Destruction of massive fragments in protostellar disks and crystalline silicate production

1 MB·English

by  Eduard I. Vorobyov

Accepted by The AstrophysicalJournalLetters
PreprinttypesetusingLATEXstyleemulateapjv.08/13/06
DESTRUCTION OF MASSIVE FRAGMENTS IN PROTOSTELLAR DISKS AND CRYSTALLINE SILICATE
PRODUCTION
Eduard I. Vorobyov1,2,3
Accepted by The Astrophysical Journal Letters
ABSTRACT
We present a mechanism for the crystalline silicate production associated with the formation and
1 subsequent destruction of massive fragments in young protostellar disks. The fragments form in the
1 embeddedphaseofstarformationviadiskfragmentationatradialdistances&50−100AUandanneal
0 smallamorphousgrainsintheirinteriorwhenthegastemperatureexceedsthecrystallizationthreshold
2 of ∼800 K. We demonstrate that fragments that formin the early embedded phase canbe destroyed

n beforetheyeitherformsolidcoresorvaporizedustgrains,thusreleasingtheprocessedcrystallinedust
a into various radial distances from sub-AU to hundred-AU scales. Two possible mechanisms for the
J destruction of fragments are the tidal disruption and photoevaporationas fragments migrate radially

0 inwardandapproachthe centralstar and also dispersalby tidal torques exertedby spiralarms. As a
2 result, most of the crystalline dust concentrates to the disk inner regions and spiral arms, which are
the likely sites of fragment destruction.

]
R Subject headings: circumstellar matter — hydrodynamics — stars: protostars — stars: formation —
accretion disks
S
.
h
p 1. INTRODUCTION tingweaker,mayopenagapinthediskandmatureinto
- Theembeddedphaseoflow-massstarformation,start- gas giants on wide orbits but the probability for such
o a ”fortunate” outcome is rather low (Vorobyov & Basu
ing from the formation of a disk and ending with the
r 2010b).
t clearing of a parent cloud core, has recently drawn a
s Ironicasitmayseem,butthedestructionoffragments
renewed interest due to the possibility of planet forma-
a
(hereafter, planet/brown-dwarf embryos or simply em-
[ tion in this phase. Indeed, circumstellar disks are most
massive in the embedded phase (Andrews & Williams bryos)may be as important for the disk and stellar evo-
1 lution as their survival followed by massive giant planet
2005; Vorobyov 2009a; Greaves & Rice 2010) and nu-
v orbrowndwarfformation. Embryosthataredriveninto
merical hydrodynamics simulations indicate that, un-
2 the disk inner regions may form solid cores in their inte-
der certain conditions, embedded disks can fragment
8 riorviadustsedimentationordenseandcompactatomic
and form either protoplanetary embryos or proto-
9 hydrogencoresviadissociationofmolecularhydrogen. If
brown dwarfs, especially in the disk outer regions
3
one or both of those processes take place before the em-
where stellar irradiation and viscous heating are mer-
.
1 ciful (e.g. Durisen et al. 2007; Stamatellos & Whitworth bryo is destroyed on its approach to the central star, a
0 planet can emerge on orbit of order several AU or less
2009;Boley2009;Machida et al.2010;Vorobyov & Basu
1 (Nayakshin 2010a; Boley et al. 2010). If both processes
2010b; Cha & Nayakshin 2010).
1 fail,then the releaseofgravitationalenergyfromthe ac-
Whilediskfragmentationintheembeddedphaseseems
: creted embryo can trigger a luminosity outburst similar
v certainly feasible, the prospects for the survival of frag-
in magnitude those of FU Orionis or EX Lupi family
i mentsandformationofgasgiantsorbrowndwarfsondis-
X (Vorobyov & Basu 2006, 2010b). In addition, short but
tances of order tens or hundreds AU are gloomy. Grav-
r itational instability in the embedded phase is strong, intense bursts of accretion onto the star caused by the
a consumptionofembryoscanlowerthelithiumabundance
fuelled with a continuing infall of gas from a parent
in young solar-type stars (Baraffe & Chabrier 2010), ex-
cloud core, and resultant gravitationaland tidal torques
plaintheluminosityspreadinH-Rdiagramsof1-Myr-old
are rampant. As a consequence, part of the fragments
star clusters (Baraffe et al. 2009) and resolve the long-
are dispersed by the tidal torques exerted by the spi-
standing luminosity problem (Dunham et al. 2010).
ral arms (Vorobyov & Basu 2010b; Boley et al. 2010).
