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At least 235 records · Page 13
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DOE OSTI2011

THE SINTERING REGION OF ICY DUST AGGREGATES IN A PROTOPLANETARY NEBULA

Icy grain aggregates are formed in the outer region of a protoplanetary nebula. The infall of these aggregates to the central star is due to gas drag, and their temperature increases as the infall proceeds. The icy molecules on the grain move to the neck where the grains get connected through sublimation and condensation of the molecules. This process is called sintering. As the sintering proceeds, the mechanical strength of the neck changes considerably, strongly affecting the collisional evolution of the aggregates. The timescale required for sintering is determined in this study, based on which the region where the sintering proceeds within a prescribed timescale is obtained. It is found that the region covers a substantial fraction of the protoplanetary nebula, and the location of the region depends on the temperature distribution inside the nebula. If the aggregate is stirred up and the temperature of the aggregate increases temporally, the sintering region spreads to the whole nebula.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

THE PHOTOEVAPORATIVE WIND FROM THE DISK OF TW Hya

Photoevaporation driven by the central star is expected to be a ubiquitous and important mechanism for dispersing the circumstellar dust and gas from which planets form. Here, we present a detailed study of the circumstellar disk surrounding the nearby star TW Hya and provide observational constraints to its photoevaporative wind. Our new high-resolution (R {approx} 30,000) mid-infrared spectroscopy in the [Ne II] 12.81 {mu}m line confirms that this gas diagnostic traces the unbound wind component within 10 AU of the star. From the blueshift and asymmetry in the line profile, we estimate that most (>80%) of the [Ne II] emission arises from disk radii where the midplane is optically thick to the redshifted outflowing gas, meaning beyond the 1 or 4 AU dust rim inferred from other observations. We re-analyze high-resolution (R {approx} 48,000) archival optical spectra searching for additional transitions that may trace the photoevaporative flow. Unlike the [Ne II] line, optical forbidden lines from O I, S II, and Mg I are centered at stellar velocity and have symmetric profiles. The only way these lines can trace the photoevaporative flow is if they arise from a disk region physically distinct from that traced by the [Ne II] line, specifically from within the optically thin dust gap. However, the small ({approx}10 km s{sup -1}) FWHM of these lines suggests that most of the emitting gas traced at optical wavelengths is bound to the system rather than unbound. We discuss the implications of our results for a planet-induced gap versus a photoevaporation-induced gap.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

KINETIC CONDENSATION AND EVAPORATION OF METALLIC IRON AND IMPLICATIONS FOR METALLIC IRON DUST FORMATION

Metallic iron is one of the most abundant condensing materials in systems of solar abundance. Because metallic iron is responsible for the continuum opacity of dust particles, it has a large contribution to the thermal structure of circumstellar environments and hence to dust evolution itself. In order to understand the formation processes of metallic iron in circumstellar environments, condensation and evaporation kinetics of metallic iron were studied experimentally. Metallic iron condenses at the maximum rate with the condensation coefficient (a parameter ranging from 0 to 1 to represent kinetic hindrance for surface reaction) of unity under high supersaturation conditions, and evaporates nearly ideally (evaporation coefficient of unity) in vacuum. On the other hand, evaporation of metallic iron takes place with more kinetic hindrance in the presence of metallic iron vapor. It is also found that metallic iron atoms nucleate heterogeneously on Al{sub 2}O{sub 3}. Metallic iron does not necessarily condense homogeneously in circumstellar environments, but might condense through heterogeneous nucleation on pre-existing dust. Metallic iron formation proceeds with little kinetic hindrance for highly unequilibrated conditions, but the effects of kinetic hindrance may appear for evaporation and condensation occurring near equilibrium with a timescale of months to years in protoplanetary disks.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

