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11Accepted by The Astrophysical Journal LettersPreprint typeset using LATEX style emulateapj v. 08/13/06

DESTRUCTION OF MASSIVE FRAGMENTS IN PROTOSTELLAR DISKS AND CRYSTALLINE SILICATEPRODUCTION

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 andsubsequent destruction of massive fragments in young protostellar disks. The fragments form in theembedded phase of star formation via disk fragmentation at radial distances & 50−100 AU and annealsmall amorphous grains in their interior when the gas temperature exceeds the crystallization thresholdof ∼ 800 K. We demonstrate that fragments that form in the early embedded phase can be destroyedbefore they either form solid cores or vaporize dust grains, thus releasing the processed crystalline dustinto various radial distances from sub-AU to hundred-AU scales. Two possible mechanisms for thedestruction of fragments are the tidal disruption and photoevaporation as fragments migrate radiallyinward and approach the central star and also dispersal by tidal torques exerted by spiral arms. As aresult, most of the crystalline dust concentrates to the disk inner regions and spiral arms, which arethe likely sites of fragment destruction.

Subject headings: circumstellar matter — hydrodynamics — stars: protostars — stars: formation —accretion disks

1. INTRODUCTION

The embedded phase of low-mass star formation, start-ing from the formation of a disk and ending with theclearing of a parent cloud core, has recently drawn arenewed interest due to the possibility of planet forma-tion in this phase. Indeed, circumstellar disks are mostmassive in the embedded phase (Andrews & Williams2005; Vorobyov 2009a; Greaves & Rice 2010) and nu-merical hydrodynamics simulations indicate that, un-der certain conditions, embedded disks can fragmentand form either protoplanetary embryos or proto-brown dwarfs, especially in the disk outer regionswhere stellar irradiation and viscous heating are mer-ciful (e.g. Durisen et al. 2007; Stamatellos & Whitworth2009; Boley 2009; Machida et al. 2010; Vorobyov & Basu2010b; Cha & Nayakshin 2010).While disk fragmentation in the embedded phase seems

certainly feasible, the prospects for the survival of frag-ments and formation of gas giants or brown dwarfs on dis-tances of order tens or hundreds AU are gloomy. Grav-itational instability in the embedded phase is strong,fuelled with a continuing infall of gas from a parentcloud core, and resultant gravitational and tidal torquesare rampant. As a consequence, part of the fragmentsare dispersed by the tidal torques exerted by the spi-ral arms (Vorobyov & Basu 2010b; Boley et al. 2010).Others are quickly driven into the disk inner regions,and probably onto the star, due to the loss of angu-lar momentum caused by the gravitational interactionwith the trailing spiral arms (Vorobyov & Basu 2006,2010b; Cha & Nayakshin 2010). Only those fragmentsthat happen to form in the late embedded phase, whengravitational instability and associated torques are get-

1 Institute for Computational Astrophysics, Saint Mary’s Uni-versity, Halifax, B3H 3C3, Canada; vorobyov@ap.smu.ca.

2 Research Institute of Physics, Southern Federal University,Stachki 194, Rostov-on-Don, 344090, Russia.

3 Visiting Scientist, Department of Physics and Astronomy, TheUniversity of Western Ontario, London, ON N6A 3K7, Canada

ting weaker, may open a gap in the disk and mature intogas giants on wide orbits but the probability for sucha ”fortunate” outcome is rather low (Vorobyov & Basu2010b).Ironic as it may seem, but the destruction of fragments

(hereafter, planet/brown-dwarf embryos or simply em-bryos) may be as important for the disk and stellar evo-lution as their survival followed by massive giant planetor brown dwarf formation. Embryos that are driven intothe disk inner regions may form solid cores in their inte-rior via dust sedimentation or dense and compact atomichydrogen cores via dissociation of molecular hydrogen. Ifone or both of those processes take place before the em-bryo is destroyed on its approach to the central star, aplanet can emerge on orbit of order several AU or less(Nayakshin 2010a; Boley et al. 2010). If both processesfail, then the release of gravitational energy from the ac-creted embryo can trigger a luminosity outburst similarin magnitude those of FU Orionis or EX Lupi family(Vorobyov & Basu 2006, 2010b). In addition, short butintense bursts of accretion onto the star caused by theconsumption of embryos can lower the lithium abundancein young solar-type stars (Baraffe & Chabrier 2010), ex-plain the luminosity spread in H-R diagrams of 1-Myr-oldstar clusters (Baraffe et al. 2009) and resolve the long-standing luminosity problem (Dunham et al. 2010).On the other hand, embryos are sites of acceler-

ated dust growth and high-temperature processing (Boss1998; Boss et al. 2002; Boley et al. 2010; Nayakshin2010a,b) and their in situ destruction by tidal torquesmay release processed dust directly into the disk outerregions.Whichever mechanism of embryo destruction is real-

ized in nature, the consequences of this process are far-stretching. In this Letter, we report another interest-ing by-product of the embryo dispersal—the enrichmentof embedded circumstellar disks with crystalline silicatesformed in the depths of massive embryos via thermalannealing of amorphous dust grains. We use numeri-