On the other hand, embryos are sites of acceler-
Others are quickly driven into the disk inner regions,
ateddustgrowthandhigh-temperatureprocessing(Boss
and probably onto the star, due to the loss of angu-
1998; Boss et al. 2002; Boley et al. 2010; Nayakshin
lar momentum caused by the gravitational interaction
2010a,b) and their in situ destruction by tidal torques
with the trailing spiral arms (Vorobyov & Basu 2006,
may release processed dust directly into the disk outer
2010b; Cha & Nayakshin 2010). Only those fragments
regions.
that happen to form in the late embedded phase, when
Whichever mechanism of embryo destruction is real-
gravitational instability and associated torques are get-
ized in nature, the consequences of this process are far-
1Institute for Computational Astrophysics, Saint Mary’s Uni- stretching. In this Letter, we report another interest-
versity,Halifax,B3H3C3,Canada; [email protected]. ing by-product of the embryo dispersal—the enrichment
2Research Institute of Physics, Southern Federal University, ofembeddedcircumstellardiskswithcrystallinesilicates
Stachki 194,Rostov-on-Don,344090, Russia.
3VisitingScientist,DepartmentofPhysicsandAstronomy,The formed in the depths of massive embryos via thermal
UniversityofWesternOntario,London,ONN6A3K7,Canada annealing of amorphous dust grains. We use numeri-
2 Vorobyov
calhydrodynamicssimulationsofthediskformationand guidelines described in Dullemond et al. (2006). We as-
long-term evolution complemented with equations de- sume that dust is passively transported with gas and
scribing the transformation of micron-sized amorphous neglect the dust radial drift caused by the dust-gas
dust grains into the silicate form. We show that part drag force. The latter simplification is of little con-
of the crystalline-silicate-bearing embryos are destroyed sequence for the dynamics of dust grains with sizes
beforetheyvaporizedustgrainsintheirinteriorsorform . 10 µm on timescales of interest for the present pa-
solidcoresviadustsedimentation,thusenrichingthegas per, . 0.5 Myr (Takeuchi & Lin 2002). Therefore, our
disk with crystalline silicates on radial distances from results are strictly applicable only to sufficiently small
sub-AU to hundred-AU scales. dust grains showing sharpfeatures in the 5–35µm band
ofthemid-infraredspectrum. Inthissimplescheme,two
2. SOURCESOFCRYSTALLINESILICATESIN additionalcontinuityequationsforthesurfacedensityof
CIRCUMSTELLARDISKS amorphous and crystalline silicates, Σ and Σ , re-
a.s. c.s.
Circumstellar disks originate during the gravitational spectively, are
collapse of rotating prestellar cloud cores. The degree ∂Σ
in crystallinity of silicates in prestellar cores is similar a.s. +∇p·(Σa.s.vp)=−S, (1)
∂t
to that of the interstellar medium, which has an up-
∂Σ
per limit of 0.2 ± 0.2% in the direction of the Galac- c.s. +∇ ·(Σ v )=+S, (2)
p c.s. p
tic center (Kember et al. 2004). On the other hand, the ∂t
crystalline-silicatefractionintheinnerregionsofcircum- wherev =v rˆ+v φˆ isthegasvelocityinthediskplane
p r φ
stellar disks around young stellar objects (YSOs) can and S = ν Σ . All dust grains in a collapsing cloud
cr a.s.
varyinwide limits fromessentiallynone toalmost100% coreareinitiallyamorphous,theycrystallizeatarateν
cr
(Watson et al.2009),implyinginsituproductionofcrys- provided by the Arrhenius formula
talline silicates in at leastsome YSOs. Two mechanisms
T
for dust crystallization have been put forward. ν s−1 =2×1013exp − c , (3)
cr
(cid:18) T (cid:19)
(cid:2) (cid:3) g
1. Evaporationoftheoriginal,amorphousdustgrains where T is the gas midplane temperature, 2 × 1013
g
followed by re-condensation under conditions of is the lattice vibrational frequency, and T =38100 K
c
hightemperatureanddensity(e.g.Grossman1972) (Bockel´ee-Morvanet al.2002). Weassumethatdustand
gas are thermalized. The initial gas and dust radial sur-
2. Thermal annealing of the amorphous grains at face density profiles and angular velocities are given by
temperatures (800–1300)K,somewhatbelow their equations(12)and(13)inVorobyov& Basu(2010b)and
vaporization point, via viscous heating (e.g. Gail theinitialdust-to-gasratiois0.01. Theinitialcoremass
2001), shock waveheating (Harker & Desch 2002), isMcore =0.78M⊙andtheratioofrotationaltogravita-
or disk surface heating during EX-Lupi-like out- tionalenergyofthecoreisβ =8.8×10−3. Forsimplicity,
bursts (A´brah´am et al. 2009). we also assume that all dust is made of silicate grains.
