Preplanetary scavengers: Growing tall in dust collisions
Thorsten Meisner, Gerhard Wurm, Jens Teiser, Mathias Schywek
AAstronomy & Astrophysics manuscript no. PreplanetaryScavengers c (cid:13)
ESO 2018October 17, 2018
Preplanetary scavengers: Growing tall in dust collisions
Thorsten Meisner , Gerhard Wurm , Jens Teiser , and Mathias Schywek Faculty of physics, University of Duisburg-Essen, Lotharstr. 1, D-47057 Duisburge-mail: [email protected]
Received ; accepted
ABSTRACT
Dust collisions in protoplanetary disks are one means to grow planetesimals, but the destructive or constructive nature of high speedcollisions is still unsettled. In laboratory experiments, we study the self-consistent evolution of a target upon continuous impactsof submm dust aggregates at collision velocities of up to 71 m / s. Earlier studies analyzed individual collisions, which were morespeculative for high velocities and low projectile masses. Here, we confirm earlier findings that high speed collisions result in massgain of the target. We also quantify the accretion e ffi ciency for the used SiO (quartz) dust sample. For two di ff erent average massesof dust aggregates (0.29 µ g and 2.67 µ g) accretion e ffi ciencies are decreasing with velocity from 58% to 18% and from 25% to 7%at 27 m / s to 71 m / s, respectively. The accretion e ffi ciency decreases approximately as logarithmic with impact energy. At the impactvelocity of 49 m / s the target acquires a volume filling factor of 38%. These data extend earlier work that pointed to the filling factorleveling o ff at 8 m / s to a value of 33%. Our results imply that high speed collisions are an important mode of particle evolution. Itespecially allows existing large bodies to grow further by scavenging smaller aggregates with high e ffi ciency. Key words.
Methods: laboratory – Protoplanetary disks – Planets and satellites: formation
1. Introduction
Particle evolution in protoplanetary disks has seen significantprogress over the last few decades with a number of turns indi ff erent directions.Astronomical observations of disks in the visible and near-infrared provide information of dust properties at the surfaceof disks, which shows amorphous or crystalline dust particlesof micron size (van Boekel et al. 2005; Olofsson et al. 2009).Aggregation, the change of particle size by sticking collisions,is visible in such observations if submicron grains are assumedto be the building blocks. These aggregates are still small withrespect to planet formation and it is important to note that smallparticles are observed over the whole lifetime of protoplanetarydisks of a few million years. To understand this it is necessary tostudy collisional evolution. It is not necessarily only “positive”aggregation, but it is also the destruction of larger bodies in col-lisions that might provide the small grains (Wurm et al. 2005;Teiser & Wurm 2009b; Beitz et al. 2011; Schr¨apler & Blum2011).The experiments in this paper also clearly have this destruc-tive element and in fact, Dullemond & Dominik (2005) showedthat aggregation without fragmentation would be so e ffi cientthat no small grains would remain observable after a short time.Besides collisional fragmentation other destructive mechanismsare thinkable. These include gas drag (erosion by wind) as dis-cussed by Paraskov et al. (2006) or particle erosion by stellarinsolation (Wurm & Krauss 2006; Kelling & Wurm 2009; deBeule et al. 2013; Kocifaj et al. 2010). It has also been suggestedthat the e ff ect of aggregation is diminished by electrical chargingand repulsion of aggregates (Okuzumi 2009).In any case, the initial mode of particle evolution likely startsfrom submicron or micron size particles and is the aggregationby hit-and-stick collisions. Much work has been carried out inthis field. As far as astrophysical applications are considered, aggregation has been studied numerically (see, e.g., Ossenkopf(1993); Dominik & Tielens (1997); Paszun & Dominik (2009);Wada et al. (2009) or Suyama et al. (2008), and this list is farfrom complete). It has also been studied experimentally. Cluster-Cluster aggregation by Brownian motion has been found inmicrogravity experiments (Blum & Wurm 2000; Krause et al.2011) and further experiments have studied aggregation of suchaggregates (Wurm & Blum 1998; Blum & Wurm 2000). Thegrowth of aggregates in a turbulent cloud still marks special re-gions of space as enigmatic regarding the formation of smallaggregates. The core shine in interstellar clouds discovered re-cently might be one example (Steinacker2010).Within cold environments especially with water ice, a mostabundant solid, sublimation, condensation, and sintering areother mechanisms to be considered that can change the initialaggregates (Saito & Sirono 2011; Sirono et al. 2006; Aumatell& Wurm 2011; Ros & Johansen 2013; Tanaka et al. 2013). Hightemperature equivalents of sintering might be found very closeto a star (Sirono 2011; Poppe et al. 2010). The presence of agranular medium or more solid impactors, for example, sinteredtogether, might change the overall picture as well (Colwell et al.2008).Besides the observable small particle size