LOW-VELOCITY COLLISIONS OF CENTIMETER-SIZED DUST AGGREGATES

Collisions between centimeter- and decimeter-sized dusty bodies are important in understanding the mechanisms leading to the formation of planetesimals. We performed laboratory experiments to study the collisional behavior of dust aggregates in this size range at velocities below and around the fragmentation threshold. We developed two independent experimental setups with the same goal: to study the effects of bouncing, fragmentation, and mass transfer in free particle-particle collisions. The first setup is an evacuated drop tower with a free-fall height of 1.5 m, providing us with 0.56 s of microgravity time, so that we observed collisions with velocities between 8 mm s{sup -1} and 2 m s{sup -1}. The second setup is designed to study the effect of partial fragmentation (when only one of the two aggregates is destroyed) and mass transfer in more detail. It allows for the measurement of the accretion efficiency because the samples are safely recovered after the encounter. At very low velocities, we found that bouncing was as expected, while the fragmentation velocity of 20 cm s{sup -1} was significantly lower than expected. We present the critical energy for disruptive collisions Q*, which were at least two orders of magnitude lower than previous experiments in the literature. In the wide range between bouncing and disruptive collisions, only one of the samples fragmented in the encounter, while the other gained mass. The accretion efficiency on the order of a few percentage points of the particle's mass depends on the impact velocity and the sample porosity. Our results will have consequences for dust evolution models in protoplanetary disks as well as for the strength of large, porous planetesimal bodies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

PROTOPLANETARY DISK MASSES IN IC348: A RAPID DECLINE IN THE POPULATION OF SMALL DUST GRAINS AFTER 1 Myr

We present a 1.3 mm continuum survey of protoplanetary disks in the 2-3 Myr old cluster, IC348, with the Submillimeter Array. We observed 85 young stellar objects and detected 10 with 1.3 mm fluxes greater than 2 mJy. The brightest source is a young embedded protostar driving a molecular outflow. The other nine detections are dusty disks around optically visible stars. Our millimeter flux measurements translate into total disk masses ranging from 2 to 6 Jupiter masses. Each detected disk has strong mid-infrared emission in excess of the stellar photosphere and has H{alpha} equivalent widths larger than the average in the cluster and indicative of ongoing gas accretion. The disk mass distribution, however, is shifted by about a factor of 20 to lower masses, compared to that in the {approx}1 Myr old Taurus and Ophiuchus regions. These observations reveal the rapid decline in the number of small dust grains in disks with time and probably their concomitant growth beyond millimeter sizes. Moreover, if IC348 is to form planets in the same proportion as detected in the field, these faint millimeter detections may represent the best candidates in the cluster to study the progression from planetesimals to planets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

X-RAY IONIZATION OF HEAVY ELEMENTS APPLIED TO PROTOPLANETARY DISKS

The consequences of the Auger effect on the population of heavy-element ions are analyzed for the case of relatively cool gas irradiated by keV X-rays with intended applications to the accretion disks of young stellar objects. Highly charged ions are rapidly reduced to the doubly charged state in neutral gas, so the aim here is to derive the production rates for these singly and doubly charged ions and to specify their transformation by recombination, charge transfer, and molecular reactions. The theory is illustrated by calculations of the abundances of 11 of the most cosmically abundant heavy elements in a model of a typical T Tauri star disk. The physical properties of the gas are determined with an X-ray irradiated thermal-chemical model, which shows that the disk atmosphere consists of a hot atmosphere overlaying the mainly cool body of the disk. There is a warm transition layer where hydrogen, carbon, and oxygen are transformed from atomic to molecular species and the ionization drops by several orders of magnitude. The doubly charged ions are then largely confined to the hot outer layers of the disk. The nature of the dominant ions below the transition depends sensitively on the poorly constrained abundances of the heavy elements. Observational consequences and connections with the active layers of the magnetorotational instability are briefly discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