2 Vorobyov

cal hydrodynamics simulations of the disk formation andlong-term evolution complemented with equations de-scribing the transformation of micron-sized amorphousdust grains into the silicate form. We show that partof the crystalline-silicate-bearing embryos are destroyedbefore they vaporize dust grains in their interiors or formsolid cores via dust sedimentation, thus enriching the gasdisk with crystalline silicates on radial distances fromsub-AU to hundred-AU scales.

2. SOURCES OF CRYSTALLINE SILICATES INCIRCUMSTELLAR DISKS

Circumstellar disks originate during the gravitationalcollapse of rotating prestellar cloud cores. The degreein crystallinity of silicates in prestellar cores is similarto that of the interstellar medium, which has an up-per limit of 0.2 ± 0.2% in the direction of the Galac-tic center (Kember et al. 2004). On the other hand, thecrystalline-silicate fraction in the inner regions of circum-stellar disks around young stellar objects (YSOs) canvary in wide limits from essentially none to almost 100%(Watson et al. 2009), implying in situ production of crys-talline silicates in at least some YSOs. Two mechanismsfor dust crystallization have been put forward.

1. Evaporation of the original, amorphous dust grainsfollowed by re-condensation under conditions ofhigh temperature and density (e.g. Grossman 1972)

2. Thermal annealing of the amorphous grains attemperatures (800–1300) K, somewhat below theirvaporization point, via viscous heating (e.g. Gail2001), shock wave heating (Harker & Desch 2002),or disk surface heating during EX-Lupi-like out-bursts (Abraham et al. 2009).

Both mechanisms are thought to work mostly in the inner1 AU from the star (except for shock heating that mayoperate at somewhat larger radial distances r . 10 AU)and some means of outward radial transport of crys-tallized dust is necessary to account for the non-zerocrystalline-silicate fraction in comets at distances of or-der tens of AU (e.g. Gail 2001; Bockelee-Morvan et al.2002; Ciesla 2007).

3. MODEL DESCRIPTION AND INITIAL CONDITIONS

Our numerical model is explained in detail inVorobyov & Basu (2010b). Here, we provide only a briefoverview and describe modifications done to the numer-ical code. We compute the gravitational collapse of ro-tating cloud cores in the thin-disk approximation andstart our simulations from the pre-stellar phase, advancethrough the disk formation and early evolution phase,and terminate with almost a complete clearing of the na-tal core. The following physical effects are taken into ac-count in our model: stellar irradiation, background irra-diation with temperature Tbg = 10 K, viscous and shockheating, radiative cooling from the disk surface, and diskself-gravity. Turbulent viscosity is parameterized usingthe usual α-prescription. A spatially and temporally con-stant α is set to 0.005.In the current version, we have implemented a sim-

ple mechanism describing the transformation of amor-phous dust grains into the crystalline form following the

guidelines described in Dullemond et al. (2006). We as-sume that dust is passively transported with gas andneglect the dust radial drift caused by the dust-gasdrag force. The latter simplification is of little con-sequence for the dynamics of dust grains with sizes. 10 µm on timescales of interest for the present pa-per, . 0.5 Myr (Takeuchi & Lin 2002). Therefore, ourresults are strictly applicable only to sufficiently smalldust grains showing sharp features in the 5–35 µm bandof the mid-infrared spectrum. In this simple scheme, twoadditional continuity equations for the surface density ofamorphous and crystalline silicates, Σa.s. and Σc.s., re-spectively, are

∂Σa.s.

∂t+∇p · (Σa.s.vp) = −S, (1)

∂Σc.s.