scale, the nextsize steps are currently of critical importance in understandingplanet formation. After initial fractal growth, the compactionof dust aggregates follows as energies in collisions get largeenough that particles can restructure. This also occurs in numer-ical simulations as well as experiments (Meakin & Donn 1988;Dominik & Tielens 1997; Wada et al. 2011; Blum & Wurm2000). Depending on the details of particle size and contactphysics, from mm or cm upward, particles are no longer frac-tal but compact with a porosity or volume filling factor subjectto further evolution. This is also a subject of this paper.Volume filling factor and porosity are complementary, butdescribe the same thing and are both used randomly thoughout a r X i v : . [ a s t r o - ph . E P ] N ov horsten Meisner et al.: Preplanetary scavengers: Growing tall in dust collisions the literature. We note this here to prevent confusion. The vol-ume filling factor FF is defined as FF = V solid V total , (1)where V solid is the volume in an aggregate covered by solidsand V total is the total volume of the aggregate. Porosity refersto the void space instead of the solid space covered and there-fore is 1 − FF . To connect to earlier work, we will use thefilling factor when referring to quantitative values here. Wheninitial restructuring occurs aggregates can have very low fillingfactors of FF << . ff erent porosities lead to very di ff er-ent results (sticking, bouncing, fragmentation) as described byLangkowski et al. (2008); Wurm et al. (2005); Meisner et al.(2012); Blum et al. (2006); Schr¨apler et al. (2012); Meru et al.(2013); Geretshauser et al. (2011); Sch¨afer et al. (2007).In principle, the filling factor can span a large range of be-tween 0 and 1. It seems to be restricted, however, if it is estab-lished by collisions. Teiser et al. (2011b) and earlier work useddust targets prepared manually and in those studies 33 % ± ff . Meru et al. (2013) find in numerical simulations that a fillingfactor of 37 % sets a boundary in numerical simulations of col-lisions between 1 and 27.5 m / s in velocity. Much higher fillingfactors can be produced only using omnidirectional compressionin the laboratory (G¨uttler et al. 2009; Meisner et al. 2012) orin numerical simulations (Seizinger et al. 2012). The questionremains open if there are typical porosities for bodies in proto-planetary disks evolving through collisions, and this is one partof this paper.A few experiments at moderate collision velocities exist. Inthe experiments by Kothe et al. (2010), the resulting filling factorreaches up to 40 % at 6 m / s as projectiles always hit the samespot. A lower value of about 30 to 33 % results in Teiser et al.(2011a) and Meisner et al. (2012). A thick layer of dust is grownwith random impact sites in those experiments. The experimentsreported here extend these two latter works.Porosity is important in collisions as it determines thestrength of a dust aggregate and its ability to dissipate energy.In low porosity aggregates particles stick together more rigidly.If the energy of a collision is not su ffi cient to break contact, thecollision will be elastic and will result in bouncing. Bouncingis supposedly the dominant outcome of collisions under proto-planetary disk conditions once compact aggregates of mm to cmin size have formed (Blum & Wurm 2008). As bouncing pre-vents further aggregate growth, Zsom et al. (2010) called this thebouncing barrier. Even if compact aggregates stick to each otherthe contacts are very weak and the forming aggregates might bedestroyed again (Jankowski et al. 2012). Recent experiments onlong-term observations of a particle system show that the bounc-ing barrier in a system of mm aggregates is a very robust result(Kelling et al. 2013).However, if one of the collisional partners is large enough,collision velocities increase and growth is possible again. Wurmet al. (2005), Teiser & Wurm (2009b), and Teiser et al. (2011b)carried out collision experiments and showed that a large dusty body in a collision with a submm to mm aggregate gains mass.Teiser & Wurm (2009b) sketch a model where larger bodiesgrow at the expense of small particles. Windmark et al. (2012a)carried out numerical simulations and found that growth is pos-sible if a larger seed is introduced into the system. In anotherwork, Windmark et al. (2012b) as well as Garaud et al. (2013)argue that the velocity distribution in a turbulent disk might pro-vide a few seeds by chance if some particles collide at very lowspeeds. Jankowski et al. (2012) speculate that aggregates con-sisting of larger grains (by chance) might also provide seeds forfurther growth.In this work, we aim to provide quantitative data to supple-ment numerical models like those in Windmark et al. (2012a),as we measured the accretion e ffi ciencies in “high speed” dustcollisions for the first time.There is an alternative model to sticking collisions for plan-etesimal formation based on gravitational instabilities. The basicideas go back to Goldreich & Ward (1973) and Safronov (1969).A dense dust subdisk forms that eventually collapses due to itsown gravity. Weidenschilling et