EFFECT OF AMBIPOLAR DIFFUSION ON THE NONLINEAR EVOLUTION OF MAGNETOROTATIONAL INSTABILITY IN WEAKLY IONIZED DISKS

We study the role of ambipolar diffusion (AD) on the nonlinear evolution of the magnetorotational instability (MRI) in protoplanetary disks using the strong coupling limit, which applies in very weakly ionized gas with electron recombination time much shorter than the orbital time so that a single-fluid treatment is sufficient. The effect of AD in this limit is characterized by the dimensionless number Am, the frequency at which neutral particles collides with ions normalized to the orbital frequency. We perform three-dimensional unstratified shearing-box simulations of the MRI over a wide range of Am as well as different magnetic field strengths and geometries. The saturation level of the MRI turbulence depends on the magnetic geometry and increases with the net magnetic flux. There is an upper limit to the net flux for sustained turbulence, corresponding to the requirement that the most unstable vertical wavelength be less than the disk scale height. Correspondingly, at a given Am, there exists a maximum value of the turbulent stress {alpha}{sub max}. For Am {approx}< 1, the largest stress is associated with a field geometry that has both net vertical and toroidal flux. In this case, we confirm the results of linear analyses that show the fastest growing mode has a non-zero radial wavenumber with a growth rate exceeding that of the pure vertical field case. We find there is a very tight correlation between the turbulent stress {alpha} and the plasma ({beta}) {identical_to} P{sub gas}/P{sub mag} {approx} 1/2{alpha} at the saturated state of the MRI turbulence regardless of field geometry, and {alpha}{sub max} rapidly decreases with decreasing Am. In particular, we find {alpha}{sub max} {approx} 7 x 10{sup -3} for Am = 1 and {alpha}{sub max} {approx} 6 x 10{sup -4} for Am = 0.1.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

THREE-DIMENSIONAL LAGRANGIAN TURBULENT DIFFUSION OF DUST GRAINS IN A PROTOPLANETARY DISK: METHOD AND FIRST APPLICATIONS

In order to understand how the chemical and isotopic compositions of dust grains in a gaseous turbulent protoplanetary disk are altered during their journey in the disk, it is important to determine their individual trajectories. We study here the dust-diffusive transport using Lagrangian numerical simulations using the popular 'turbulent diffusion' formalism. However, it is naturally expressed in an Eulerian form, which does not allow the trajectories of individual particles to be studied. We present a simple stochastic and physically justified procedure for modeling turbulent diffusion in a Lagrangian form that overcomes these difficulties. We show that a net diffusive flux F of the dust appears and that it is proportional to the gas density ({rho}) gradient and the dust diffusion coefficient D{sub d}: (F = D{sub d} /{rho} x grad({rho})). It induces an inward transport of dust in the disk's midplane, while favoring outward transport in the disk's upper layers. We present tests and applications comparing dust diffusion in the midplane and upper layers as well as sample trajectories of particles with different sizes. We also discuss potential applications for cosmochemistry and smoothed particle hydrodynamic codes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

THE REBOUND CONDITION OF DUST AGGREGATES REVEALED BY NUMERICAL SIMULATION OF THEIR COLLISIONS

Collisional growth of dust aggregates is a plausible root of planetesimals forming in protoplanetary disks. However, a rebound of colliding dust aggregates prevents dust from growing into planetesimals. In fact, rebounding aggregates are observed in laboratory experiments but not in previous numerical simulations. Therefore, the condition of rebound between dust aggregates should be clarified to better understand the processes of dust growth and planetesimal formation. We have carried out numerical simulations of aggregate collisions for various types of aggregates and succeeded in reproducing a rebound of colliding aggregates under specific conditions. Our finding is that in the rebound process, the key factor of the aggregate structure is the coordination number, namely, the number of particles in contact with a particle. A rebound is governed by the energy dissipation along with restructuring of the aggregates and a large coordination number inhibits the restructuring at collisions. Results of our numerical simulation for various aggregates indicate that they stick to each other when the mean coordination number is less than 6, regardless of their materials and structures, as long as their collision velocity is less than the critical velocity for fragmentation. This criterion of the coordination number would correspond to a filling factor of {approx}0.3, which is somewhat larger than that reported in laboratory experiments. In protoplanetary disks, dust aggregates are expected to have low bulk densities (<0.1 g cm{sup -3}) during their growth, which would prevent dust aggregates from rebounding. This result supports the formation of planetesimals with direct dust growth in protoplanetary disks.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

