suggests that the metallic elements lost from the chondrules were mostly recovered by the matrix (e.g., Grossman and Wasson 1985). Isotopic complementarity is a very severe restriction, especially in non-mass-dependent isotopic fractionations, as it suggests some sort of genetic link between them Budde et al. (2016a, b).
The above four constraints, viz., a, b, c and d disqualify the heat sources or heating mechanisms which raise temperatures of the gas on a large scale in the disk, where fine dust, a source of matrix materials, are immersed. They include supernova and nebular shock waves, magnetic reconnection flares, current sheets, and shocks in the envelopes of giant protoplanets.
Planetesimal bow shock and lightning discharge should involve only localized heating of the disk gas, thus most of the fine dust in the disk would escape from heating. They are scrutinized by the second line of evaluation method in the followings.
4.4.2 Scrutinization of planetesimal bow shock model
As described in “Origin of Chondrule Chemistry” in paper (I) and in Section 3.5 in the present paper, jet-droplets are postulated to have ejected from the boiling surface of dustons starting with vaporization degree of MLB from less than 10% and ending with more than 80%. In our experiments (paper I), the MLB completed evaporation (VD >90%) within several seconds. A large size of duston would require more time, typically ≥10 seconds for jet-droplets to be ejected with a wide range of VD.
A high speed planetesimal moving in PPD (with a typical speed of 6 km s −1 relative to the gas) accompanies a bow shock on its front side. According to Ciesla et al. (2004), the thickness of bow shocked zone is about three times of the radius (Rp) of the planetesimal. With Rp= 10, 100 or 1000 km, its thickness is 30, 300 or 3000 km. Then, large dust aggregates immersed in the gas would be heated for duration of 5, 50 or 500 seconds, which is long enough in our criteria. The calculated temperature of a compact dust aggregate of 0.1 cm in diameter in the bow shock, however, reaches only 1600 K. Even with an assumed emissivity of dust being 0.1, which is unrealistically low, the maximum temperature reached is 2000 K, which is still too low to make the dust aggregate boil. Hood (1998) obtained a maximum temperature 2000 K for a dust aggregate by assuming a planetesimal of Rp=70 km and the same values for size and emissivity of dust grain as Ciesla et al. (2004).
Much larger dust aggregates like dustons (>3 cm) would decouple from the gas more efficiently and hence would be more strongly heated in bow shock, although we do not have a quantitative estimate. Even if boiling occurred, however, the vapor cloud would be immediately destroyed by shock wave. Dustons would be also smashed into pieces by impact with the planetesimal.
Miura et al. (2010) have proposed a possibility of liquid condensation for origin of chondrules that fine dust in the bow shock once evaporate and then condense. They, however, admitted that the condensed material should have the same composition as that of the former dust. Then it would not cause chemical fractionations in chondrules and chondrites from the dust.
We conclude that the bow shock is not a viable heat source for our model of chondrule formation.
4.4.3 Lightning discharge: our last hope
In the terrestrial atmosphere, lightning discharge releases its energy in an extremely confined path (a typical discharge path width is ∼2 mm; Pilipp et al. 1992). This leaves most of the atmospheric volume free of heating except for vicinity of the path which are heated with radiation (Whipple 1966). The path width of lightning discharge postulated for PPD is ∼5000 times of the electron mean free path, viz., ∼5 km for gas density n(H2) ∼1020 m −3 (Pilipp et al. 1992), which is very narrow considering the spatial scale of PPD. Therefore, the lightning discharge clears the first line of evaluation procedure, the coexistence of the matrix.
Muranushi (2010) has raised three problems to be overcome for the lightning discharge to be a feasible heat source for chondrule formation: energetics problem, neutralization problem, and destruction problem. We add another constraint: charging-mechanism problem. In the followings we give preliminary but plausible solutions to the four problems, and show that the lightning discharge is compatible with our model of chondrule and chondrite formation.
4.4.3.1 Charging mechanism
The generally accepted concept for the development of the thundercloud charge dipole in the terrestrial atmosphere is the physical separation of oppositely charged particles within the cloud (Saunders 2008). The principal charge carriers are believed to be H2O ice particles and their charge separation mechanism has been studied for a long time (reviewed by National Research Council 1986). The H2O ice is the most abundant solid substance in PPD and is naturally assumed as a main charge carrier for lightning discharge in space.