al. (1989) found that the shearbetween the dense midplane and upper layers would create tur-bulence that would disperse the particles again and lower thedensity. However, numerical modeling of particle motion in tur-bulent disks in recent years show that turbulence might actuallybe beneficial to enhance particle densities. Gravitoturbulenceand streaming instabilities or density enhancements in pressuremaxima or eddies produced otherwise are currently consideredone way to jump from cm or dm size to planetesimals without thehassle of sticking or bouncing collisions (Johansen et al. 2007;Klahr & Lin 2005; Dittrich et al. 2013; Cuzzi et al. 2003; Youdin& Johansen 2007; Chiang & Youdin 2010).If the needed initial particle size behind this model coincideswith the aggregate size at the bouncing barrier, this would be anice connection between the two mechanisms. If the bouncingbarrier is at mm size and instabilities need larger particles, theremight still be a need to overcome the bouncing barrier in whichcase collisional growth would eventually be able to proceed aswell (Windmark et al. 2012a). In any case, collisions in the densecluster of particles will also occur in these models. At the typicalcollision velocities of tens of m / s these collisions will definitlybe destructive and lead to fragmentation into smaller particlesagain (Schr¨apler et al. 2012; Deckers & Teiser 2013). The scav-enging of fragments by other bodies is eventually of importancein this model as well.Here, we report on the first experiments with a novel setupthat allow a target to grow by a large number of successive col-lisions with small dust aggregates. In particular, we quantify anaccretion e ffi ciency at high velocity for the first time and providea measure of the porosity evolution of large growing bodies.
2. Experiment basics
To study collisions of dust grains with velocities up to 71 m / s,we use a centrifuge, which accelerates submm dust grains in avacuum chamber. We were able to analyze the small dust ag-glomerates and their behavior concerning collisions with targetsusing a high speed camera. Larger and denser dust agglomeratescould be produced by the impinging dust particles. The basic element of the setup is the fast rotation of a meshed,hollow cylinder (a centrifuge), placed into a vacuum chamber (Fig. 1). Di ff erent rotational velocities are realized by using afrequency converter for the engine. The centrifuge itself is de-signed with a narrow, hollow channel at its outer radius. A fine- Fig. 1.
A centrifuge rotates inside of a vacuum chamber. Dust isinjected at points A or B in a sequence of filling a dust reservoirand opening a valve which sucks in the dust into the centrifuge.Dust aggregates of certain size leave the mesh of the centrifugetangentially and hit impact areas at the inner surface of the cham-ber.meshed netting wire (mesh size: 500 µ m) is placed at the out-side of the centrifuge. We injected dust into the centrifuge in asequence of filling a dust reservoir at the outside of the cham-ber, which is sucked into the centrifuge if a valve is opened.The pressure within the chamber is kept between P =
30 Pa and80 Pa. The dust enters the centrifuge and part of it moves to-ward the mesh where it is tangentially launched toward the innersurface of the vacuum chamber (Fig. 1). At di ff erent positionswindows or targets can be placed to observe the impacts with acamera at up to 8443 frames / s. We denote the launch directionas z-axis. The target layer is described by an x-y-plane perpen-dicular to the z-axis. The y-direction is the line of sight of thecamera. Depending on the experiment and details to be studied,we use an observation with continous illumination, flash lamps,and a post-experiment analysis of the target with respect to massand volume (filling factor). Our dust material is quartz dust withparticle sizes ranging from 0.1 µ m to 10 µ m (80% are in a rangebetween 1 µ m and 5 µ m). This quartz dust was used in severalprevious experiments (Teiser & Wurm (2009a,b); Meisner et al. (2012); Beitz et al. (2011)). We assume a volume filling factorof 0.32 for the launched dust aggregates. This value is typicalfor locally-compressed dust agglomerates (Teiser et al. (2011a);Meisner et al. (2012)). However, in this context, the value of thevolume filling factor is uncertain and cannot be further quanti-fied. During the experiments an accumulation of dust could be tracedon the inner surface of the vacuum chamber at a maximum of135 ◦ away from the injection point along the direction of ro-tation. As impacts and impacting particles have di ff erent veloc-ity regimes, we determined the impact velocity for a free-flyingdust particle first. This allows us to set the collision velocity andis correlated to the frequency of the engine converter.. As wecannot trace every incoming dust aggregate, we consider thesecalibrated values to be impact velocities.We used two flash lamps for a double exposure of dust vol-leys from the injection. The time delay between the two pulsesvaried between 60 µ s - 200 µ s. Fig. 2 shows an example of this.By measuring the lengths between the same features and given Fig. 2.