ON THE INTERACTION BETWEEN A PROTOPLANETARY DISK AND A PLANET IN AN ECCENTRIC ORBIT: APPLICATION OF DYNAMICAL FRICTION

We present a new analytic approach to the disk-planet interaction that is especially useful for planets with eccentricity larger than the disk aspect ratio. We make use of the dynamical friction formula to calculate the force exerted on the planet by the disk, and the force is averaged over the period of the planet. The resulting migration and eccentricity damping timescale agree very well with previous works in which the planet eccentricity is moderately larger than the disk aspect ratio. The advantage of this approach is that it is possible to apply this formulation to arbitrary large eccentricity. We have found that the timescale of the orbital evolution depends largely on the adopted disk model in the case of highly eccentric planets. We discuss the possible implication of our results for the theory of planet formation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

VERY LARGE TELESCOPE/NACO POLARIMETRIC DIFFERENTIAL IMAGING OF HD100546-DISK STRUCTURE AND DUST GRAIN PROPERTIES BETWEEN 10 AND 140 AU

We present polarimetric differential imaging (PDI) data of the circumstellar disk around the Herbig Ae/Be star HD100546 obtained with Very Large Telescope/NACO. We resolve the disk in polarized light in the H and K{sub s} filter between {approx}0.''1 and 1.''4 (i.e., {approx}10-140 AU). The innermost disk regions are directly imaged for the first time and the mean apparent disk inclination and position angle are derived. The surface brightness along the disk major axis drops off roughly with S(r){proportional_to}r {sup -3} but has a maximum around 0.''15 suggesting a marginal detection of the main disk inner rim at {approx}15 AU. We find a significant brightness asymmetry along the disk minor axis in both filters with the far side of the disk appearing brighter than the near side. This enhanced backward scattering and a low total polarization degree of the scattered disk flux of 14{sup +19}{sub -8}% suggest that the dust grains on the disk surface are larger than typical interstellar medium grains. Empirical scattering functions reveal the backward scattering peak at the largest scattering angles and a second maximum for the smallest scattering angles. This indicates a second dust grain population preferably forward scattering and smaller in size. It shows that, relatively, in the inner disk regions (40-50 AU) a higher fraction of larger grains is found compared to the outer disk regions (100-110 AU). Finally, our images reveal distinct substructures between 25 and 35 AU physical separation from the star and we discuss the possible origin for the two features in the context of ongoing planet formation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

IDENTIFICATION OF THREE NEW PROTOPLANETARY NEBULAE EXHIBITING THE UNIDENTIFIED FEATURE AT 21 {mu}m

Among its great findings, the Infrared Astronomical Satellite mission showed the existence of an unidentified mid-IR feature around 21 {mu}m. Since its discovery, this feature has been detected in all C-rich protoplanetary nebulae (PPNe) of intermediate spectral type (F-G) and-weakly-in a few PNe and asymptotic giant branch (AGB) stars, but the nature of its carriers remains unknown. In this paper, we show the detection of this feature in the spectra of three new stars transiting from the AGB to the PN stage obtained with the Spitzer Space Telescope. Following a recent suggestion, we try to model the spectral energy distributions of our targets with amorphous carbon and FeO, which might be responsible for the unidentified feature. The fit thus obtained is not completely satisfactory, since the shape of the feature is not well matched. In an attempt to relate the unidentified feature to other dust features, we retrieved mid-IR spectra of all 21 {mu}m sources currently known from Infrared Space Observatory and Spitzer online archives and noticed a correlation between the flux emitted in the 21 {mu}m feature and that emitted at 7 and 11 {mu}m (polycyclic aromatic hydrocarbon bands and hydrogenated amorphous carbon broad emission). Such a correlation may point to a common nature of the carriers.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