A solution of the time-dependent part of Equation 2
Bothmechanismsarethoughttoworkmostlyintheinner (excluding advection terms) demonstrates that it takes
1 AU from the star (except for shock heating that may about 40 yr to completely transform amorphous dust
operate at somewhat larger radial distances r .10 AU) into the crystalline form at T = 800 K. The corre-
g
and some means of outward radial transport of crys- sponding timescale for T = 900 K is 0.1 yr, while for
g
tallized dust is necessary to account for the non-zero T =700K the crystallizationtimescale is 20000yr. Ob-
g
crystalline-silicate fraction in comets at distances of or- viously, the latter value is much longer than the typ-
der tens of AU (e.g. Gail 2001; Bockel´ee-Morvanet al. ical orbital period and crystallization temperatures of
2002; Ciesla 2007). T = 800− 900 K are most relevant to circumstellar
cr
disks. Laboratoryexperiments tend to yield even higher
3. MODELDESCRIPTIONANDINITIALCONDITIONS T & 1000 K (Hallenbeck et al. 2000), possibly due to
cr
Our numerical model is explained in detail in the same timescale arguments.
Vorobyov & Basu(2010b). Here,we provideonlyabrief If temperature exceeds the evaporation threshold for
overview and describe modifications done to the numer- dustgrainsT ≈1400K,wesetbothΣ andΣ to
evap c.s. a.s.
ical code. We compute the gravitational collapse of ro- zero in the corresponding computational cell. The exact
tating cloud cores in the thin-disk approximation and valueofT isdensitydependentandiscalculatedfrom
evap
startoursimulationsfromthe pre-stellarphase,advance the opacity tables of Bell & Lin (1994).
through the disk formation and early evolution phase, Equations (1) and (2) are solved simultaneously with
andterminatewithalmostacompleteclearingofthena- equations of hydrodynamics describing the formation
talcore. Thefollowingphysicaleffects aretakenintoac- and evolution of circumstellar disks (eqs (1)–(3) in
count in our model: stellar irradiation, backgroundirra- Vorobyov& Basu 2010b). We employ the method of fi-
diationwith temperature T =10 K,viscous andshock nite differences with a time-explicit, operator-split solu-
bg
heating,radiativecoolingfromthedisksurface,anddisk tionprocedureinpolarcoordinates(r,φ)onanumerical
self-gravity. Turbulent viscosity is parameterized using grid with 512×512 grid zones. The advection part of
theusualα-prescription. Aspatiallyandtemporallycon- Equations (1) and (2) (i.e., with S set to zero) is solved
stant α is set to 0.005. usingapiece-wiseparabolicadvectionscheme. Thetime
In the current version, we have implemented a sim- updateofΣ andΣ duetothesource/sinktermS is
a.s. c.s.
ple mechanism describing the transformation of amor- done using an (unconditionally stable) backward differ-
phous dust grains into the crystalline form following the ence scheme supplemented with a subcycling procedure
Crystalline silicate production 3
to guarantee accuracy, wherein the change in both Σ tom row of Figure 1—there is a notable increase in ξ
a.s. c.s.
andΣ overoneglobalhydrodynamicaltimestepislim- with time. Crystalline silicates concentrate in the disk
c.s.
itedto10%. Ifthisconditionisviolated,localsubcycling inner regions and at/near spiral arms, which are likely
with smaller timesteps is invoked until the desired accu- sites of embryo formation and destruction. This implies
racy is reached. that the abundance of crystalline silicates may increase
The radial points in our numerical grid are logarith- with radius, at least in the early disk evolution, if most
mically spaced. The innermost grid point is located at ofthe embryosaretidally destroyedinthe disk outer re-
the position of the sink cell r = 6 AU and the size of gionsratherthandrivenintothestar. Ifsuchanincrease
sc
thefirstadjacentcellis0.08AU.Thiscorrespondstothe isobservationallyconfirmed,it couldbecomea hallmark
radial resolution of △r=1.3 AU at 100 AU. We impose for the proposed process.
