2D condensation model for the inner Solar Nebula: an enstatite-rich environment

1.4 MB·

by  Francesco C. Pignatale

Mon.Not.R.Astron.Soc.000,1–14(2002) Printed8January2016 (MNLATEXstylefilev2.2)
2D condensation model for the inner Solar Nebula: an
enstatite-rich environment
F. C. Pignatale1,2(cid:63), Kurt Liffman2, Sarah T. Maddison2, Geoffrey Brooks3
1 Universit´e de Lyon, Lyon, F-69003, France; Universit´e Lyon 1, Observatoire de Lyon, 9 avenue Charles Andr´e, Saint-Genis Laval, F-69230, France;
6
CNRS, UMR 5574, Centre de Recherche Astrophysique de Lyon; Ecole Normale Sup´erieure de Lyon, F-69007, France
1
2Centre for Astrophysics and Supercomputing, Swinburne University of Technology, Hawthorn, VIC 3122, Australia
0
3FSET, Swinburne University of Technology, Hawthorn, VIC 3122, Australia
2

n
a
AcceptedinMNRASon2015December23.Received2015December16;inoriginalform2015May04.
J

7

ABSTRACT
]
P Infraredobservationsprovidethedustcompositionintheprotoplanetarydiscssurface
layers, but can not probe the dust chemistry in the midplane, where planet forma-
E
tion occurs. Meteorites show that dynamics was important in determining the dust
.
h distribution in the Solar Nebula and needs to be considered if we are to understand
p the global chemistry in discs. 1D radial condensation sequences can only simulate one
-
disc layer at a time and cannot describe the global chemistry or the complexity of
o
r meteorites.Toaddresstheselimitations,wecomputeforthefirsttimethetwodimen-
t sional distribution of condensates in the inner Solar Nebula using a thermodynamic
s
a equilibrium model, and derive timescales for vertical settling and radial migration of
[ dust.

Wefindtwoenstatite-richzoneswithin1AUfromtheyoungSun:aband∼0.1AU
1
v thick in the upper optically-thin layer of the disc interior to 0.8 AU, and in the
6 optically-thick disc midplane out to ∼0.4 AU. The two enstatite-rich zones support
8 recent evidence that Mercury and enstatite chondrites shared a bulk material with
4 similar composition. Our results are also consistent with infrared observation of pro-
1 toplanetary disc which show emission of enstatite-rich dust in the inner surface of
0 discs.
1. The resulting chemistry and dynamics suggests that the formation of the bulk
0 material of enstatite chondrites occurred in the inner surface layer of the disc, within
6 0.4 AU. We also propose a simple alternative scenario in which gas fractionation and
1 vertical settling of the condensates lead to an enstatite-chondritic bulk material.
:
v Key words: protoplanetary discs — meteorites, meteors, meteoroids — astrochem-
i
X istry
r
a
1 INTRODUCTION solar gas mixture, provide general agreement with the de-
rivedbulkchemicalcompositionoftheSolarSystemplanets
Infrared spectroscopy probes the chemistry of the surface
(Yoneda&Grossman1995;Gail1998),buttheycannotpro-
layers of protoplanetary discs, but provides little informa-
videmoredetailedinsightssuchasthecomplexchemistryof
tionaboutthedustcompositionoflayersdeepinsidethedisc
meteorites,andthelocationinwhichtheirbulkcomposition
and the midplane (Chiang 2004; Henning & Meeus 2011).
formed.Furthermore,1Dcondensationsequencescansimu-
Furthermore,thederivedchemistryfromtheupperlayersof
late only one layer of the disc at time and cannot account
discs is unlikely to reflect the dust composition of the mid-
for the global chemistry of discs.
plane,sincethephysicalconditionsoftheseregionsmaybe
very different. Thus, information about the bulk chemistry The dust in protoplanetary disc is subject to a series
of the disc, where the planet formation process takes place, of dynamical processes (Armitage 2011). In particular, ver-
is missing and hence modelling is required. tical and radial transport of grains clearly played a role in
One dimensional radial condensation sequences, which theearlySolarSystemindeterminingthedustdistribution
resemble the midplane of the Solar Nebula with an initial throughout the disc (Barri`ere-Fouchet et al. 2005). The be-
haviour of the dust due to aerodynamic drag is determined
by the stopping time, t = (ρ s )/(c ρ ), where ρ and s
s d d s g d d
(cid:63) E-mail:[email protected] are the intrinsic density and the size of the dust grains and
(cid:13)c 2002RAS
2 Pignatale et al.
c and ρ are the gas sound speed and the gas density at a tion of the enstatite chondrites’ bulk material, and suggest
s g
givenlocation(Weidenschilling1977;Barri`ere-Fouchetetal. mechanisms of formation. In section 5 we discuss the theo-
2005). Thus, the decoupling of the dust grains is regulated retical and observable consequences of our results, and link
by its aerodynamic parameter, ζ =ρ s (Cuzzi & Weiden- infrareddiscobservationswiththebulkmaterialofenstatite
d d
schilling2006):denserand/orlargergrainhavelongerstop- chondrites and the dust in the Solar Nebula midplane. Our
ping times than smaller and/or lighter grains. conclusions are presented in section 6.