∂t+∇p · (Σc.s.vp) = +S, (2)

where vp = vrr+vφφ is the gas velocity in the disk planeand S = νcrΣa.s.. All dust grains in a collapsing cloudcore are initially amorphous, they crystallize at a rate νcrprovided by the Arrhenius formula

νcr[

s−1]

= 2× 1013 exp

(

−Tc

Tg

)

, (3)

where Tg is the gas midplane temperature, 2 × 1013

is the lattice vibrational frequency, and Tc=38100 K(Bockelee-Morvan et al. 2002). We assume that dust andgas are thermalized. The initial gas and dust radial sur-face density profiles and angular velocities are given byequations (12) and (13) in Vorobyov & Basu (2010b) andthe initial dust-to-gas ratio is 0.01. The initial core massisMcore = 0.78M⊙ and the ratio of rotational to gravita-tional energy of the core is β = 8.8×10−3. For simplicity,we also assume that all dust is made of silicate grains.A solution of the time-dependent part of Equation 2

(excluding advection terms) demonstrates that it takesabout 40 yr to completely transform amorphous dustinto the crystalline form at Tg = 800 K. The corre-sponding timescale for Tg = 900 K is 0.1 yr, while forTg =700 K the crystallization timescale is 20000 yr. Ob-viously, the latter value is much longer than the typ-ical orbital period and crystallization temperatures ofTcr = 800 − 900 K are most relevant to circumstellardisks. Laboratory experiments tend to yield even higherTcr & 1000 K (Hallenbeck et al. 2000), possibly due tothe same timescale arguments.If temperature exceeds the evaporation threshold for

dust grains Tevap ≈ 1400 K, we set both Σc.s. and Σa.s. tozero in the corresponding computational cell. The exactvalue of Tevap is density dependent and is calculated fromthe opacity tables of Bell & Lin (1994).Equations (1) and (2) are solved simultaneously with

equations of hydrodynamics describing the formationand evolution of circumstellar disks (eqs (1)–(3) inVorobyov & Basu 2010b). We employ the method of fi-nite differences with a time-explicit, operator-split solu-tion procedure in polar coordinates (r, φ) on a numericalgrid with 512 × 512 grid zones. The advection part ofEquations (1) and (2) (i.e., with S set to zero) is solvedusing a piece-wise parabolic advection scheme. The timeupdate of Σa.s. and Σc.s. due to the source/sink term S isdone using an (unconditionally stable) backward differ-ence scheme supplemented with a subcycling procedure

Crystalline silicate production 3

to guarantee accuracy, wherein the change in both Σa.s.

and Σc.s. over one global hydrodynamical timestep is lim-ited to 10%. If this condition is violated, local subcyclingwith smaller timesteps is invoked until the desired accu-racy is reached.The radial points in our numerical grid are logarith-

mically spaced. The innermost grid point is located atthe position of the sink cell rsc = 6 AU and the size ofthe first adjacent cell is 0.08 AU. This corresponds to theradial resolution of △r=1.3 AU at 100 AU. We imposea free outflow boundary condition so that the matter isallowed to freely flow through the sink cell to form acentral star plus some dynamically inactive inner region.

4. RESULTS

The top row in Figure 1 presents the gas surface den-sity in the inner several hundred AU at three distinctevolution times since the formation of the central star.The middle and bottom rows show the correspondinggas midplane temperature and crystalline silicate frac-tion ξc.s. = Mc.s./(Mc.s. + Ma.s.), respectively, whereMc.s and Ma.s. are crystalline and amorphous silicatemasses. The red circle in the coordinate center repre-sents schematically the central star plus sink cell. Thethree time snapshots in Figure 1 are chosen specificallyto illustrate disk fragmentation and embryo formation(red dots at 50–100 AU). We note that each snapshotshows in fact different embryos—their inward migrationand/or tidal destruction timescales are of order severalorbital periods (Torb = 700 yr for M∗ = 0.25 M⊙,r = 50 AU, t = 0.074 Myr and Torb = 1600 yr forM∗ = 0.4, r = 100 AU, t = 0.178 Myr), which are con-siderably shorter than the time span between the images(∼ 5× 104 yr).We find that the gas temperature Tg in the interiors

of massive embryos can exceed 800 K (see middle row inFigure 1), necessary for the thermal annealing of amor-phous dust grains to commence. The prospects for diskenrichment with crystalline silicates stored in these em-bryos will depend on characteristic timescales for inwardmigration and/or tidal destruction of embryos (τdest),dust sedimentation and solid core formation in the em-bryo interiors (τsed), and dust vaporization at Tg > Tevap