We postulate that the chondrule formation occurred in large vortices in PPD as described in Section 4.2. Theoretical works predict that a pressure bump near the snow-line (e.g., Kretke and Lin 2007) induces Rossby wave instability by which anticyclonic vortices develop (e.g., Lovelace and Romanova 2014; Lin and Pierens 2018). If a large vortex (Huang et al. 2018) encompasses the snow-line, the icy dust trapped in it would experience evaporation and condensation in its every rotation period.
According to Saunders (2008), the most promising of all possible charging mechanisms of ice grains in the terrestrial atmosphere is a charging induced by condensation: If the growth rate of ice grains is fast during condensation, more defects (pairs of OH − and H3O +) are created on the ice surface. The H3O + diffuses into inside of the ice grains, leaving OH − trapped on the surface. When small ice particles collide with the large ice grains, they remove OH − and become negatively charged, while the large ice grains having lost OH − become positively charged. Takahashi (1978) and Takahashi and Miyawaki (2002) conducted ice charging experiments showing that an ice crystal (∼10 µm in diameter) removed a maximum charge of ∼3.3×10−14 C per collision, which translates into a charge surface density of 10 −4 C m −2. This is more than enough to explain activities of terrestrial thunderclouds (Takahashi 1978). According to Takahashi (1978), however, the charge surface density and its polarity depend strongly on temperature and density of H2O molecules in the atmosphere. Since there are no data available for the range of temperature and H2O density in PPD, it may be premature to conclude the charging efficiency per collision for nebular ice.
We find a similar situation in the vortex which by anticyclonic rotation would bring trapped dustons from warm (inside the snow-line) to cold (outside) environment. If the mass function of stony dust is biased to large sizes, viz., dustons and their embryos rather than fine dust, most of H2O vapor would not immediately condense but supersaturate up until homogeneous condensation generates a numerous number of ultra-fine ice particles (probably sub-micron in size). Dustons and their embryos, on the other hand, would be covered with an icy layer or frost. Dustons gradually decouple from the gas (which also contains fine dust of ice and stone) and spiral down into the center of the vortex, while the fine dust collide with the front and bottom sides of the dustons. They are similar to the large ice grains in the terrestrial atmosphere, that grow by condensation of water in updrafts of thunderclouds while small ice particles continuously collide with their bottoms. The separation of positively charged dustons and negatively charged ice particles develops an electric field between the two populations. Once the electric field is established, the dustons and their embryos are electrically polarized so that rebounding ice particles can deprive more negative charges from them, leaving them more positively charged. This results in an enforcement of the field (Saunders 2008). If the vortex radius is comparable to the scale height of the disk gas, it would look like a cylindrical capacitor with electric charges of opposite polarities arranged in concentric circles.
4.4.3.2 Energetics problem
This problem has been recognized as a most formidable one since Whipple (1966) suggested a lightning discharge as a heat source of chondrules. The ultimate energy source (gravitational potential of the protoplanetary disk) is sufficient to melt the chondrules, but most of the energy earned by ingoing larger dust go to the outgoing gas by the angular momentum exchange; little contribute to the random motion, the energy source for the lightning (Muranushi 2010). According to our new chondrule formation mechanism, however, the energy shortage seems easy to overcome because only the surface, a few mm in thickness, of dustons needs melting and evaporation to generate chondrules. The larger the duston’s average size, the smaller the total energy would be required if the total stony dust mass in the protoplanetary disk is assumed constant.
The energy source of lightning discharge in the terrestrial atmosphere is the latent heat of water vapor during its condensation in thunderclouds, partially transferred to turbulence and updraft in the developed cells, then partially to charge separation between icy grains (Rakov and Uman 2003). We assume the latent heat of water vapor as the source of the electric energy stored in the nebular vortex, and calculate the minimum radius of the average dustons, whose surface is exposed to lightning discharge and boils to produce jet-droplets and vapor cloud.
For simplicity, the mass ratio of ice to stone in the vortex is assumed to be 3:1, and all the stone is used for making dustons of single size (radius, R). It is assumed that all ice once evaporates on a warm side of the vortex and then condense totally on a cold side, releasing the latent heat. This latent heat is eventually used to heat the dustons. We further assume that the duston’s surface with a thickness of ΔR is kept molten at 2600 K, and that its one-third thickness, (1/3) ΔR evaporates. The initial temperature of the duston is assumed to be 100 K. A thermal diffusion into the duston below the thickness ΔR is not considered. The adopted duston’s thermodynamic properties are: Cp=1.46 kJ kg −1 K −1; ΔHm=6.27×102 kJ kg −1; ΔHv=8.37×103 kJ kg −1 (all data refer to enstatite liquid; Chase et al. 1985). The water’s heat of vaporization is 2.45×103 kJ kg −1. The radiative loss of energy (emissivity = 1) from the duston surface is assumed equal to that for silicate vaporization, which is valid at 2600 K (Hashimoto and Nakano, in preparation).
