Water transport in protoplanetary disks and the hydrogen isotopic composition of chondrites
Highlights
► We set to explain the D/H ratio of water locked in carbonaceous chondrites. ► We model mixing between water equilibrated with hydrogen and cometary water in the disk. ► The (analytical) synthetic distribution of D/H ratios peaks near the snowline value. ► Observations require efficient turbulent diffusion (low radial Schmidt number).
Introduction
The isotopic composition of hydrogen (as expressed by the D/H ratio) is a valuable tracer of the origin of water in the Solar System (Robert, 2006). Primitive meteorites (chondrites), presumably the building blocks of terrestrial planets, allow a glimpse at the D/H ratio of water in the protoplanetary disk that surrounded our Sun 4.57 Ga ago. Indeed, many chondrites, in particular carbonaceous chondrites, contain clays formed through alteration of originally anhydrous silicates by water presumably incorporated as ice along with rock during accretion (Brearley, 2003, Ghosh et al., 2006).
The measured D/H ratios of bulk carbonaceous chondrites1 (see Fig. 5), generally thought to reflect that of accreted water (but see Alexander et al., 2012b), span a range of to (excluding CR chondrites). The distribution, which is skewed to heavy isotopic compositions, has a mean close to the estimated for the bulk Earth (Lécuyer et al., 1998)—consistent with a chondritic source for terrestrial water. The D/H ratios of carbonaceous chondrites is systematically lower than that exhibited by many Oort-cloud comets (; Hartogh et al., 2011), although D/H ratios of and have been determined for Jupiter-family Comet Hartley 2 and Oort-cloud Comet Garradd, respectively (Hartogh et al., 2011, Bockelée-Morvan et al., 2012). The composition of interplanetary dust particles, though broadly similar to that of carbonaceous chondrites (e.g. Engrand and Maurette, 1998, Bradley, 2005), has a significant tail extending to cometary values and beyond. Both chondritic and cometary domains of variation are markedly distinct from both the estimated protosolar value (; Geiss and Gloeckler, 2003), dominated by the isotopic composition of hydrogen gas, and the high values (D/H ≳) determined in molecular clouds for molecules other than H2, consistent with predictions from ion–molecule reactions (see e.g. Robert, 2006). However, high D/H values ≳ have been reported at the micrometer scale in clays of the Semarkona chondrite (Piani et al., 2012, Piani, 2012) and may reflect the composition of pristine interstellar ice grains.
In the protoplanetary disk, the D/H ratio of water evolves mainly through isotopic exchange with the hydrogen gas (whose composition remains essentially fixed at the protosolar value because it contains the bulk of the H of the system), that is, via the reaction:
The equilibrium fractionation factor (D/H)H2O/(D/H)H2 is unity at high temperatures (≳1000 K), but increases with decreasing temperature (Richet et al., 1977).
Using one-dimensional disk models, Drouart et al. (1999) showed that reaction (1) was unable to account for the chondritic or cometary D/H ratios if water was assumed to have formed in the protoplanetary disk with the protosolar D/H value. Indeed reaction kinetics would have been prohibitively slow in those cold regions of the disk where sufficient D enrichment would have been predicted by thermodynamic equilibrium. On the other hand, Drouart et al. (1999) found that cometary compositions could be obtained if water was inherited from the protosolar cloud (with heavy D/H ∼ 10−3). Water would have evolved toward isotopically lighter compositions in the inner disk and diffused in the colder regions owing to turbulence, a result also obtained by Mousis et al., 2000, Hersant et al., 2001. Transport and mixing would have been particularly efficient in the early stages of disk evolution, if the disk was first built compact and then expanded because of turbulence (Yang et al., 2012). Such a picture is also consistent with the presence of crystalline silicates in comets (Bockelée-Morvan et al., 2002).
While these previous works focused on reproducing D/H value observed in comets, implications on the composition of water in the inner Solar System, and in particular the fairly large domain of variations of the D/H ratio in chondrites have yet to be worked out in this framework. This is the purpose of this paper.