Double exposure image of dust particles launched by thecentrifuge. Measuring the lengths between two similar featuresat a known delay time gives the velocity of the particles. Thedirection to the centrifuge is top-left.a predetermined time delay of the flash lamps we get the (col-lision) velocities of the dust aggregates for di ff erent engine fre-quencies. In Fig. 3 our measured velocities are plotted against the rotation frequency of the centrifuge as well as the converterfrequency of the engine. The dust is expelled from the centrifuge Fig. 3.
Particle velocities follow a linear dependence on en-gine / centrifuge frequency.only for frequencies larger than 8 Hz and the linear fit is o ff set,but not crossing the origin. Otherwise, as expected, there is alinear increase in measured velocities v in [m / s] of the launcheddust with frequency f of the centrifuge given as: v ( f ) = .
65 [m] · f − .
64 [m / s] . (2)This dependency is used to calculate a collision velocity for apreset converter frequency, which is accurate to about 1 m / s. To determine the particle size and mass of particles producedby the centrifuge, we imaged particles in higher resolution. Forthe analysis at engine frequencies of 15 Hz, 30 Hz, and 50 Hz(12.0 m / s, 27.1 m / s, and 48.7 m / s respectively), we counted be-tween 2400 and 7800 particles. A typical image before and afterprocessing (binary image) is seen in Fig. 4. The binary imagesonly contain information about particles that are located in thefocal plane. We set the black / white level of the binary imagesmanually. Based on the two-dimensional images, we calculated Fig. 4.
Example of a bright field image of dust launched fromthe centrifuge (left). After processing we use the binary image(right) for further analysis.the radius of an equivalent cross-section sphere for a particle.We multiplied the volume with a density of 2.6 g / cm and a vol-ume filling factor, so as to get the particle mass. We assumed a volume filling factor of 0 .
32 for the dust particle which is typicalfor locally compressed dust agglomerates (Meisner et al. 2012;Teiser et al. 2011a). For small particles, we reach the resolu-tion limit of the optical system. At very large sizes only fewaggregates exist. In between these sizes, the data follow a powerlaw. All distributions are roughly proportional to m − / . A sys-tematic change of the distributions with velocity cannot be seen.Hence, the mass distributions at velocities of 12.0 m / s, 27.1 m / sand 48.7 m / s are added to one total distribution in Fig. 5. The to- Fig. 5.
Mass distribution of dust launched by the centrifugethrough meshes with a size of 500 µ m at the ejection velocities of12.0 m / s, 27.1 m / s, and 48.7 m / s. Because the mass distributiondoes not depend on the ejection velocity all data are combinedinto one total distribution. The mass distribution decreases to thepower of 1.60 and the mean value of the launched masses is lo-cated at 0.29 µ g.tal distribution is proportional to m − . . The average value for theparticle mass is 0.29 µ g. This corresponds to an average particleradius of 43.4 µ m. We also carried out a similar set of experi-ments, but with larger mesh size of the centrifuge. This producedlarger impacting aggregates with an average mass of 2.67 µ g (av-erage particle radius of 91.5 µ m), approximately ten times moremassive. A systemic change of the distributions with velocitycannot be seen. In Fig. 6, the mass distributions at velocities of27.1 m / s, 48.7 m / s, and 71.2 m / s are added to one total distribu-tion. It is proportional to m − . .
3. Impact experiments
With the means to generate a beam of small aggregates at di ff er-ent velocities with a typical mass of 0.3 mg at a size of about 45 µ m, we carried out impact experiments. We placed targets at dif-ferent positions at the inner wall of the vacuum chamber wherethey are continuously hit by dust aggregates. A round plastic disk was placed as a target at the bottom of thetarget zone in Fig. 1. Dust accumulates on the target due to di-rect sticking and reaccretion of ejecta by gravity. The influenceof reaccretion is studied on targets further up in the target zonewhere gravity does not return ejecta. This is described later inthis article. Here, we study the ejection process of fragments af-ter an impact onto an accumulated dust bed. We recorded the
Fig. 6.