We obtain R/ΔR∼4.0 \(\Phi _{c}^{-1}\), where Φc is the energy conversion efficiency of the water latent heat to the total energy involved in lightning discharge, multiplied by the conversion efficiency of the latter to the heating of dustons. If ΔR=3 mm and Φc=1, R=12 mm. This would be a minimum size of dustons, but Φc would be significantly smaller than 1; if Φc=0.001 (for the same ΔR=3 mm), the duston’s radius should be as large as 12 m, which may be too large. Not all dustons would be struck by thunderbolts, but only their small proportion would be, considering the rarity and unpredictable nature of lightning on earth. This would reduce the optimum size of dustons significantly. If we presume Φc much smaller than 0.001, the productivity of chondrules should be very low, but it would be more favorable from the energy limitation.
4.4.3.3 Neutralization problem
The protoplanetary disk is not an ideal place for electric fields to build due to its low gas density. If the gas is even slightly ionized, the field is rapidly neutralized by Ohmic currents (Muranushi 2010). Because of the large mean free path of electrons in PPD compared to that in the earth atmosphere, the breakdown field is very small, of the order of ∼10 V m −1 (Muranushi et al. 2015), while on earth it is ∼106 V m −1 (Rakov 2013). This prevents a large electric field from building up, as small discharges always wipe it out. Nevertheless, Pilipp et al. (1998) contended that global electric fields strong enough to induce lightning could have been generated by gravitational sedimentation of dust particles and size sorting due to gas drag on these particles (Morfill et al. 1993), (1) only if charge transfer processes operated in grain-grain collisions, (2) if the gas phase ionization rate were much lower than that usually assumed for molecular clouds, almost as low as that resulting from decay of long-lived radioactive elements (40K) trapped in the grains alone, (3) if precursors of chondrules were compact with a specific mass density not much lower than 1 g cm −3, (4) and if the electrical energy was stored in much larger structures. We agree to their assertions except that the driving force for charge separation is the Coriolis force in vortices rather than the disk gravity. The vertical component of gravity in the disk midplane, where much of dust are concentrated, is negligibly small; therefore an updraft with large velocities of unknown origin is needed to lift dust of various sizes to high altitudes, e.g., a disk scale height, where the vertical component becomes significant and causes separation of dust by size difference.
The vortices must have formed in an MRI-inactive, ‘dead zone’ (e.g., Kretke and Lin 2007), where the ionization source would be limited to radioactive elements and cosmic rays. Pilipp et al. (1998) assumed only 40K for ionization source, which they found marginal to keep a maximum allowable ionization from triggering global discharges. They did not consider a decay of 26Al, which could be a strong source of ionization. As Desch and Cuzzi (2000) pointed out, we may take it in a reversed logic that the chondrule formation occurred because 26Al was already dead due to the time gap between chondrules and CAIs, or because 26Al was not present in the chondrule formation zone due to its heterogeneous distribution (e.g., Larsen et al. 2011; Krot et al. 2012). We consent to the latter possibility because some types of chondrites (CO and LL chondrites) must have formed at the same time as CAIs, and another types of chondrites (CV, CM and E chondrites) could have formed even before the CAI formation. We also propose that any radioactive elements could not have been an effective ionization source because of the large size of dustons and because of the mass function biased to large aggregates. The electron (and perhaps positron) penetration depth is proportional to their energy, ∼1.7 mm per MeV (Kanaya and Okayama 1972). Therefore, only a few mm surface layer of the dustons may be liable to contribute to ionization of the gas; most of the mass which resides inside the dustons would not.
4.4.3.4 Destruction problem
Muranushi (2010), in his rebuttal argument to the experiment by Güttler et al. (2008), pointed out that either the electron mean free path is many orders of magnitude shorter or the electron kinetic energy is much larger compared to the protoplanetary disk environment.