A MAGELLAN MIKE AND SPITZER MIPS STUDY OF 1.5-1.0 M{sub sun} STARS IN SCORPIUS-CENTAURUS

We obtained Spitzer Space Telescope Multiband Imaging Photometer for Spitzer (MIPS) 24 {mu}m and 70 {mu}m observations of 182 nearby, Hipparcos F- and G-type common proper motion single and binary systems in the nearest OB association, Scorpius-Centaurus. We also obtained Magellan/MIKE R {approx} 50,000 visual spectra at 3500-10500 A for 181 candidate ScoCen stars in single and binary systems. Combining our MIPS observations with those of other ScoCen stars in the literature, we estimate 24 {mu}m F+G-type disk fractions of 9/27 (33% {+-} 11%), 21/67 (31% {+-} 7%), and 25/71 (35% {+-} 7%) for Upper Scorpius ({approx}10 Myr), Upper Centaurus Lupus ({approx}15 Myr), and Lower Centaurus Crux ({approx}17 Myr), respectively. We confirm previous IRAS and MIPS excess detections and present new discoveries of 41 protoplanetary and debris disk systems, with fractional infrared luminosities ranging from L{sub IR}/L{sub *} = 10{sup -5} to 10{sup -2} and grain temperatures ranging from T{sub gr} = 40-300 K. We searched for an increase in 24 {mu}m excess at an age of 15-20 Myr, consistent with the onset of debris production predicted by coagulation N-body simulations of outer planetary systems. We found such an increase around 1.5 M{sub sun} stars but discovered a decrease in the 24 {mu}m excess around 1.0 M{sub sun} stars. We additionally discovered that the 24 {mu}m excess around 1.0 M{sub sun} stars is larger than predicted by self-stirred models. Finally, we found a weak anti-correlation between fractional infrared luminosity (L{sub IR}/L{sub *}) and chromospheric activity (R'{sub HK}), that may be the result of differences in stellar properties, such as mass, luminosity, and/or winds.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

TRANSITIONAL DISKS AS SIGNPOSTS OF YOUNG, MULTIPLANET SYSTEMS

Although there has yet been no undisputed discovery of a still-forming planet embedded in a gaseous protoplanetary disk, the cleared inner holes of transitional disks may be signposts of young planets. Here, we show that the subset of accreting transitional disks with wide, optically thin inner holes of 15 AU or more can only be sculpted by multiple planets orbiting inside each hole. Multiplanet systems provide two key ingredients for explaining the origins of transitional disks. First, multiple planets can clear wide inner holes where single planets open only narrow gaps. Second, the confined, non-axisymmetric accretion flows produced by multiple planets provide a way for an arbitrary amount of mass transfer to occur through an apparently optically thin hole without overproducing infrared excess flux. Rather than assuming that the gas and dust in the hole are evenly and axisymmetrically distributed, one can construct an inner hole with apparently optically thin infrared fluxes by covering a macroscopic fraction of the hole's surface area with locally optically thick tidal tails. We also establish that other clearing mechanisms, such as photoevaporation, cannot explain our subset of accreting transitional disks with wide holes. Transitional disks are therefore high-value targets for observational searches for young planetary systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

EVOLUTION OF SNOW LINE IN OPTICALLY THICK PROTOPLANETARY DISKS: EFFECTS OF WATER ICE OPACITY AND DUST GRAIN SIZE

Evolution of a snow line in an optically thick protoplanetary disk is investigated with numerical simulations. The ice-condensing region in the disk is obtained by calculating the temperature and the density with the 1+1D approach. The snow line migrates as the mass accretion rate ( M-dot ) in the disk decreases with time. Calculations are carried out from an early phase with high disk accretion rates ( M-dot {approx}10{sup -7} M{sub sun} yr{sup -1}) to a later phase with low disk accretion rates ( M-dot {approx}10{sup -12} M{sub sun} yr{sup -1}) using the same numerical method. It is found that the snow line moves inward for M-dot {approx}>10{sup -10} M{sub sun} yr{sup -1}, while it gradually moves outward in the later evolution phase with M-dot {approx}<10{sup -10} M{sub sun} yr{sup -1}. In addition to the silicate opacity, the ice opacity is taken into consideration. In the inward migration phase, the additional ice opacity increases the distance of the snow line from the central star by a factor of 1.3 for dust grains {approx}< 10 {mu}m in size and of 1.6 for {approx}> 100 {mu}m. It is inevitable that the snow line comes inside Earth's orbit in the course of the disk evolution if the viscosity parameter {alpha} is in the range 0.001-0.1, the dust-to-gas mass ratio is higher than a tenth of the solar abundance value, and the dust grains are smaller than 1 mm. The formation of water-devoid planetesimals in the terrestrial planet region seems to be difficult throughout the disk evolution, which imposes a new challenge to planet formation theory.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