Mass distribution of dust launched by the centrifuge at theejection velocities of 27.1 m / s, 48.7 m / s and 71.2 m / s. The massdistribution decreases to the power of 2.34 and the mean valueof the launched masses is located at 2.67 µ g.trajectories of single fragments with a high-speed camera at2036 frames / s. A typical impact scenario with marked fragmentsis shown in Fig. 7.For bouncing collisions, the energy loss can be quantifiedby the ratio between the velocity after and before bouncing.Similarly, the ejecta can also be characterized by a coe ffi cientof restitution, which we define here as C R = v f v c (3)with collision velocity v c and ejecta velocity v f . As can be seenin Fig. 7, the dust target is placed almost perpendicular (up to7 ◦ ) to the impinging dust particles on the target. To a good ap-proximation the x-component of the collision velocity can beneglected. The fragment velocity v f can be calculated as v f = (cid:113) v x + v y + v z = (cid:113) · v x + v z (4)In this case, the z-direction coincides with the vertical directionand v x and v y are the horizontal velocities and v z is the verticalejecta velocity with respect to the target surface. Since we onlyuse one camera, v y is unknown. We assume that it is independentof, but on the same order as, v x .The horizontal velocity v x is easy to deduce from the imagesas it does not change with time. In vertical direction, gravity hasto be considered acting with acceleration g = / s and thevelocity is given as v z = ∆ z − g ∆ t ∆ t . (5)We determined fragment velocities for 27.1 m / s and 48.7 m / scollision velocities. In total, we analyzed 56 and 58 fragmentvelocities, respectively, in this work and they are illustrated infigures 8 and 9.At 27.9 m / s the average horizontal velocity and the standarddeviation are v x = ± / s and vertical ejecta veloci-ties are v z = ± / s. At 49.5 m / s the average valuesare v x = ± / s and v z = ± / s.We used these values to calculate a coe ffi cient of restitution.We compare the values to measurements by Teiser et al. (2011a) Fig. 7.
Aggregate impact at 27.1 m / s. The frame rate was setto 2036 frames / s. The impacting projectile is a stretched trailcaused by an exposure time of 55 µ s. As an example of ejectathe positions of two fragments (1 and 2) are marked on subse-quent images.at lower collision velocities on particles of the same composi-tion. Those aggregates were somewhat larger (250 µ m in diame-ter). This is shown in Fig. 10. The data can be well approximatedby a power law within the range of data C ( v c ) = . · v c − / . (6)We do not attempt to motivate this power law here but only takeit as one of the most simple analytic expressions that fits the data Fig. 8.
Ejecta velocities for collision velocity v c = ± / s Fig. 9.
Ejecta velocities for collision velocity v c = ± / s. Fig. 10.
Coe ffi cients of restituion for ejecta of a SiO aggregateimpacts. The dashed line is a power law of C ( v c ) = . · v − / c between 1 m / s and 50 m / s. As long as we use submmsize dustprojectiles, the fragment velocity in relation to the velocity of theprojectiles fits this analytic expression very well, independentfrom variations in particle sizes.There have to be deviations to very small and very large ve-locities. At low velocity, the coe ffi cient of restitution cannot belarger than 1. At high velocity is is likely that C levels o ff once the aggregate is completely fragmenting to individual grains andno more energy can be dissipated by breaking contacts. As illustrated in Fig. 11, dust projectiles impact targets in threedi ff erent settings. Fig. 11.
1. Target configuration: dust projectiles enter a smallaperture within a tube and impact onto a thin bar. 2. Target con-figuration: dust projectiles impact an inclined metal plate abovethe centrifuge directly (no reaccretion due to gravity) 3. Targetconfiguration: in a first step (a), the local mass distribution isprobed by measuring the masses inside neighboring tubes, whichcollect all of the dust. In a second step (b), the mass of an aggre-gate grown on an exposed target is measured with calibrationtubes collecting dust at the same time.
1. Small target:
In a first setup of a target the goal was todetect growth or erosion of a target in individual collisions. Toprevent particles from returning by gravity, the target is placedhigher than the centrifuge at an incline. Injection of dust isplaced in position B in Fig. 1. Every nonsticking particle doesnot return to the target. As our first target, we chose a 2 mmmetal bar, which was mounted inside a tube (Fig. 11.1). Dustprojectiles entered the tube only through an aperture slightlylarger than the target. Otherwise, the tube shielded the target from opaque and unfocused “dust storms”, which makes it im-possible to observe single collisions on the edge of the bar. Weset the frame rate to 8443 frames / s. In the bright-field image (Fig.12), we could identify the direct addition of mass at the bar‘sedge as well as removal of dust. After the experiment, a small Fig. 12.
On the left is an example of simoultaneous mass accre-tion and erosion. As can be compared in the highlighted framesbefore and after an impact of a fast dust particle (v = / s)225 µ m in diameter, the small hill on top is lost. At the sametime, a new small hill is built up again where the particle im-pacted the target. On the right is an example for mass accretion.After a multiple impact of dust particles < µ m in diameter(v = / s), new small hills are built up.steep dust crest was created on the target. The importance ofthese experiments is as follows. Without exact number densities,which are hard to observe, and without at least simple model-ing, we cannot rule out a priori that ejected particles are nothit by later projectiles while airborne. Such secondary collisionsclose to the target might lead to follow-up collisions at di ff erentspeeds, which would spoil the analysis of the experiment. Wesee only very few such secondary collisions and they cannot berelated to target growth. Therefore, this part of the impact exper-iments show that the densities in the experiments are su ffi cientlylow that impacts can be regarded as individual events.