a free outflow boundary condition so that the matter is On the other hand, if τ greater than either τ or
dest sed
allowed to freely flow through the sink cell to form a τ , then most of the processed crystalline dust will
evap
centralstarplus somedynamicallyinactiveinnerregion. be either locked up in solid terrestrial-like cores or va-
porized. The latter mechanism is implemented in the
4. RESULTS current numerical model, while the effect of the former
The top row in Figure 1 presents the gas surface den- is discussed in more detail later in the text.
sity in the inner several hundred AU at three distinct To better illustrate the process of disk enrichment
evolution times since the formation of the central star. withcrystallinesilicates,Figure2presentsvariousmodel
The middle and bottom rows show the corresponding characteristics as a function of time. In particular, the
gas midplane temperature and crystalline silicate frac- crystalline silicate fraction ξc.s. and amorphous silicate
tion ξc.s. = Mc.s./(Mc.s. + Ma.s.), respectively, where fraction ξa.s. = Ma.s./(Mc.s.+Ma.s.) are plotted in pan-
M and M are crystalline and amorphous silicate elsAandB,respectively. Morespecifically,black,green,
c.s a.s.
masses. The red circle in the coordinate center repre- and blue lines depict the corresponding fractions in the
sents schematically the central star plus sink cell. The disk (ξdisk and ξdisk), envelope (ξenv and ξenv), and sink
c.s. a.s. c.s. a.s.
three time snapshots in Figure 1 are chosen specifically cell(ξsc andξsc ),respectively. Wedistinguishbetween
c.s. a.s.
to illustrate disk fragmentation and embryo formation the disk and envelope using a scheme based on the typ-
(red dots at 50–100 AU). We note that each snapshot ical transitional gas surface density and radial gas ve-
shows in fact different embryos—their inward migration locity field explained in detail in Vorobyov (2010). We
and/or tidal destruction timescales are of order several notethatξdisk andξdisk areinfactcrystallineandamor-
c.s. a.s.
orbital periods (Torb = 700 yr for M∗ = 0.25 M⊙, phous silicate fractions stored in both the disk and the
r = 50 AU, t = 0.074 Myr and T = 1600 yr for embryos. Panel C shows the crystalline silicate fraction
orb
M∗ = 0.4, r = 100 AU, t = 0.178 Myr), which are con- inthedisk(blackline)andmaximummidplanegastem-
siderablyshorterthanthetime spanbetweentheimages perature Tmax (red line), whereas panel D presents the
g
(∼5×104 yr). mass accretion rate onto the star M˙ (red line) and the
We find that the gas temperature T in the interiors
g crystalline silicate fraction in the disk (black line).
of massiveembryoscanexceed 800K (see middle row in
Thereare sevenepisodes ofcrystalline silicate produc-
Figure 1), necessary for the thermal annealing of amor- tion in the disk manifested by a sharp increase in ξdisk,
phous dust grains to commence. The prospects for disk c.s.
allassociatedwiththeformationofembryosmassiveand
enrichment with crystalline silicates stored in these em-
hotenough to crystallize dust in their interior. Episodes
bryoswilldependoncharacteristictimescalesforinward
4, 6, and 7 (from left to right) correspond to the for-
migration and/or tidal destruction of embryos (τ ),
dest mation of embryos shown in the left, middle, and right
dust sedimentation and solid core formation in the em-
columns of Figure 1. From panel C it is evident that
bryointeriors(τsed),anddustvaporizationatTg >Tevap ξdisk increases sharply eachtime the maximum gas tem-
(τevap). If τdest is smaller than both τsed and τevap, then pce.rs.ature Tmax exceeds the crystallization temperature
allprocesseddustwillbereleasedintothediskatvarious T ≈ 800gK (horizontal dash-dotted line). After each
radialdistances,depending onwhichdestructionmecha- cr
suchepisode,prolongedperiodsofgradualdeclineinξdisk
nismprevails. Ascurrentnumericalsimulationsindicate, c.s.
follow, which are caused by dilution of the disk material
embryos may be destroyed by tidal torques from spiral
withpristineamorphousdustaccretedontothediskfrom
arms, preferentially releasing the crystalline silicates to
the infalling envelope.