KEPLER EXOPLANET CANDIDATE HOST STARS ARE PREFERENTIALLY METAL RICH

We find that Kepler exoplanet candidate (EC) host stars are preferentially metal rich, including the low-mass stellar hosts of small-radius ECs. The last observation confirms a tentative hint that there is a correlation between the metallicity of low-mass stars and the presence of low-mass and small-radius exoplanets. In particular, we compare the J-H-g-r color-color distribution of Kepler EC host stars with a control sample of dwarf stars selected from the {approx}150, 000 stars observed during Q1 and Q2 of the Kepler mission but with no detected planets. We find that at J - H = 0.30 characteristic of solar-type stars, the average g-r color of stars that host giant ECs is 4{sigma} redder than the average color of the stars in the control sample. At the same J - H color, the average g-r color of solar-type stars that host small-radius ECs is indistinguishable from the average color of the stars in the control sample. In addition, we find that at J - H = 0.62 indicative of late K dwarfs, the average g-r color of stars that host small-radius ECs is 4{sigma} redder than the average color of the stars in the control sample. These offsets are unlikely to be caused by differential reddening, age differences between the two populations, or the presence of giant stars in the control sample. Stellar models suggest that the first color offset is due to a 0.2 dex enhancement in [Fe/H] of the giant EC host population at M{sub *} {approx} 1 M{sub sun}, while Sloan photometry of M 67 and NGC 6791 suggests that the second color offset is due to a similar [Fe/H] enhancement of the small-radius EC host population at M{sub *} {approx} 0.7 M{sub sun}. These correlations are a natural consequence of the core-accretion model of planet formation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

THE STRUCTURE OF A SELF-GRAVITATING PROTOPLANETARY DISK AND ITS IMPLICATIONS FOR DIRECT IMAGING OBSERVATIONS

We consider the effects of self-gravity on the hydrostatic balance in the vertical direction of a gaseous disk and discuss the possible signature of the self-gravity that may be captured by direct imaging observations of protoplanetary disks in the future. In this paper, we consider a vertically isothermal disk in order to isolate the effects of self-gravity. The specific disk model we consider in this paper is the one with a radial surface density gap, at which the Toomre's Q-parameter of the disk varies rapidly in the radial direction. We calculate the vertical structure of the disk including the effects of self-gravity. We then calculate the scattered light and the dust thermal emission. We find that if the disk is massive enough and the effects of self-gravity come into play, a weak bump-like structure at the gap edge appears in the near-infrared (NIR) scattered light, while no such bump-like structure is seen in the submillimeter (sub-mm) dust continuum image. The appearance of the bump is caused by the variation of the height of the surface in the NIR wavelength. If such a bump-like feature is detected in future direct imaging observations, combined with sub-mm observations, it will give us useful information about the physical states of the disk.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

EVOLUTION OF SIZE DISTRIBUTION OF ICY GRAINS BY SUBLIMATION AND CONDENSATION

In the outer part of a protoplanetary disk, dust grains consist of silicate core covered by an ice mantle. A temporal heating event in the disk results in sublimation of the ice mantle. After the end of the heating event, as the temperature decreases, H{sub 2}O molecules recondense on the surface of the dust grain. Ultimately, the dust grain is covered by an ice mantle. Because the equilibrium vapor pressure on the grain surface decreases with the grain size, a large grain grows faster than a small grain. As a result, the size of an icy dust grain changes as a result of the heating event. The change in size also affects the mechanical properties of the dust aggregates formed by the icy grains. In this paper, we investigated the evolution of the size distribution of icy dust grains during sublimation and condensation. We found that the size evolution of icy grains can be divided into two stages. In the first stage, the icy grains grow through condensation of H{sub 2}O molecules. In the second stage, the size of grains changes further as H{sub 2}O molecules are transferred between icy grains while the surrounding gas condenses. The size distribution of the icy dust grains becomes bimodal, with a small number of relatively large grains and many small grains without an icy mantle. Possible effects of the size change on the evolution of icy dust aggregates are discussed.

36 MATERIALS SCIENCE↗