Theeffectofdynamicprocessesonthecompositionand
distribution of the dust in discs becomes clear when the
morphology of meteorites is analysed. Chondrites are char-
acterized by heterogeneous compositions (Brownlee 2005) 2 METHOD
which show mixtures of compounds and features (calcium-
Inthissectionwedescribethepropertiesofourfiducialdisc
aluminium-rich inclusion, chondrules, etc.) resulting from
model, the thermodynamic equilibrium model used to cal-
several processes (condensation, aqueous alteration and
culate the condensate distribution, and the analytical ap-
metamorphism)thatoccurredindifferentenvironmentsand
proach we use to solve for the vertical settling and radial
at different times during the protoplanetary disc phase of
migration of the dust in the disc and the location of the
ourSolarSystem(Scott&Krot2005).Theprocesseswhich
dead zone.
aggregated high and low temperature materials are still
Beforeproceeding,westressthelimitationsofourther-
unconstrained. Moreover, analysis of rare objects like en-
modynamic calculations. In the low temperature regions of
statite chondrites suggest that very unique chemical con-
the disc, kinetic barriers will prevent some chemical pro-
ditions must have been present in the early Solar Nebula
cesses from occurring. Therefore, the true composition of
(Weisberg & Kimura 2012). To date, there is no general
the dust in these zones can diverge from the compositions
consensus on the chemical pathways which generated the
predicted when assuming complete equilibrium. Given the
enstatite chondrites or the location in the Solar Nebula in
degree of complexity of the systems we consider, this work
which they formed.
onlyfocusesonthethermodynamicaspectinordertobuild
In order to address these limitations and obtain more
the necessary framework for future work, which could in-
informationontheprocessesthatoccurredintheearlySolar
vestigate kinetics and test the reliability of the proposed
Nebula,anewapproachinthestudyofthechemistryofpro-
scenarios. In the following sections we stress the regions of
toplanetary dust is needed. Detailed disc models have been
the discs for which equilibrium is a valid assumption and
developed in recent years which incorporate thermal and
where it is not.
dynamical processes to study their structure and evolution
(Birnstieletal.2010;Dullemondetal.2008;D’Alessioetal.
1999,1998).Thesediscmodelsprovidethetwodimensional
2.1 Disc model
temperature and pressure distribution within each zone of
thedisc,fromthemidplanetothesurface,andcanbeused The temperature and pressure distribution within the disc,
to couple physical, dynamical and chemical studies of gas T(R,Z) and P(R,Z), are determined using the 2D disc
and dust in discs. Furthermore, the availability of chemi- modelofD’Alessioetal.(1998,1999).Heatingsourcesinthe
cal software packages and computational resources allow us discincludeviscousdissipationandradioactivedecay,which
to study complex systems which could not be investigated cangenerateheatateachlocationofthedisc.Also,thereare
before. cosmicraysandstellarirradiation,whichpenetratethedisc
Wepresentanewstudywhichattemptstolinktheob- from the surface and interact with the gas and dust. The
servedchemistryindiscs,andthechemicalevidencederived effects of disc irradiation by accretion shocks on the stel-
from analysis of meteorites. Our aims are to (i) provide in- lar surface are also included. We chose stellar parameters
sights into the possible origin of the crystalline silicates ob- to mimic the young Sun, with M = 1M , R = 2.6R ,
∗ (cid:12) ∗ (cid:12)
served in protoplanetary discs, (ii) determine the locations T = 4278 K, L = 2.069 L , M˙ = 10−8M yr−1, and
∗ ∗ (cid:12) (cid:12)
in which the bulk of rare objects, such as enstatite chon- viscosity parameter α = 0.01, assuming a 1 Myr old star
drites, might have formed, and (iii) provide insight into the withisochronescalculatedfromSiessetal.(1997,2000).At
chemicalcompositionofthelayersdeepinsidethediscwhich this relatively late evolutionary phase, the accretion rate is
cannot be probed by infrared observations. low and the central star has already accreted most of the
In this work we utilise a 2D disc model to derive, for material which will constitute its final mass. We therefore
the first time, the condensates distribution within the So- assume that the remaining dust in the disc will constitute
lar Nebula, mainly focusing on the main silicates observed the building blocks of larger objects. 1 Myr is a reasonable
in discs: forsterite (Mg SiO ) and enstatite (MgSiO ). The time to overcome all the kinetic barriers which can affect
2 4 3
resultingdistributioniscomparedwithobservationsofpro- dust formation (condensation and/or annealing), especially
toplanetarydiscsandcombinedwithanalyticalcalculations intheinnerregionsofthediscwherethetemperatureishigh
of dynamical processes (radial migration and vertical set- enough, and we can use this evolutionary phase to consider
tling of dust and the extension of the dead zone). equilibrium.
Thepaperisorderedasfollows:wedescribeourmethod The temperature range in the disc spans 50(cid:54)T(K)(cid:54)
anditslimitationsinsection2,aswellaspresentourfiducial 1450 and the pressure ranges 10−16 (cid:54) P(bar) (cid:54) 10−4.
disc model which represents our initial condition, describe In Fig. 1 we present the disc structure and also show the
the thermodynamic model used and the analytical treat- τ =1 surface under which the disc becomes optically thick
ment of dynamics. Our results are presented in section 3. (D’Alessio et al. 1998, 1999). The disk “surface” is defined
In section 4 we investigate the possible locations of forma- by the edge of the D’Alessio et al. (1998, 1999) grid for the
(cid:13)c 2002RAS,MNRAS000,1–14
2D condensation model for the inner Solar Nebula: an enstatite-rich environment 3
disc model we are using. In the midplane, the stellar radia- size,theirstoppingtimechanges.Growinggrainscandecou-
tionisstrongenoughtoheatthedisctoover1000K.Thus, plefromthegasandsettletowardsthemidplaneofthedisc
equilibriumcanbeareasonableassumptionfortheoptically (Weidenschilling 1977; Barri`ere-Fouchet et al. 2005; Laibe
thinsurfacelayeroutto0.8AUandinthemidplaneoutto et al. 2008).
0.4AU.Theopticallythickzoneofthediscbeyond0.4AU, Thus,inordertounderstandtheevolutionofthechemi-
where the temperature decreases dramatically, will not be calcontentofthedisc,itisalsocrucialtoconsidertheeffects
considered in our discussions. ofdifferentdynamicalprocessesonthedustdistribution.In
thisworkwefocusonthreemainprocesses:theverticalset-
tling and the radial migration of the dust, and the effect of
2.2 Thermodynamic model the dead zone on the dust motion.
Wederivethe2Ddistributionofcondensatesbydetermining
the thermodynamic equilibrium of an initial gas mixture, 2.3.1 Dust vertical settling and radial migration
given a set of temperatures and pressures, using the Gibbs
Thereisalargebodyofworkintheliteraturewhichinvesti-
free energy minimisation technique (DeHoff 1993).
gates the dynamics of dust in discs: Dullemond & Dominik
We utilise the FactSage software package (Bale et al.