(τevap). If τdest is smaller than both τsed and τevap, thenall processed dust will be released into the disk at variousradial distances, depending on which destruction mecha-nism prevails. As current numerical simulations indicate,embryos may be destroyed by tidal torques from spiralarms, preferentially releasing the crystalline silicates tolarge radial distances where these embryos form. Al-ternatively, embryos may be photoevaporated and tornapart by stellar irradiation and tidal torques as they mi-grate radially inward and approach the central star. Inthis case, part of the processed dust will be brought intothe disk inner few AU (through the sink cell) and prob-ably onto the star and part will be pushed to larger diskradii during a transient episode of disk expansion (causedby the conservation of angular momentum) following theembryo tidal disruption. It is thus feasible to depositcrystalline silicates to various orbital distances startingfrom sub-AU scales and up to several hundred AU, ac-counting for the crystalline silicate features observed inthe spectra of the Solar system comets. This process ofcrystalline silicate enrichment is illustrated in the bot-

tom row of Figure 1—there is a notable increase in ξc.s.with time. Crystalline silicates concentrate in the diskinner regions and at/near spiral arms, which are likelysites of embryo formation and destruction. This impliesthat the abundance of crystalline silicates may increasewith radius, at least in the early disk evolution, if mostof the embryos are tidally destroyed in the disk outer re-gions rather than driven into the star. If such an increaseis observationally confirmed, it could become a hallmarkfor the proposed process.On the other hand, if τdest greater than either τsed or

τevap, then most of the processed crystalline dust willbe either locked up in solid terrestrial-like cores or va-porized. The latter mechanism is implemented in thecurrent numerical model, while the effect of the formeris discussed in more detail later in the text.To better illustrate the process of disk enrichment

with crystalline silicates, Figure 2 presents various modelcharacteristics as a function of time. In particular, thecrystalline silicate fraction ξc.s. and amorphous silicatefraction ξa.s. = Ma.s./(Mc.s. +Ma.s.) are plotted in pan-els A and B, respectively. More specifically, black, green,and blue lines depict the corresponding fractions in thedisk (ξdiskc.s. and ξdiska.s. ), envelope (ξenvc.s. and ξenva.s.), and sinkcell (ξscc.s. and ξsca.s.), respectively. We distinguish betweenthe disk and envelope using a scheme based on the typ-ical transitional gas surface density and radial gas ve-locity field explained in detail in Vorobyov (2010). Wenote that ξdiskc.s. and ξdiska.s. are in fact crystalline and amor-phous silicate fractions stored in both the disk and theembryos. Panel C shows the crystalline silicate fractionin the disk (black line) and maximum midplane gas tem-perature Tmax

g (red line), whereas panel D presents the

mass accretion rate onto the star M (red line) and thecrystalline silicate fraction in the disk (black line).There are seven episodes of crystalline silicate produc-

tion in the disk manifested by a sharp increase in ξdiskc.s. ,all associated with the formation of embryos massive andhot enough to crystallize dust in their interior. Episodes4, 6, and 7 (from left to right) correspond to the for-mation of embryos shown in the left, middle, and rightcolumns of Figure 1. From panel C it is evident thatξdiskc.s. increases sharply each time the maximum gas tem-perature Tmax

g exceeds the crystallization temperatureTcr ≈ 800 K (horizontal dash-dotted line). After eachsuch episode, prolonged periods of gradual decline in ξdiskc.s.follow, which are caused by dilution of the disk materialwith pristine amorphous dust accreted onto the disk fromthe infalling envelope.In the last two episodes, Tmax

g goes above the dustevaporation temperature Tevap and this leads to an im-mediate sharp drop in ξdiskc.s. . This exemplifies cases withτevap < τdest. The dust evaporation timescale can beapproximated (excluding factors of unity) as (Nayakshin2010a)

τevap = 1.5× 104(

Memb

10MJ

)−2

yr. (4)

For the typical embryo masses of Memb=5–20 MJ, thecorresponding τevap lies in the 4000–60000 yr range. Infact, this is a lower estimate simply because embryos mayexperience several contraction and expansion episodesbefore actually reaching Tevap. Embryos that form in the

4 Vorobyov

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-2.5

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-2

-1.75

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-1

-0.75

-0.5

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0

midplane gas temperature

crystalline silicate fraction

Fig. 1.— Gas surface density (g cm−2, top row), gas midplane temperature (Kelvin, middle row), and crystalline silicate fraction (bottomrow) at three times since the formation of the central star: t = 0.074 Myr (left column), t = 0.132 Myr (middle column), and t = 0.178 Myr(right column).