large radial distances where these embryos form. Al-
In the last two episodes, Tmax goes above the dust
ternatively, embryos may be photoevaporated and torn g
evaporation temperature T and this leads to an im-
apartby stellarirradiationandtidal torques asthey mi- evap
grate radially inward and approach the central star. In mediate sharp drop in ξcd.iss.k. This exemplifies cases with
this case,partof the processeddust willbe broughtinto τevap < τdest. The dust evaporation timescale can be
the disk inner few AU (through the sink cell) and prob- approximated(excludingfactorsofunity)as(Nayakshin
ably onto the star and partwill be pushed to largerdisk 2010a)
radiiduringatransientepisodeofdiskexpansion(caused M −2
bytheconservationofangularmomentum)followingthe τevap =1.5×104 emb yr. (4)
(cid:18)10M (cid:19)
embryo tidal disruption. It is thus feasible to deposit J
crystalline silicates to various orbital distances starting For the typical embryo masses of M =5–20 M , the
emb J
from sub-AU scales and up to several hundred AU, ac- corresponding τ lies in the 4000–60000 yr range. In
evap
counting for the crystalline silicate features observed in fact,thisisalowerestimatesimplybecauseembryosmay
the spectra of the Solar system comets. This process of experience several contraction and expansion episodes
crystalline silicate enrichment is illustrated in the bot- beforeactuallyreachingT . Embryosthatforminthe
evap
4 Vorobyov
-150 -100 -50 0 50 100 150 -300 -200 -100 0 100 200 300 -300 -200 -100 0 100 200 300
0.074 Myr 0.132 Myr 0.178 Myr 4
150
U) 100 3
A
e ( 50
c 2
n
sta 0
di 1
al -50
di
a
R-100 0
-150
gas -1
3
150 2.8
2.6
U) 100
A 2.4
ce ( 50 2.2
n
sta 0 2
di
al -50 1.8
di 1.6
a
R-100
1.4
-150
1.2
midplane gas temperature
0
-0.25
150
-0.5
U) 100
A -0.75
e ( 50 -1
c
n
sta 0 -1.25
di
al -50 -1.5
di -1.75
a
R-100
-2
-150
-2.25
crystalline silicate fraction
-2.5
-150 -100 -50 0 50 100 150 -300 -200 -100 0 100 200 300 -300 -200 -100 0 100 200 300
Radial distance (AU) Radial distance (AU) Radial distance (AU)
Fig. 1.—Gassurfacedensity(gcm−2,toprow),gasmidplanetemperature(Kelvin,middlerow),andcrystallinesilicatefraction(bottom
row)atthreetimessincetheformationofthecentralstar: t=0.074Myr(leftcolumn),t=0.132Myr(middlecolumn),andt=0.178Myr
(rightcolumn).
early disk evolution are of lower mass and closer to the 10−5 M⊙ yr−1) mass accretion bursts, also contributes
star than those that form later in the embedded phase to the decrease in ξdisk but leads to an increase in ξsc .
c.s. c.s.
(because disk grows in mass and size with time). As Notethatepisodes3and4arenotassociatedwithstrong
a consequence, first embryos take longer time to evap- massaccretionbursts,indicating that the corresponding
orate dust and shorter time to migrate into the star, embryos are dispersed by tidal torques exerted by spiral
an effect found in our numerical simulations and also arms,before they actually fallthroughthe sink cell onto
noted by Cha & Nayakshin (2010). For these first em- the star. The process of disk fragmentation diminishes
bryos, migration timescales are just several orbital peri- after t≈0.2 Myr, no embryos survive beyond this time,
ods(Torb=700–1600yr)andareoftenshorterthanτevap. and the subsequent evolution shows a gradualdecline in
As time passes and more massive embryos on wider or- ξdisk. From this moment on, ξdisk represents the crys-
c.s. c.s.
bits start to form, the migration/destruction time scale talline silicate fraction in the disk only.