In this paper, we consider a disk model pertaining to the classical T Tauri phase, that is, after infall has ceased and the disk radius has become large compared to the heliocentric distances of interest. This is the epoch where chondrite accretion is believed to have taken place. At that time, the D/H ratio of water ice in the outer disk is assumed to have been already set and homogenized at the value of ∼ measured in most comets as a result of early disk processes (this would correspond to the plateau in the simulation of Yang et al. (2012), whose level varies little after infall has stopped). Close to the Sun, isotopic exchange between (gaseous) water and hydrogen gas (reaction (1)) is still going on. However, beyond a certain heliocentric distance (corresponding to a temperature of ∼500 K, as we shall argue later), the kinetics of this reaction are so slow that essentially no isotopic exchange occurs there. Due to gas turbulence, however, some of the water equilibrated with H2 sunward of this heliocentric distance will be transported outward and will reach the snow line, where ice condenses. Water beyond the snow line—sampled by chondrites—will thus be a mixture of two components: equilibrated water having diffused from the hot inner regions of the disk, and cometary water drifting inward from the outer disk.
A radial gradient in D/H ratio is thus established by the competition between outward diffusion and inward advection which sets the proportions of equilibrated water and cometary water as a function of heliocentric distance. The range of D/H ratios of water-bearing bodies thus extends from cometary compositions down to the composition of water condensed at the snow line. The composition sampled at the snow line is hence intermediate between cometary values and those expected from equilibration with H2. This schematic description provides a framework to account for the fairly large variations of the D/H ratio in water of Solar System bodies. A cartoon of the scenario is presented in Fig. 1.
The goal of this paper is to calculate analytically the distribution of D/H ratios of chondritic water that results from this picture and compare it to the observational data, in order to constrain the model parameters. In particular, the calculation will be constrained by the asymmetrical shape of the distribution and its position relative to cometary values. We stress that here the cometary value is a starting, observationally given parameter of the model. Our model does not aim at reproducing the composition of comets in contrast to the studies of Drouart et al., 1999, Mousis et al., 2000, Hersant et al., 2001, Yang et al., 2012; rather, in complementarity to those, it focuses on chondrite parent bodies, that is, the inner regions of the Solar System. Also in complementarity to these numerical studies, our work, in being analytic in nature, allows us to nail down, under certain simplifying assumptions, the relevant parameters (essentially two) that govern the distribution of chondritic D/H ratios, namely: the range of heliocentric distances sampled by chondrites and the radial Schmidt number—which essentially ratios the efficiencies of angular momentum transport and turbulent diffusion. We will find that low values of the radial Schmidt number yield D/H variations consistent with observations. The paper is organized as follows: We describe the model assumptions in Section 2, present and discuss the results in Sections 3 Results, 4 Discussion, respectively. In Section 5, we conclude. For the sake of clarity, specific derivations are deferred to appendices.
Section snippets
Modeling
In this section, we introduce our notations and modeling principles. We successively consider the disk model (Section 2.1), the transport of water (Section 2.2), its D/H ratio (Section 2.3) and our prescription for accretion and delivery to Earth (Section 2.4).
Results
Under the above hypotheses, meteoritic water, having been accreted from a range of heliocentric distances (between the snow line and ) and at various times, will necessarily exhibit a range of D/H ratios and one can define a probability distribution function (PDF) for that quantity. The derivation and the expression of the PDF are presented in C and plots of it are shown in Fig. 4. It is notable that they are independent of α, (1 AU) and κ and depend on , (D/H)h,
Implications
From the above results, it appears that the distribution of D/H ratios of carbonaceous chondrites can be accounted for in a scenario of isotopic exchange with hydrogen gas, with cometary D/H values prevailing at large heliocentric distances, under the condition that the radial Schmidt number be small (). The peak value of the carbonaceous chondrite population would be essentially dictated by the isotopic composition of water near the snow line, where accretion of condensed water would
Summary
We have considered a simplified analytic model for water transport and isotopic evolution in an evolving disk based on the following main assumptions:
- (i)
The regions of interest of the disk are approximated by a stationary model, with a constant turbulence parameter α.
- (ii)
Accretion is inefficient and does not significantly affect the transport of nebular water.
- (iii)
Water far from the Sun is assumed to have the same D/H ratio as cometary water, and any batch of water having experienced temperatures above a
Acknowledgments
We thank the two anonymous referees for their reviews which improved the clarity of the paper in particular as to the effects of radial drift and the transition to cometary isotopic signatures.
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