(2008)studieddustsedimentationfromthesurfaceinatur-
2002,2009),whichusestheminimisationmethoddescribed
bulent disc and its effect on the resulting 10 µm infrared
by Eriksson & Hack (1990) and Eriksson & Konigsberger
spectra, Birnstiel et al. (2010) also included in their model
(1995). The thermodynamic data for each compound are
takenfromthedatabaseprovidedbyFactSage1.Theinitial theeffectofgasdrag,radialdriftandturbulenceinthestudy
oftheevolutionofthedustgrowthanddustandgasmixing
gas mixture is composed of the 15 most abundant elements
processes,whileBraueretal.(2008)investigatedtheeffects
of the solar photosphere from Asplund et al. (2009), with
of dust coagulation (sticking) and fragmentation on the ra-
their abundances normalised to 100 kmol (see Table 1, col-
dial drift of dust particles. 3D models have been developed
umn S). We assume that the gas is initially homogeneous
as well: Laibe et al. (2008) used a two-phase (gas+dust)
throughout the disc and we perform equilibrium calcula-
Smoothed Particles Hydrodynamics code to investigate the
tions using (T,P) at each location (R,Z) in the disc. The
verticalsettlingandradialmigrationofgrowingdustgrains
list of possible compounds that can condense comprise 170
withinprotoplanetarydiscs.Allthesestudiesshowthatdust
gases and 317 solids.
mixing is an important process in the redistribution of gas
We use the ideal solution for modelling the phase be-
and dust within discs.
haviour in this region of the disc, which is widely used in
In this work, we follow the approach of Liffman &
astrophysics to compute the chemical bulk material which
Brown (1996) and Liffman & Toscano (2000) to derive
characterise discs and exoplanets (Pasek et al. 2005; Bond
the timescale of dust vertical settling and radial migration
etal.2010;Madhusudhanetal.2012).Itisknownthatthe
within our disc model. The vertical dust settling timescale,
ideal solution model is often a poor approximation of the
τ , is given by
phase behaviour especially in the low temperature regime. set
However, the choice of the ideal solution model was made
for several reasons: (i) at high temperatures, which charac- (cid:16) ρg (cid:17)(cid:0) vt (cid:1)(cid:0) R (cid:1)3
10−11 g cm−3 1 km s−1 1 AU
terise the zone of the disc in which we focus our research, τ =125,000 yr, (1)
set (cid:16) (cid:17)(cid:16) (cid:17)(cid:16) (cid:17)
thesolutionbehaviourofphasesapproachestheideal(Kap- M(cid:63) ap ρp
M(cid:12) 0.1µm 1g cm−3
tay 2012);(ii)thereisnosignificantchange,inmacroscopic
whereρ isthegasmassdensity,v istheMaxwellianspeed
scales,ofthecondensationsequenceandcondensedamount g t
ofthegas,a istheparticleradius,ρ istheparticledensity
for the chemical compounds presented in this work when p p
and R is the radial distance of the dust particle from the
differentsolutionmodelsareapplied(Pignataleetal.2011);
star.
(iii) solution models become important when micro-scales
Since we aim to derive the magnitude of the dynamic
systems are considered, and (iv) the number of phases in
timescales, we approximate the radial velocity of migrating
our simulations is large.
particle via dR/dt ≈ −3ν/(2R) (Hartmann 2000), where
t is the time and ν is the average kinematic viscosity. The
migration timescale for a particle at distance R from the
2.3 Dust dynamics
star is obtained by integrating this equation, which gives
Thestandardaccretiondiscmodelprovidesadetailedther-
R2−R2
modynamic structure of protoplanetary discs (D’Alessio et τ =∆t= in yr, (2)
mig 3ν
al. 1998, 1999). However, protoplanetary discs are evolving
anddynamicobjects(Armitage2011).Dustgrainswilllikely where Rin is the inner boundary of the disc, which we set
be transported from the location in which they formed to to 0.1 AU. Since in this work we are focusing on silicate
different environments and these motions will likely affect grains, for these calculations the value of the dust density,
their chemistry. Dust grains which condense out from the ρp, is chosen to represent the average density of silicates: 3
gas at different temperatures, will have different intrinsic g cm−3.
densities(compositions)and,asaconsequence,differentre-
sponsestoaerodynamicdrag.Furthermore,astheygrowin
2.3.2 MRI and the dead zone
TheMagneto-RotationalInstability(MRI)isthoughttobe
1 http://www.crct.polymtl.ca/fact/documentation/ an efficient source of the viscosity which drives accretion
(cid:13)c 2002RAS,MNRAS000,1–14
4 Pignatale et al.
Figure 1.ResultingdiscstructurefromtheD’Alessioetal.(1998)model.Left:temperaturedistribution.Right:pressuredistribution.