early disk evolution are of lower mass and closer to thestar than those that form later in the embedded phase(because disk grows in mass and size with time). Asa consequence, first embryos take longer time to evap-orate dust and shorter time to migrate into the star,an effect found in our numerical simulations and alsonoted by Cha & Nayakshin (2010). For these first em-bryos, migration timescales are just several orbital peri-ods (Torb=700–1600 yr) and are often shorter than τevap.As time passes and more massive embryos on wider or-bits start to form, the migration/destruction time scalemay exceed that of dust evaporation, as indeed occurredduring the last two episodes of crystalline dust produc-tion.Migration of embryos into the disk inner regions and

through the sink cell, as manifested by strong (& 5 ×

10−5 M⊙ yr−1) mass accretion bursts, also contributesto the decrease in ξdiskc.s. but leads to an increase in ξscc.s..Note that episodes 3 and 4 are not associated with strongmass accretion bursts, indicating that the correspondingembryos are dispersed by tidal torques exerted by spiralarms, before they actually fall through the sink cell ontothe star. The process of disk fragmentation diminishesafter t ≈ 0.2 Myr, no embryos survive beyond this time,and the subsequent evolution shows a gradual decline inξdiskc.s. . From this moment on, ξdiskc.s. represents the crys-talline silicate fraction in the disk only.We do not take into account a possible formation of

solid cores (and associated reduction in disk enrichmentwith crystalline dust) but we can estimate its efficiencybased on the work of Nayakshin (2010a). For Memb =3−10MJ, Nayakshin found τsed ≈ (4−6)×103 yr. This is

Crystalline silicate production 5

Time (Myr)0.0 0.1 0.2 0.3 0.4

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C Dmaximum temperaturecrystalline silicate fraction

accretion rate onto the starcrystalline silicate fraction

Fig. 2.— Crystalline (panel A) and amorphous (panel B) silicate fractions in the disk (black), envelope (green), and star+sink cell(blue) as a function of time passed since the formation of the central star. Panel C shows the maximum temperature in the disk (red) andcrystalline silicate fraction in the disk (black), while panel D also shows the mass accretion rate onto the star (red).

comparable to or less than τevap & (4−16)×103 yr, whichimplies that solid cores may form before dust is vapor-ized. At the same time, τsed is comparable to or longerthan τdest = a few × Torb ≈ a few × 103 yr, certainlyfor those embryos that form first in the early embed-ded phase and are characterized by shortest migrationtimescales. This simple timescale analysis suggests thatthe solid core formation is feasible and may reduce theefficiency of crystalline dust enrichment but is unlikelyto shut down the proposed mechanism completely. Thelatest numerical hydrodynamics simulations seem to con-firm that the solid core formation is not expected to workfor every embryo in the disk (Cha & Nayakshin 2010).

5. SUMMARY

Thermal annealing of amorphous dust grains in the hotinteriors of massive fragments (or planet/brown dwarfembryos) forming in protostellar disks during the earlyembedded stages of stellar evolution, followed by subse-quent dispersal of the fragments, is a promising gatewayfor the production of crystalline silicates. This mech-anism can release processed dust to various radial dis-tances from (sub-)AU scales, if fragments are destroyedon their approach to the central star, to hundred-AUscales, if they are dispersed by tidal torques exerted byspiral arms. More studies, including the effect of dustgrowth and solid core formation, are needed to furtherexplore the efficiency of this mechanism.

We have run another eight models with β = (3.2−12)×10−3 and Mcore = 0.3− 1.25 M⊙. The net result is thatthe dust processing is correlated with disk fragmentationand models that do not form embryos (e.g., models withlow Mcore and β and consequently with disks of low massand size) show little crystalline silicates, reinforcing ourconclusions.We stress that our proposed mechanism can coexist

with other crystallization mechanisms, localized to theinner few AU, and complements them by providing adirect source of crystalline silicates at large distances.Some outward transport may still takes place and ac-count for the fact that comet Wild 2 has crystalline sil-icates with the chemical and isotopic composition simi-lar to that of the chondritic meteorites originated in theterrestrial planet region (McKeegan et al. 2006). Con-versely, chondritic meteorites may have formed in theatmospheres of protoplanetary embryos via dust sedi-mentation and released into the inner few AU when theembryos were dispersed by tidal torques near the youngProtosun. The apparent presence of refractory CalciumAluminum Inclusions in the cometary material does notinvalidate this scenario since temperatures in at leastsome of the embryos can exceed 1300 K (panel C in Fig-ure 2). We do not take into account possible opacitydependence on the composition and properties of dustgrains due to the complexity of physics involved. Nev-ertheless, dust growth and crystallization are likely to

6 Vorobyov

decrease opacities (Mennella et al. 1998; D’Alessio et al.2001), thus enhancing disk fragmentation and crystallinesilicate production.

The author is grateful to the anonymous referee forvery useful comments and to Prof. Shantanu Basu

for hospitality. Support from an ACEnet Fellowshipis gratefully acknowledged. Numerical simulations weredone on the Atlantic Computational Excellence Network(ACEnet). This project was also supported by RFBRgrant 10-02-00278 and by the Ministry of Educationgrant RNP 2.1.1/1937.

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