We rather pay attention to the conclusion by Güttler et al. (2008) that the fragmentation of experimental dust aggregates is attributed to the expansion of the discharge channel. In PPD the discharge channel is presumably very wide (e.g., 5 km; Morfill et al. 1993) compared to that in the experiment (Güttler et al. 2008; no description but maybe ≤1 mm) and the discharge would continue for much longer duration (e.g., 10-100 s; Morfill et al. 1993) as compared to ∼60 µs in their experiment. Therefore, dust aggregates in the discharge channel in PPD would be completely molten before the channel explosively expands as a result of the vanishing magnetic fields around the channel.
4.4.4 Lightning discharge: consistency with our new model
We place three conditions on evaluating the lightning discharge as a possible heating mechanism for chondrule formation: (i) the temperature of the duston’s surface is kept above its boiling point for duration of 10 s or longer; (ii) the vapor cloud is kept for the same duration; and (iii) the matrix-forming fine dust coexist nearby at low temperatures. We also add one more condition, (iv) that the chondrules that formed in the lightning bolt should possess a large NRM (natural remnant magnetization) because of the magnetic field formed around the discharge path.
Morfill et al. (1993) estimated the energy available from a high temperature plasma of ∼30 eV for heating dust grains in the discharge path, using a scaling of the typical terrestrial bolt of lightning applied to a low density nebular gas. Due to a large mean free path of electrons, ∼1 m for n(H2) ∼1020 m −3, the discharge path width is ∼5000 m and the duration of a lightning pulse is of the order 10-100 s (Morfill et al. 1993). Because of the wide cross section of the path and the prolonged duration of heating, the energy to impart to dust grains is diluted as opposed to the terrestrial one (width ∼1 mm; duration <1 millisecond). This could be enough to melt grains as small as chondrules (Morfill et al. 1993; Horányi et al. 1995), but is in no way sufficient for boiling the surface of dustons.
We predict a new mechanism for heating dustons, a direct strike by the lightning bolt. The allowable electric field in the nebula is restricted by the dielectric strength of the molecular hydrogen. This limits the electric field inside vortices of the order of 10 V m −1 (0.14-30 V m −1 depending on the models of dielectric strength; Muranushi et al. (2015). This field is so weak compared to a typical terrestrial thundercloud field of 1-2 ×105 V m −1 (Rakov 2013) that a large scale charge separation, 106-108 m, is required to build an electric potential of 107-109 V, typical of terrestrial thunderclouds. Therefore, the discharge path in the nebular gas might be a very long trail. Our concern, however, is not the trail itself (which is usually assumed a heating scene of involved dust aggregates) but its destination: how the discharge tip of the stepped leader (e.g., Rakov and Uman 2003), a pathfinder so to speak, finds its partner in opposite polarity. Our hypothetical dustons are the one, since their ‘point charge’ fields stand out in the general field, like trees and lightning rods as a terrestrial analogue. One unlucky duston struck by the leader is among a large number of dustons which we postulate distributing equally-spaced in a plane that extends laterally more than thousands of km. A swarm of secondary electrons and ions from the attacked duston may find another duston nearby, and the discharge process should cascade.
Once the duston’s surface temperature rises high enough for evaporation of the icy layer and other volatiles, the first vapor cloud forms whose density exceeds that of the nebular gas by orders of magnitude. This would make a mean free path shorter by the same magnitude and converge the wide discharge path into a narrow string similar to the terrestrial lightning. From this on until discharge ends (for 10-100 s), the duston’s surface continues to boil and the vapor cloud is maintained.
The cold fine dust exists outside of the discharge path. If the path is more confined by being shepherded by dustons, rather than being spread over kilometers, a nearby volume of the nebular gas around the vapor clouds may be also free of heating and ready to mix its contained fine dust with chondrules.
Wasilewski and Dickinson (2000) found that the tetrataenite-bearing chondrules in Bjurbole (L/LL4) and Chainpur (LL3) chondrites exhibited very high REM values (the ratio of NRM/SIRM) of >100×10−3, indicating that these chondrules were magnetized in a strong magnetic field of the order of 100 mT (1000 G). According to their arguments, this high REM in the terrestrial rocks is associated only with a direct strike by lightning discharge. In our new chondrule formation mechanism, supercooled liquid droplets solidify and cool below the curie temperature (770 ∘C for tetrataenite; Herndon and Rowe 1974) inside the vapor cloud that exists only during the lightning discharge because the discharge path expands explosively at the moment electric currents vanish.
Our postulate, the lightning discharge as a heat source of boiling dustons, needs quantitative interrogation. We do not deny a more plausible mechanism to be found in future.