Thedashedlineistheτ =1surfaceofthediscandthedashed-dotlinerepresentsthediscsurface.
in discs (Balbus & Hawley 1991). The dead zone is a con- (and36.3eVistheaverageenergyneededtoproduceanion
sequence of the MRI: when the ionisation processes drop pairinH gas),n isthehydrogenabundance,andΣisthe
2 H
below a critical value, the gas will not be coupled to the disc surface density.
magneticfield.Gammie(1996)studiedtheefficiencyofion- ThethermalionisationparameterisdescribedbyMar-
isation processes in a layered disc model and found a zone tin et al. (2012) as
inthemidplane,containedbetweentwomagneticallyactive
(cid:16) T (cid:17)3/4
layers, for which neither local ionisation nor thermal ioni- x = 6.47×10−13(10−7)1/2 ×
th 103K
sation are efficient at driving MRI. This zone would likely
be a magnetically inactive zone in which turbulence is sup- × (cid:16)2.4×1015(cid:17)1/2 e−25188/T , (5)
pressed. The extent of this zone has been subject of nu- nn 1.15×10−11
merous studies (Salmeron & Wardle 2008; Latter & Balbus where n is the total number density given by n =
n n
2012; Martin et al. 2012) which show that the size of the n exp(−0.5(z/H )2),withztheheightabovethemidplane,
c p
dead zone depends on several factors such as the number H thediscscaleheightandn theelectronnumberdensity
p c √
density of the electrons and the chemistry and the size of at the mid-plane given by n = Σ/( 2πµm H ), where µ
c H p
the dust (Dullemond et al. 2007). In this work, to solve for is the mean molecular weight and m the atomic mass of
H
the extent of the dead zone in the disc, we follow the pro- hydrogen.
cedures described by Gammie (1996) and D’Alessio et al. We set the parameter values as follows: a = 0.1 µm,
p
(1998). ρ = ρ(R,Z) g cm−3 and Σ = Σ(R) g cm−2 (D’Alessio et
We calculate the magnetic Reynolds number, ReM, at al. 1998), λd = 3×10−14 s−1, N = 10−10, E = 3.16 MeV
each location in the disc following Gammie (1996): and Σ = 100 g cm−2 (Stepinski 1992), n = 1013 cm−3
0 H
R =7.4×1013xα1/2(cid:16) R (cid:17)3/2(cid:16) T (cid:17)(cid:16)M(cid:63)(cid:17)−1/2, (3) (Gammie 1996), µ = 2.3, and mH = 1.007 amu (Martin et
eM 1AU 500K M(cid:12) al. 2012). The maximum of (xep,xth) is used as input for
the total ionisation fraction x, for the computation of the
whereαistheaccretionparameter,xistheionisationfrac-
magneticReynoldsnumberR inequation(3).Thechoice
tion,andT isthelocaltemperature.TheMRI,whichdrives eM
of the maximum of (x ,x ) is justified by the difference
accretioninthedisc,willbesuppressedifR (cid:54)1(Gammie ep th
eM betweenthetwoionisationfactors,whichcanbethreeorders
1996).
of magnitude (D’Alessio et al. 1998).
FollowingD’Alessioetal.(1998),weconsiderenergetic
particles, x , and thermal ionisation, x , as the main ion-
ep th
isation sources (Stepinski 1992; Gammie 1996; D’Alessio et
al.1998;Martinetal.2012).Thelocalionisationparameter
3 RESULTS
is described by Stepinski (1992) as
In Fig. 2 we show the resulting 2D chemical distribution
xep = 5.2×10−18a−p1T1/2× from our model. The top row shows the distribution of
(cid:115) enstatite (MgSiO ) and forsterite (Mg SiO ); the middle
× (cid:16) 1+1.0×10−17rg2r(χR+χCR) −1(cid:17), (4) row shows the loc3ation where the calciu2m-al4uminium bulk
ρ2T
components condense (or CAI bulk components)2 and the
where χ is the rate of ionisation by a radioactive element,
R
given by χ = λ NEn /36.3, and χ the rate of ionisa-
R d H CR
tion by cosmic rays, given by χCR =10−17nHe−Σ/Σ0, 2 These include hibonite (CaAl O ), gehlenite (Ca Al SiO ),
12 19 2 2 7
and λd the decay constant, N the abundance relative akermanite (Ca2MgSi2O7), Mg-spinel (MgAl2O4), grossite
to hydrogen, E the average energy available for ionisation (CaAl O )andanorthite(CaAl Si O ).
4 7 2 2 8
(cid:13)c 2002RAS,MNRAS000,1–14
2D condensation model for the inner Solar Nebula: an enstatite-rich environment 5
Figure 2. Resulting chemical distribution from our 2D model. Top row: enstatite and forsterite distribution. Mid row: CAI bulk
componentsandforsterite-to-enstatite(fo/en)ratio.Bottomrow:H S(g)andFeSdistribution.Notethechangeofscales.Thedashed
2
lineistheτ =1surfaceofthediscandthedashed-dotlinerepresentsthediscsurface.
forsterite-to-enstatite (fo/en) ratio; and the bottom row bility zone in the midplane reaches out to 1 AU. However,
shows the H S(g) and FeS distribution. as previously stated, the region beyond 0.4 AU falls in the
2
non-equilibrium zone.
We find that stable enstatite is limited to two well-
defined zones within the disc: a band ∼0.1 AU thick in the There are also two stability zones in the inner 1 AU
upper layer of the disc interior to 1 AU, and in the disc of the disc where CAI bulk components are present: one
midplane out to ∼0.4 AU. Forsterite is more abundant in a in the upper layer of the disc between 0.2 (cid:54) R(AU) (cid:54) 0.5
wider zone in the outer upper layer of the disc and the sta- and another 0.01 AU thick zone in the midplane between
(cid:13)c 2002RAS,MNRAS000,1–14
6 Pignatale et al.
the inner boundary of the disc and 0.3 AU. A “cloud” of ment in which they formed (Baedecker & Wasson 1975;
H S(g)isstablebetween0.25and0.5AUbelowthesurface Larimer & Bartholomay 1979). Thus, ECs likely formed
2
of the disc, and a thick zone of stability out to 0.4 AU is from a very unique reservoir of materials and experienced
presentinthemidplane.However,H S(g)canbestablealso post-formation alteration.