mayexceedthatofdustevaporation,asindeedoccurred We do not take into account a possible formation of
during the last two episodes of crystalline dust produc- solid cores (and associated reduction in disk enrichment
tion. with crystalline dust) but we can estimate its efficiency
Migration of embryos into the disk inner regions and based on the work of Nayakshin (2010a). For M =
emb
through the sink cell, as manifested by strong (& 5 × 3−10M ,Nayakshinfoundτ ≈(4−6)×103yr. Thisis
J sed
Crystalline silicate production 5
Time (Myr) Time (Myr)
0.0 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.5
0.5 1.2
n A disk B n
actio 0.4 esinnvke cloeplle 1.0 actio
e fr 0.3 e fr
at 0.8 at
c c
ne sili 0.2 0.6 us sili
rystalli 0.1 deinsvkelope 0.4 morpho
C 0.0 sink cell A
7e-5
K) C maximum temperature D accretion rate onto the star 1)
e ( crystalline silicate fraction crystalline silicate fraction 6e-5 -yr
r 2500
u
at 5e-5 M(cid:1)
er e (
mp 2000 4e-5 at
r
e n
as t 1500 3e-5 etio
g r
al 2e-5 cc
m a
u 1000 s
xi 1e-5 as
a M
M
500 0
0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.5
Time (Myr) Time (Myr)
Fig. 2.— Crystalline (panel A) and amorphous (panel B) silicate fractions in the disk (black), envelope (green), and star+sink cell
(blue)asafunctionoftimepassedsincetheformationofthecentralstar. PanelCshowsthemaximumtemperatureinthedisk(red)and
crystallinesilicatefractioninthedisk(black), whilepanelDalsoshowsthemassaccretionrateontothestar(red).
comparabletoorlessthanτ &(4−16)×103yr,which Wehaverunanothereightmodelswithβ =(3.2−12)×
evap
implies that solid cores may form before dust is vapor- 10−3 and Mcore =0.3−1.25 M⊙. The net result is that
ized. At the same time, τ is comparable to or longer thedustprocessingiscorrelatedwithdiskfragmentation
sed
than τ = a few × T ≈ a few × 103 yr, certainly andmodels that do not formembryos(e.g., models with
dest orb
for those embryos that form first in the early embed- lowM andβ andconsequentlywithdisksoflowmass
core
ded phase and are characterized by shortest migration and size) show little crystalline silicates, reinforcing our
timescales. This simple timescale analysis suggests that conclusions.
the solid core formation is feasible and may reduce the We stress that our proposed mechanism can coexist
efficiency of crystalline dust enrichment but is unlikely with other crystallization mechanisms, localized to the
to shut down the proposed mechanism completely. The inner few AU, and complements them by providing a
latestnumericalhydrodynamicssimulationsseemtocon- direct source of crystalline silicates at large distances.
firmthatthesolidcoreformationisnotexpectedtowork Some outward transport may still takes place and ac-
for every embryo in the disk (Cha & Nayakshin 2010). count for the fact that comet Wild 2 has crystalline sil-
icates with the chemical and isotopic composition simi-
5. SUMMARY lar to that of the chondritic meteorites originated in the
terrestrial planet region (McKeegan et al. 2006). Con-
Thermalannealingofamorphousdustgrainsinthehot
versely, chondritic meteorites may have formed in the
interiors of massive fragments (or planet/brown dwarf
atmospheres of protoplanetary embryos via dust sedi-
embryos) forming in protostellar disks during the early
mentation and released into the inner few AU when the
embedded stages of stellar evolution, followed by subse-
embryos were dispersed by tidal torques near the young
quent dispersalof the fragments, is a promising gateway
Protosun. The apparent presence of refractory Calcium
for the production of crystalline silicates. This mech-
Aluminum Inclusions in the cometary material does not
anism can release processed dust to various radial dis-
invalidate this scenario since temperatures in at least
tances from (sub-)AU scales, if fragments are destroyed
someof the embryoscanexceed1300K (panelC inFig-
on their approach to the central star, to hundred-AU
ure 2). We do not take into account possible opacity
scales, if they are dispersed by tidal torques exerted by
dependence on the composition and properties of dust
spiral arms. More studies, including the effect of dust
grains due to the complexity of physics involved. Nev-
growth and solid core formation, are needed to further
ertheless, dust growth and crystallization are likely to
explore the efficiency of this mechanism.
6 Vorobyov
decrease opacities (Mennella et al. 1998; D’Alessio et al. for hospitality. Support from an ACEnet Fellowship
2001),thusenhancingdiskfragmentationandcrystalline is gratefully acknowledged. Numerical simulations were
silicate production. doneontheAtlanticComputationalExcellenceNetwork
(ACEnet). This project was also supported by RFBR
grant 10-02-00278 and by the Ministry of Education
The author is grateful to the anonymous referee for
grant RNP 2.1.1/1937.
very useful comments and to Prof. Shantanu Basu
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