2. Large targets
With the knowledge that there is insignif-icant interaction between the ejecta cloud and the projectilecloud, larger targets can be grown to analyze the volume fill-ing factor of the forming aggregates. Instead of the tube with thethin bar, we now only place a free metal plate into the path ofthe projectiles (Fig. 11.2). As in the setup before the target wasplaced higher than the centrifuge to prevent reaccretion. We useda velocity of about 50 m / s here and produced two grown dust ag-gregates. The plate with the grown dust was carefully removedfrom the vacuum chamber after growing for some time. The dustaggregates had sizes of about 3 cm in length and 0.6 cm in heightas can be seen in Fig. 13.To determine the volume filling factor, mass and volumehave to be known. The mass is easily measurable to high accu-racy. The volume was determined with a new procedure. By il-luminating the agglomerate from above and shadowing a part ofthe target we could image the projected cross-sections along theterminator. Within the illuminated cross-sections, pixels werecounted and were calculated into an area. The terminator wasmoved incrementally in 1 mm steps. In relation to 3 cm lengthof the agglomerates, we could calculate volumes for equidistantslices that are thin enough that the volume of the whole agglom-erate could be approximated very well. This method is compa- Fig. 13.
One of the produced dust agglomerates built by colli-sions of dust grains on a metal plate with v c = / s. Its lengthis about 3 cm and the height is 0.6 cm.rable in precision to the measurement of volumes in Teiser et al.(2011a). We chose the new method because the method of Teiseret al. (2011a) has its shortcomings for asymmetric targets. Thisway volume filling factors of 0.38 and 0.39 were found. The un-certainties due to the volume determination are 5%.If we place the target at the bottom of the chamber, reac-cretion can lead to slow secondary collisions. These rebound-ing ejecta might build a high porosity top layer on a target.Subsequent high speed impacts by the next set of projectilesmight compact this layer, but the total volume filling factor mightstill be smaller as energy is dissipated in this process. This wasnot observed in experiments at low speed by Teiser & Wurm(2009a), but might be present at high speed collisions.To estimate such e ff ects we grew dust aggregates on targetsthat were placed below the rotating centrifuge. In this setup con-figuration, ejecta from fast collisions could partly settle downonto the developing dust aggregate. The volume filling factorsmeasured were 0.29 and 0.32. Fig. 14 shows the results withearlier findings at lower velocities by (Teiser et al. 2011a). To Fig. 14.
Volume filling factors of aggregates. See text for detailson f(x) equation (7).give an analytic expression we fit the following function to our data: f ( x ) = ab + e − c · x (7)with a = = = / m. At 48.7 m / s for the im-pact velocity of projectiles, we measured two values of fillingfactors for both positions of the target (with and without gravi-tational reaccretion). We found slightly higher filling factors atcollision velocities of nearly 50 m / s because for that case the po-sition of the target (above the centrifuge and hence, the surfaceadjusted downwards) did not allow the reaccretion of ejecta. Thedust agglomerate grew almost entirely by direct sticking of dustprojectiles at this high velocity. That is in contrast to Teiser et al.(2011a), where the agglomerates grew with a mixture of bothe ff ects: direct sticking and reaccretion. This case is simulatedwhen changing the position of the target (lower side of the cham-ber). The saturation level of the filling factor assumed around0.32 by Teiser et al. (2011a) is within the error bars of the twodatapoints with reaccreted ejectas.