2
towards lower temperatures since the formation of FeS via The differences in the bulk composition between EHs
H S(g)canbeinhibitedbykineticbarriersandtheeffective and ELs suggest that these two groups of ECs followed dif-
2
presence of metallic Fe (see section 5.1). ferent pathways of formation. The presence of refractory
Regions in which fo/en (cid:54) 1 are present in both the dust in the EHs also suggests that they formed at higher
surfaceandmidplaneofthedisc.Theaveragegraincompo- temperatures than the ELs.
sitionwherefo/en(cid:54)1isforsterite(Mg SiO )20.2wt%,en- Nittler et al. (2011) and Weider et al. (2012) found
2 4
statite (MgSiO ) 29.6 wt%, metals (Fe-Ni) 47.2 wt%, diop- thatthebulkcompositionoftheenstatitechondritesprovide
3
side(CaMgSi O )1.3wt%,others1.7wt%.Nosulfidescon- goodagreementwiththecompositionandmineralogyfound
2 6
densed in this region. On the surface of the disc, the main onMercury’ssurface,withtheexceptionoftheironcontent
silicates are all distributed in the optically thin region (top which is higher compared to the enstatite chondrites. Wei-
row of Fig. 2). deretal.(2012)suggestthattheECsandMercurypossibly
In Fig. 3 we present the main dynamical results in our sharedthesameprecursormaterial.Thiswouldsuggestthat
model, showing the distribution of log(τ /τ ) and the either the bulk material that formed the ECs and Mercury
set mig
extension of the dead zone for 0.1 µm-sized grains. This were co-located in the disc, or that the Solar Nebula con-
grain size is the typical size of forsterite grains as derived tained two distinct zones with similar composition.
by infrared spectral modelling (Bouwman et al. 2008). In In the next two sections we discuss the possible con-
the upper layers of the disc the settling timescale, τ , is nections between the resulting distribution of enstatite-rich
set
shorterthantheradialmigrationtimescale,τ ,andhence condesates in our 2D disc model, the derived vertical dust
mig
grains formed in the upper layers of the disc will generally settling timescales, and the chemistry of the ECs. We also
settle to the midplane before radially migrating. The two introduce a simple model that suggests a research path to
timescales are comparable close to the midplane. However, explain the formation of the bulk composition of ECs.
in the midplane the dead zone will likely affect the radial
migration, and grains are expected to accumulate at the
4.1 Secondary alteration of enstatite-rich grains
boundary of the dead zone. From equation (1) we see that
largergrainswillsettlefasterthansmallergrainsofthesame Given (1) the similarities observed between Mercury and
density, and different species of grains of the same size will theenstatitechondritesbulkmaterial,(2)ourfindingofthe
have different settling timescales due to their density. This twoenstatite-richzoneswithsimilarcomposition(oneinthe
in accordance with the expected behaviour dictated by the optically thin surface layer and one in the midplane of our
stoppingtime(Weidenschilling1977;Barri`ere-Fouchetetal. disc),(3)thepresenceofhighrefractorymaterialonthesur-
2005). faceofourdisc,(4)theproposedcommonoriginoftheCAIs
incarbonaceousandenstatitechondrites(Guanetal.2000),
and(5)thelocationofformationofCAIsplacedintheinner
upperlayeroftheSolarnebula(MacPhersonetal.2011,and
4 FORMING THE BULK MATERIALS OF
references within), we suggest that the bulk material which
THE ENSTATITE CHONDRITES
formedtheECswasderivedfromtheenstatite-richdustlo-
The mineralogical properties of enstatite chondrites (ECs) cated in the inner surface layer of our 2D disc.
differ significantly from the composition of ordinary chon- Wesuggestapossibleformationscenarioasfollows:the
drites,makingthemanunusualgroupofmeteorites.Nearly enstatite-rich dust (for which fo/en(cid:54)1) aggregated in the
pure enstatite (MgSiO ) is the main pyroxene compound, hotupperlayeroftheinnerdisc,accretingtherefractoryma-
3
and olivines such as forsterite (Mg SiO ) constitute only terialswhichisstillabundantinthesamezone(seeFig.2).
2 4
minor phases. Monoatomic sulfides (e.g. niningerite (MgS) The resulting bulk material might have then vertically set-
andoldhamite(CaS))arealsopresent,togetherwithtroilite tledintothesulfide-richregionwheresulfidationcouldhave
(FeS)(Weisberg&Kimura 2012).Themineralsdonotshow occurred.
aqueousalterationandprobablydidnotmixwithices,while The presence of niningerite in the EHs strongly sup-
their oxygen isotopic distribution place them along the ter- ports high temperature sulfidation processes (Lehner et al.
restrial fractionation line (Weisberg & Kimura 2012). 2013).Lehneretal.(2013)showedthatsulfidationcouldoc-
TheECsaredividedintwosub-groups:thosehighinFe cur if the environment is reduced in H content and C-rich.
(EHs)andthoselowinFe(ELs),whichdifferintheirFe/Si This can allow the presence of the necessary free S(g) to
and Mg/Si ratios: 0.8(cid:54)Fe/Si(cid:54)1.1 and 0.7(cid:54)Mg/Si(cid:54)0.8 initialise sulfidation at high temperatures. However, disso-
for the EHs, and 0.5 (cid:54) Fe/Si (cid:54) 0.7 and 0.8 (cid:54) Mg/Si (cid:54) 0.9 ciation of H S(g) can occur via other mechanisms such as
2
for ELs (Sears 1997). The EH hosts trace of refractory ma- UV-photodissociation (Chakraborty et al. 2013; Antonelli
terials, like hibonite and melilite, which are not found in et al. 2014) during transient heating events like outbursts
ELs (Weisberg & Kimura 2012). The EC assemblages do and shock waves (Lehmann et al. 1995). Such high temper-
not match the composition predicted by condensation pro- ature events will deplete the H S(g) content, enabling the
2
cesses when using solar elemental abundances (Yoneda & formation of S(g) and high temperature S-bearing gas such
Grossman 1995; Gail 1998), and it has been suggested that as HS(g) and SiS(g) (Pasek et al. 2005) or simply dissoci-
severalchemicalanddynamicalprocessesalteredboththeir ate H S(g) (Woiki & Roth 1994). However, experimental
2
pristine bulk material and the conditions of the environ- studies suggest that sulfurisation could also occur without
(cid:13)c 2002RAS,MNRAS000,1–14
2D condensation model for the inner Solar Nebula: an enstatite-rich environment 7
Figure3.Dynamicaldistributionmaps:left,log(τset/τmig),andright,ReM for0.1µm-sizedgrain.Thedashedlineistheτ =1surface
ofthediscandthedashed-dotlinerepresentsthediscsurface.
dissociating H S(g) via H S(g)-dust surface reaction (Lau- viaremovalofcondensingliquiddroplets,whichchangesthe
2 2
retta et al. 1998). chemical composition of the surrounding environment.
High concentration of sulfur and sulfidation processes
Here we present a toy model of gas fractionation due
could also have contributed to the enhancement of moder-
to dust settling and removal by the different condensation
ate volatiles such as selenium (Se) and tellurium (Te) in
temperatures and densities of compounds.
bulk enstatite chondrites (O’Neill & Palme 1998; Palme
& O’Neill 2003). Se and Te are chalcophiles and can be Before proceeding, we stress the limitations and as-
treated as a contaminant during the formation of sulfides sumptions of the following calculations. As a first approx-
(Lodders 2003; Fegley & Schaefer 2010). However, there imation we assume that the condensing solids are totally
are several other proposed processes that can account for removedfromtheenvironmentinwhichtheycondenseand,
the abundances of Se and Te in enstatite chondrites, such once formed, they do not react with the environment. The
as partial vaporization, incomplete condensation, weather- kinetics of the condensing dust is not taken into account.
ing, secondary oxidation of sulfides, sulfur loss, and highly Equation 1 applied to the D’Alessio et al. (1998, 1999)
reducing conditions (Kadlag & Becker 2015). model, for a silicate grain of a =0.1 µm, returns a settling
p
Enstatite-rich grains preferentially found in lower tem- timescale in the order of τ 10−5 yr on the surface of the
set
peraturezonesappearnottohaveaccretedany(orquantita- disc (less than one hour). This timescale will likely not al-
tivelyless)refractorymaterialwithsubsequentweaksulfida- low the grain to equilibrate with the surrounding gas. The
tionprocessesoccurringatlowertemperaturesandresulting separation of a condensing particle from the gas is, thus,
in the ELs. very efficient. As settling proceeds, the local dust density
increaseswithsettlingtowardsthemidplaneand,asaconse-
quence,grainswillsettlemoreslowly.Thisisclearlyevident
4.2 A toy model for the formation of ECs
in Fig.3. However, this is the case of non-growing grain, as
The efficiency of the vertical settling of the dust also sug- graingrowthwillcontributetofurtherdecreasethesettling
gests another mechanism for the formation of ECs. As we timescales (see eq. 1).
showed in Fig. 3, vertical settling of the dust can be an
For a gas of solar composition, at a standard pressure
efficient mechanism of dust sorting, since it is a function of P = 10−3 bar, the first major solid that condenses is
of grain density and size (see equation 1). Chemical frac-
iron, then forsterite followed by enstatite with decreasing
tionation occured in the early stage of our Solar System’s
temperature (Yoneda & Grossman 1995; Gail 1998). ECs
formation as seen from analysis of chondrites, and physical
are fractionated in their Fe/Si and Mg/Si ratios compared
fractionation (involving dynamical processes) is one of the
to solar values. As such, iron and magnesium removal is
possible mechanisms to explain it (Scott & Krot 2005).
required.Iron,forexample,hasadensityalmosttwicethat
Verticalsettlingandremovalof dustcanleadtodiffer-
of forsterite so it is not unreasonable to assume that some
ent chemical products which are not predicted by the clas-
fractionofirongrainsmightleavethecondensationlocation
sical condensation sequence in which the total bulk (dust
more rapidly than forsterite.
andgas)compositiondoesnotchangewithtime(Yoneda&
Grossman1995).Theideaofmultipleseparatedstepswhich Asatentative,exploratorypathforfuture,morequan-
lead to the bulk composition of enstatite chondrites is not titative, studies we start our calculation with a high-
new.Hutson&Ruzicka(2000)investigatedthecondensation temperature gas mixture at T = 1850 K, with solar com-
0
sequence due to partially removing high temperature con- position as reported in Table 1, column S. The pressure is
densatesandgas(watervapour).Blanderetal.(2009)inves- kept constant at P = 10−3 bar. As such, we are not sub-
tigated the formation of chondrules in enstatite chondrites scribing to any specific location of the 2D disc but instead
(cid:13)c 2002RAS,MNRAS000,1–14
8 Pignatale et al.
Table1.Gasabundanceforasolarcomposition(S)andattwosubsequentfractionationcutofftemperatures.Theinitialsolargasmixture
starts at T0 =1850 K. The T1 gas shows the elemental abundances of the gas at the condensation temperature of iron, T1 =1433 K,
andtheT2 gasshowstheelementalabundancesofthegasatthecondensationtemperatureofforsterite,T2 =1380K.Thepressureis
fixedatP =10−3 bar.ThebottomrowsshowtheMg/SiandFe/Sivaluesofthegasandthenthesamevaluesnormalisedtosolar.