3. Accretion e ffi ciency: It is not only important to know that large bodies grow in collisions with smaller particles, it is alsonecessary to know the accretion e ffi ciency, which is not wellconstrained so far. As accretion e ffi ciency we define the ratio (cid:15) = m stick / m total with m stick as mass sticking to the target (mass ofthe dust pile) after a certain time and m total being the total massthat impacted during this time. To measure the total impactingdust, we placed three tubes in a row next to each other. (see Stepa, Panel 3 of Fig. 11). Dust entering the tube stays in the tube soa total mass of dust hitting the tube opening can be measured. Ina number of experimental runs we measured the ratio of massesbetween the di ff erent tubes to calibrate the di ff erence of impact-ing mass with varying tube locations. This way measuring themass in one tube yields a measure of the total impacting mass inthe other tubes or m total by adding a calibration factor. This factorwas determined to an accuracy of 8.7%, 3.5%, 3.1%, and 7.2%for velocities of 27.9 m / s, 38.7 m / s, 49.5 m / s, and 71.2 m / s, re-spectively. In a second set of runs, the center tube was replacedby a small target with the same diameter as the original tubeopening (see Fig. 11, panel 3, step b). An aggregate grows onthe target and its mass m stick is measured after a certain time.For a given collision velocity (calculated with equation (2) fromthe velocity calibration) between six and ten calibration runs andsix to seven impact runs were carried out. The accreted masses,the single accretion e ffi ciencies and measurement errors σ dueto mass determination and calibration are given in Table 1. Forintermediate and high velocities the scatter in individual experi-ment runs is larger than the individual measurement errors. Theaverage accretion e ffi ciencies and the uncertainties based on thestandard deviation are given in Table 2. These values can be re-garded as self-consistent accretion e ffi ciencies for an evolvingtarget if the dust layer is thick enough that initial e ff ects of im-pacting the plastic substrate can be neglected. The thickness ofthe dust layer can be calculated from the accreted mass m as d = m π s ρ Φ (8)where s = ρ = / cm is the dust density, and the assumed filling factor Φ is 0.38. A10 mg mass gain corresponds to a thickness of 0.13 mm. This ismuch larger than the particle size and is also several times theprojectile size. We consider this as large and argue that we mea-sured the self-consistent growth of a dust target for masses largerthan 10 mg. Most measured masses were even larger. One excep-tion are the values at 27.9 m / s. Due to technical limitations onlya small amount of dust mass could be measured here and the dust Table 1.
The mass which sticks on a target ( m stick ) and the mass,which is launched toward the target ( m total ) at a given impact ve-locity. The ratio of m stick and m total gives the accretion e ffi ciency (cid:15) . The parameter σ is the error due to mass determination andcalibration. The average value of impacting masses was 0.29 µ g. v [m / s] m stick [mg] m total [mg] (cid:15) [%] σ [%]27.9 10 20 50.0 8.16 9 66.7 13.95 8 62.5 15.611 16 68.8 10.87 14 50.0 9.84 7 57.1 16.238.7 18 56 32.1 2.48 28 28.6 4.010 25 40.0 4.718 37 48.6 3.812 33 36.4 3.615 37 40.5 3.749.5 43 133 32.3 1.439 101 38.6 1.732 104 30.8 1.564 181 35.4 1.444 103 42.7 1.864 164 39.0 1.571.2 52 547 9.5 0.767 229 29.3 2.061 258 23.6 1.559 318 18.6 1.341 235 17.4 1.27 51 13.7 2.2 layer is on the order of the projectile size. Instead, we measurethe sticking fraction of dust on the dustless plastic target here andfind no self-consistent growth that might include erosion fromthe dust layer. We have yet to find a better way to quantify thissystemic di ff erence, therefore this accretion e ffi ciency might besystemically too high. For 48.7 m / s the dust flux was largest andthe accretion e ffi ciencies were large. This allowed the buildupof targets extended enough to determine their filling factors bydirect mass and volume measurements. Table 2.
Accretion e ffi ciencies of dust (mean mass: 0.29 µ g) atgiven impact velocity. velocity [m / s] accretion e ffi ciency [%] 1 σ [%]27.9 58.4 9.138.7 38.7 7.049.5 36.8 4.771.2 18.3 6.8 In a second series of experiments we measured the accretione ffi ciencies of impacting dust particles, which are a magnitudelarger in mass (mean mass = µ g) with the same procedure asexplained above. We produced larger particles by removing thefine-meshed netting wire (mentioned in Sect. 2.1 and in Fig. 1) atthe outside of the centrifuge. Again, the determined masses, thesingle accretion e ffi ciencies and measurement errors are givenin Table 3. One additional di ff erence in view of the low massesmeasured at low velocity for small aggregates was that the plas-tic target was replaced by a precompacted dust target of 0.48 infilling factor. Therefore, the first impacts already took place ondust targets. However, the dust flux and accreted masses werelarge enough here to consider the growth as self consistent. As Table 3.
Same as Table 1, but for larger projectiles (2.67 µ g). v [m / s] m stick [mg] m total [mg] (cid:15) [%] σ [%]27.9 31 166 18.7 7.259 379 15.6 7.144 140 31.4 7.252 184 28.3 7.147 162 29.0 7.243 176 24.4 7.138.7 46 222 20.7 8.731 170 18.2 8.721 372 5.6 8.743 194 22.2 8.741 209 19.6 8.745 251 17.9 8.749.5 38 342 11.1 6.946 203 22.7 7.027 165 16.4 7.037 234 15.8 6.923 212 10.8 7.046 246 18.7 6.971.2 36 357 10.1 5.214 494 2.8 5.249 689 7.1 5.248 687 7.0 5.245 669 6.7 5.230 532 5.6 5.2 calculated for the smaller impacting particles, the average accre-tion e ffi ciencies and the scatter in terms of a 1 sigma deviationare also given for the larger particles in Table 4. Table 4.
Accretion e ffi ciencies of dust (mean mass: 2.67 µ g) atgiven impact velocity. velocity [m / s] accretion e ffi ciency [%] 1 σ [%]27.9 24.6 6.938.7 17.4 6.949.5 15.9 5.371.2 6.6 3.2 The determined values for the accretion e ffi ciency show adistinct tendency to be reduced with increasing collision veloc-ity. We fit our data from Tables 2 and 4 with linear functions(Fig. 15) each, as the most simple function in agreement withthe data. The accretion e ffi ciencies are hereby given as: (cid:15) ( v ) = − . · v +
78 (9)for the colliding particles with a mean mass of 0.29 µ g and (cid:15) ( v ) = − . · v +
35 (10)for the colliding particles with a mean mass of 2.67 µ g with (cid:15) and (cid:15) as accretion e ffi ciencies in [%] and the velocity v in [m / s].If collision velocities are increasing beyond 90 m / s, no dust ag-gregates should stick onto the target anymore. Growing dust ag-glomerates are likely being destroyed by impinging dust, whichpossesses too much kinetic energy. It might be worth consid-ering the dependence of the accretion e ffi ciency on the impactenergy. Therefore, we used the mean values of mass of the dustparticles to calculate their kinetic energies at both measurementruns; their di ff erent accretion e ffi ciencies are plotted in Fig. 16.The determined values for the accretion e ffi ciency show a dis-tinct tendency to be reduced with increasing collision energies. Fig. 15.
Accretion e ffi ciencies (cid:15) and (cid:15) of growing dust agglom-erates by impinging dust particles (mean masses m: 0.29 µ g and2.67 µ g) in dependency of their collision velocities. Fig. 16.
Accretion e ffi ciencies over impact energy of particleswith di ff erent values of their mean mass.The decrease of the accretion e ffi ciency with increasing collisionenergy for both datasets can well be described by one logarith-mic dependence as: (cid:15) ( E c ) = − . · ln ( E c ) −
52 (11)with (cid:15) ( E c ) as accretion e ffi ciency in [%] and the collision energy E c in [mJ].
4. Conclusions
The basic experimental conclusions of this work are straightfor-ward. If dust aggregates of about 50 µ m diameter, consisting ofSiO particles of a few micrometer in size, collide continuouslywith a larger body at random locations on its surface, we find thefollowing: – The larger target body growth at the expense of the smallerprojectile aggregate. – The accretion e ffi ciency for impacting dust particles with amean mass of 0.29 µ g decreases from 58 % to 18 % between27 m / s and 71 m / s. – The accretion e ffi ciency for impacting dust particles with amean mass of 2.67 µ g decreases from 25 % to 7 % between27 m / s and 71 m / s. – The accretion e ffi ciency for both data sets can be describedby a logarithmic decrease with impact energy from 58 % to7 % at impact energies from 0.1 µ J and 10 µ J. – The volume filling factor of the target will evolve to 0.38 at49 m / s. – The volume filling factor increases from 0.32 to 0.38 be-tween 7 m / s and 49 m / s. – The volume filling factor at high speed is sensitive to thesame order of a few % to the slow reaccretion of dust (bygravity here) and subsequent compaction in following colli-sions with a volume filling factor being 0.30.From earlier experiments at high speed by Wurm et al.(2005) of mm aggregates impacting up to 25 m / s, it was knownthat accretion e ffi ciencies larger than 30% occurs. This is stilltrue for aggregates of more than an order of magnitude smaller.Teiser & Wurm (2009b) showed that submm particles are likelyto stick up to 60 m / s, but these results were based on individ-ual collisions. The experiments here show that this is indeed thecase and we give quantitative values for volume filling factors ofa self-consistently produced target.Our results support the idea of particle growth of larger bod-ies through collisions as suggested by Teiser & Wurm (2009b)and shown in a model by Windmark et al. (2012a) to work ifa bouncing barrier is present. Also, in a dense environment ofclumps of cm or dm aggregates forming in an instability sce-nario (Chiang & Youdin 2010), these findings are applicable asthey provide a means to recollect the debris of a destructive col-lision at high speed. Either way large bodies are very e ffi cientscavengers in protoplanetary disks which, among other things,is certainly a dominating process in early phases of planet for-mation. Acknowledgements.
This work is funded by the
Deutsche Forschungsgemein-schaft, DFG as part of the research group FOR 759 . We thank ManfredAderholz, Ulrich Visser, and the mechanical workshop for the manufacture ofthe centrifuge.
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