Gasmixture S T1 T2
(temperature) (T0=1850K) (1433K) (1380K)
Element Abundance(kmol)
Al 2.59×10−4 1.80×10−9 1.55×10−10
Ar 2.31×10−4 2.31×10−4 2.31×10−4
C 2.47×10−2 2.47×10−2 2.47×10−2
Ca 2.01×10−4 1.79×10−7 2.15×10−8
Fe 2.91×10−3 1.69×10−3 5.91×10−4
H 92 92 92
He 7.83 7.83 7.83
Mg 3.66×10−3 3.47×10−3 1.20×10−3
N 6.22×10−3 3.11×10−3 3.11×10−3
Na 1.60×10−4 1.60×10−4 1.60×10−4
Ne 7.83×10−3 7.83×10−3 7.83×10−3
Ni 1.52×10−4 3.18×10−5 3.18×10−5
O 4.50×10−2 4.30×10−2 3.84×10−2
S 1.21×10−3 1.21×10−3 1.21×10−3
Si 2.97×10−3 2.62×10−3 1.47×10−3
(Mg/Si) 1.23 1.32 0.81
(Fe/Si) 0.98 0.64 0.40
(Mg/Si)/(Mg(cid:12)/Si(cid:12)) 1 1.07 0.66
(Fe/Si)/(Fe(cid:12)/Si(cid:12)) 1 0.65 0.41
are investigating a mechanism which can be applied to our lower than solar lead to enstatite-rich dust (Ferrarotti &
2D disc model3. Gail 2001). The bulk composition of this dust is compati-
SinceenstatitechondritesarefractionatedinFe/Siand blewiththebulkmaterialfoundintheenstatitechondrites
Mg/Si, iron and then magnesium have to be removed from (Weisberg & Kimura 2012).
the gas. Figure 4 summarises our toy model: we let the gas Figure 5 shows the Mg/Si vs Fe/Si ratios for the EHs
cool down until it reaches the condensation temperature of and ELs from Sears (1997), and for the fractionated gas
iron,T =1433K,andweassumethatthemetalandother and condensed solids derived from our calculations, all nor-
1
high-temperaturesolidswhichcondenseatthistemperature malisedtosolar.Theredcontinuouslineshowshowthegas
are removed from the environment. The composition of the withsolarcompositionwouldfractionateacrossthetemper-
resulting fractionated gas is shown in Table 1, column T , aturerangebetweenT andT .Thegreendashedlineshows
1 0 1
and results in Mg/Si = 1.07, Fe/Si= 0.66 (with all values howtheT gaswouldfractionateoverthetemperaturerange
1
normalised to solar), while the Mg/Si and Fe/Si ratios of betweenT andT .TheT gasisshownbyabluesquareand
1 2 2
the removed solids are 0.43 and 3.6 respectively. is the point at which the cooling gas reaches the forsterite
Next we let the T gas cool further to the temperature condensation temperature, T = 1388 K. In Fig. 5 we also
1 2
at which forsterite condenses, T = 1380 K. At this tem- plot the Mg/Si and Fe/Si ratios of the Fe-rich grains that
2
perature, forsterite, iron and minor silicates condense and condensedatT andwereremovedfromthegas(i.etheyare
1
leave the environment due to efficient vertical settling. The assumed to have settled vertically) and the Mg-rich grains
resulting Mg/Si and Fe/Si ratios of the gas are 0.66 and condense at T that also vertically settled.
2
0.41 respectively (with elemental abundances reported in
Table 1, column T ), while the Mg/Si and Fe/Si ratios of
2
the removed solids are 1.6 and 0.98 respectively.
Acondensationsequencestartingwiththefractionated 5 DISCUSSION
T gas, at the fixed pressure of 10−3 bar, returns enstatite,
2
In this section we present the theoretical and observational
forsterite, SiO , iron and nickel. In general, Mg/Si ratios
2 evidence which supports the results of our 2D disc model.
Sincechondritesformedearlyduringtheprotoplanetarydisc
phase,theremighthavebeenaconnectionbetweenthechon-
3 In the D’Alessio disc model, such a high pressure is only
driticbulkmaterialformingintheinnerregionoftheSolar
found in the midplane very close to the young Sun. Lower-
Nebula, the dust present (and in theory detectable) on its
ing the pressure results in the condensation temperature mov-
surface, and the dust in the midplane, which likely formed
ing towards lower values, and therefore the same condensates
can be found in both high pressure+temperature zones and planetesimals and planets.
lowerpressure+temperaturezones,withsomepossibleexceptions Thus,inthissection,weattempttolinkthesilicatedis-
whichwewilldiscussinsection5.3. tributionofourdiscpresentedinsection3andtheECsbulk
(cid:13)c 2002RAS,MNRAS000,1–14
2D condensation model for the inner Solar Nebula: an enstatite-rich environment 9
Figure 4.Schematicsummarisingthegasfractionationduetotheverticalsettlingofdust.Aparcelofgaswithsolarcomposition(at
constantpressureofP =10−3 barandinitialtemperatureofT0=1850K)iscooledtoT1=1433Kandallthesolidswhichcondense
atthistemperatureareremovedfromtheenvironmentduetotheefficientverticaldustsettling.ThefractionatedT1 gasisthenfurther
cooled to T2 = 1380 K, were it reaches the condensation temperature of forsterite. Forsterite, iron and minor silicates are efficiently
removed from the environment, and the resulting fractionated gas has Mg/Si and Fe/Si ratios of 0.66 and 0.41 respectively. Further
condensationoftheT2 gasleadstoenstatite-richcondensates.
materialdescribedinsectionsection4,withrecentevidence 0.02. This vertical section represents 1/45 of the total ex-
from the Messenger observations of Mercury and infrared tensionofourdiscmodel(0.1−1.0AU).Lookingatthe2D
observations of protoplanetary discs. Furthermore, we dis- condensate distribution, the limitations of 1D condensation
cuss in more detail the consequences and limitations of our sequences clearly emerge.
proposed alternative scenario for the formation of the EC’s The higher temperature region in the midplane which
bulk material. contains iron, nickel and enstatite is confined to the inner
0.4 AU. Beyond 0.4 AU, outside the equilibrium zone, the
dust chemistry cannot be predicted by equilibrium calcula-
5.1 Connecting enstatite-rich dust and Mercury tion. The inner enstatite-rich region in the midplane shows
similaritieswiththeenstatite-richzonefoundonthesurface
ObservationsandanalysisfromtheMessengerX-RaySpec-
of our disc. However, the zone for which fo/en<1 spans a
trometersuggestthatthesurfaceofMercurycomprisesMg-
smaller area within 0.2 AU, but the average dust composi-
richmineralslikeenstatiteanditisenrichedinsulfur(Wei-
tion in the zones where fo/en<1 and where fo/en>1 is
der et al. 2012).
thesameastherespectivezonespresentonthediscsurface.
1D condensation sequences have provided the theoret-
ical background for chemical analysis of the bulk composi- The enstatite-rich zone is also surrounded by a sulfide-
tion of the Solar Nebula (Yoneda & Grossman 1995; Gail richzone(seeFig.2),andgiventhelowertemperatures,by
1998; Pasek et al. 2005). Results of these 1D condensation amorphous dust. Here, kinetics become important in deter-
sequencesareinageneralagreementwiththechemicalgra- mining the reliability of this result. Lauretta et al. (1996)
dient found in the planets of our Solar System, when start- studied the reaction rates of iron sulfides production via Fe
ingwithaninitialsolargasmixture:refractorymaterialsat in a H2S(g)-H20(g) gas mixture under solar nebula condi-
high temperatures (T (cid:62) 1600 K), iron and silicates at in- tions.TheyfoundthatthetimescalesofFeSproductionare
termediate temperatures (650(cid:54)T(K)(cid:54)1600), iron oxides, much smaller (∼ 200 yr) than the nebula lifetime if metal
sulfides and water ice at lower temperatures (T (cid:54) 650 K). iron is present. As such, the presence of iron sulfide in this
However, 1D condensation sequences can simulate only one region should not be excluded.
layer of the disc at time and they cannot account for the ThedetectionofsodiuminthethinatmosphereofMer-
globalchemistryofdiscswithitsmultipleenvironmentsand curyandthepresenceofmoderatelyvolatilecompoundson
the variegate composition of the rocky planets. itssurface(Potter&Morgan1985;Cassidyetal.2015)raise
In the following discussion, we define the “midplane” furtherquestionsregardingthepresenceoflow-temperature
astheverticalsectionofour2Ddiscbetween0(cid:54)Z(AU)(cid:54) materialintheinnerdiscregions,astheamountofvolatiles
(cid:13)c 2002RAS,MNRAS000,1–14
10 Pignatale et al.
Figure 5. Resulting Mg/Si vs Fe/Si ratios normalised to solar values from our toy model for: the initial solar gas mix, the EHs and
ELsfromSears(1997),theT1 andT2 fractionatedgasfromTable1,theFe-richsolidsremovedafterthefirstcondensationfromT0 to
T1, and the Mg-rich solids removed after the second condensation from T1 to T2. The mixing line between the T2 gas and the Fe-rich
solidsisalsodrawn.Theredcontinuouslineshowshowthegaswithsolarcompositionwouldfractionateacrossthetemperaturerange
fromT0 (solar)andT1,whilethegreendashedlineshowshowtheT1 gaswouldfractionatefromT1 toT2.
in the solid phase should be close to zero if the planet ac- enstatite-richzones(discsurfaceandmidplane)iscompati-
creted material in the high temperature zone. blewiththescenariooftwodistinctzoneswithsimilarbulk
To investigate the distribution of moderately volatile composition. We therefore suggest that the bulk composi-
material in the midplane, we report in Fig. 6, as an ex- tion of ECs could have formed from the enstatite-rich dust
ample, the distribution of Na(g) and albite (NaAlSi O ). on the surface via the mechanism described in section 4.1,
3 8
Albite is the major Na-bearing compound at the conden- and that Mercury accreted from the enstatite-rich dust in
sation point of Na(g) according to thermodynamic equilib- the midplane.
rium.Theenstatite-richzonewherefo<eninthemidplane Sincegraingrowthinthediscmidplaneisveryefficient
is also Na(g)-rich. Albite is present together with enstatite duetothehighdensity,withgrainsreachingcm-sizeinfew
(seeFig.2)inthezonewherefo>en.Wethusfindadistri- thousandyears(Laibeetal.2008),accretionofthismixture
bution similar to FeS: the stability zone of albite surrounds in the dead zone (see Fig.3), could produce enstatite-rich
thehightemperatureregionwhereNaisinthegaseousform. planetesimal on short timescales, and the presence of low
However,albitecondensesatahighertemperaturethanFeS. temperature regions in the inner disc, could then account
At a pressure of P = 10−3 bar the condensation tempera- for the presence of sulfides and moderate volatiles in the
ture of albite is T = 970−980 K (Pignatale et al. 2011). accreting dust.
Thus, looking at Fig. 6 we see that albite becomes stable
in the midplane where R ∼ 0.3 AU. Moreover, a stability
zone of sodium-rich dust is also present in the inner hotter 5.2 Silicates distribution in the disc surface
region.
Infrared observations of the upper layers of protoplanetary
In conclusion, the midplane region of the disc up discs show a spatial variation of the forsterite and enstatite
to 0.4 AU is a chemically-variegate zone in which high- distribution, with more enstatite in the warm inner regions
temperaturecrystallinedust,enstatite,forsterite,metal-rich than in the cooler outer regions where forsterite dominates
grains, processed material, sulfides, volatiles, and unpro- (Kessler-Silacci et al. 2006; Bouwman et al. 2008; Meeus et
cessed material can coexist. The presence of the dead zone al.2009).Thereasonforthisdistributionremainsuncertain.
inthemidplane(seeFig.3)mightpreventthismixturefrom Kessler-Silacci et al. (2007) investigated the possible
leaving this zone. disc location from which the 10 µm silicate feature could
Our resulting 2D chemical distribution with two arise.The10µmsilicatefeatureisusuallymodelledassum-
(cid:13)c 2002RAS,MNRAS000,1–14