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1.
Patrick Michel  Willy Benz 《Icarus》2004,168(2):420-432
In this paper, we analyze the effect of the internal structure of a parent body on its fragment properties following its disruption in different impact energy regimes. To simulate an asteroid breakup, we use the same numerical procedure as in our previous studies, i.e., a 3D SPH hydrocode to compute the fragmentation phase and the parallel N-body code pkdgrav to compute the subsequent gravitational re-accumulation phase. To explore the importance of the internal structure in determining the collisional outcome, we consider two different parent body models: (1) a purely monolithic one and (2) a pre-shattered one which consists of several fragments separated by damaged zones and small voids. We present here simulations spanning two different impact energy regimes—barely disruptive and highly catastrophic—corresponding to the formation of the Eunomia and Koronis families, respectively. As we already found for the intermediate energy regime represented by the Karin family, pre-shattered parent bodies always lead to outcome properties in better agreement with those of real families. In particular, the fragment size distribution obtained by disrupting a monolithic body always contains a large gap between the largest fragment and the next largest ones, whereas it is much more continuous in the case of a pre-shattered parent body. In the latter case, the ejection speeds of large fragments are also higher and a smaller impact energy is generally required to achieve a similar degree of disruption. Hence, unless the internal structure of bodies involved in a collision is known, predicting accurately the outcome is impossible. Interestingly, disrupting a pre-shattered parent body to reproduce the Koronis family yields a fragment size distribution characterized by four almost identical largest objects, as observed in the real family. This peculiar outcome has been found before in laboratory experiments but is obtained for the first time following gravitational re-accumulation. Finally, we show that material belonging to the largest fragments of a family originates from well-defined regions inside the parent body (the extent and location of which are dependent upon internal structure), despite the many gravitational interactions that occur during the re-accumulation process. Hence fragment formation does not proceed stochastically but results directly from the velocity field imparted during the impact.  相似文献   

2.
In the last few years, thanks to the development of sophisticated numerical codes, a major breakthrough has been achieved in our understanding of the processes involved in small body collisions. In this review, we summarize the most recent results provided by numerical simulations, accounting for both the fragmentation of an asteroid and the gravitational interactions of the generated fragments. These studies have greatly improved our knowledge of the mechanisms that are at the origin of some observed features in the asteroid belt. In particular, the simulations have demonstrated that, for bodies larger than several kilometers, the collisional process not only involves the fragmentation of the asteroid but also the gravitational interactions between the ejected fragments. This latter mechanism can lead to the formation of large aggregates by gravitational reaccumulation of smaller fragments, and helps explain the presence of large members within asteroid families. Numerical simulations of the complete process have thus reproduced successfully for the first time the main properties of asteroid families, each formed by the disruption of a large parent body, and provided information on the possible internal structure of the parent bodies. A large amount of work remains necessary, however, to understand in deeper detail the physical process as a function of material properties and internal structures that are relevant to asteroids, and to determine in a more quantitative way the outcome properties such as fragment shapes and rotational states.  相似文献   

3.
Patrick Michel  Martin Jutzi 《Icarus》2011,211(1):535-545
The Veritas family is located in the outer main belt and is named after its apparent largest constituent, Asteroid (490) Veritas. The family age has been estimated by two independent studies to be quite young, around 8 Myr. Therefore, current properties of the family may retain signatures of the catastrophic disruption event that formed the family. In this paper, we report on our investigation of the formation of the Veritas family via numerical simulations of catastrophic disruption of a 140-km-diameter parent body, which was considered to be made of either porous or non-porous material, and a projectile impacting at 3 or 5 km/s with an impact angle of 0° or 45°. Not one of these simulations was able to produce satisfactorily the estimated size distribution of real family members. Based on previous studies devoted to either the dynamics or the spectral properties of the Veritas family, which already treated (490) Veritas as a special object that may be disconnected from the family, we simulated the formation of a family consisting of all members except that asteroid. For that case, the parent body was smaller (112 km in diameter), and we found a remarkable match between the simulation outcome, using a porous parent body, and the real family. Both the size distribution and the velocity dispersion of the real reduced family are very well reproduced. On the other hand, the disruption of a non-porous parent body does not reproduce the observed properties very well. This is consistent with the spectral C-type of family members, which suggests that the parent body was porous and shows the importance of modeling the effect of this porosity in the fragmentation process, even if the largest members are produced by gravitational reaccumulation during the subsequent gravitational phase. As a result of our investigations, we conclude that it is very likely that the Asteroid (490) Veritas and probably several other small members do not belong to the family as originally defined, and that the definition of this family should be revised. Further investigations will be performed to better constrain the definitions and properties of other asteroid families of different types, using the appropriate model of fragmentation. The identification of very young families in turn will continue to serve as a tool to check the validity of numerical models.  相似文献   

4.
5.
We present a self-consistent numerical algorithm aimed at predicting the outcomes of high-velocity impacts between asteroids (or other small bodies of the solar system), based on a set of model input parameters which can be estimated from the available experimental evidence, and including the possible gravitational reaccumulation of ejected fragments whose velocity is less than a suitably defined escape velocity. All the fragment mass distributions are modelled by truncated power laws, and a possible correlation between fragment ejection velocity and mass is taken into account in different ways, including a probabilistic one. We analyze in particular the effectiveness of the gravitational reaccumulation process in terms of different choices of the collisional parameters and the assumed relationship between fragment speed and mass. Both the transition size beyond which solid targets are likely to reaccumulate a large fraction of the fragment mass and the collision energy needed to disperse most of the fragments are sensitive functions of the assumed fragment velocity versus mass relationship. We also give some examples of how our algorithm can be applied to study the origin and collisional history of small solar system bodies, including the asteroid 951 Gaspra (recently imaged by the Galileo probe) and the asteroid families.  相似文献   

6.
Abstract— In this paper, we present numerical simulations aimed at reproducing the Baptistina family based on its properties estimated by observations. A previous study by Bottke et al. (2007) indicated that this family is probably at the origin of the K/T impactor, is linked to the CM meteorites and was produced by the disruption of a parent body 170 km in size due to the head‐on impact of a projectile 60 km in size at 3 km s?1. This estimate was based on simulations of fragmentation of non‐porous materials, while the family was assumed to be of C taxonomic type, which is generally interpreted as being formed from a porous body. Using both a model of fragmentation of non‐porous materials, and a model that we developed recently for porous ones, we performed numerical simulations of disruptions aimed at reproducing this family and at analyzing the differences in the outcome between those two models. Our results show that a reasonable match to the estimated size distribution of the real family is produced from the disruption of a porous parent body by the head‐on impact of a projectile 54 km in size at 3 km s?1. Thus, our simulations with a model consistent with the assumed dark type of the family requires a smaller projectile than previously estimated, but the difference remains small enough to not affect the proposed scenario of this family history. We then find that the break‐up of a porous body leads to different outcomes than the disruption of a non‐porous one. The real properties of the Baptistina family still contain large uncertainties, and it remains possible that its formation did not involve the proposed impact conditions. However, the simulations presented here already show some range of outcomes and once the real properties are better constrained, it will be easy to check whether one of them provides a good match.  相似文献   

7.
F. Roig  R. Duffard  D. Lazzaro 《Icarus》2003,165(2):355-370
A simple mechanical model is formulated to study the dynamics of rubble-pile asteroids, formed by the gravitational re-accumulation of fragments after the collisional breakup of a parent body. In this model, a rubble-pile consists of N interacting fragments represented by rigid ellipsoids, and the equations of motion explicitly incorporate the minimal degrees of freedom necessary to describe the attitude and rotational state of each fragment. In spite of its simplicity, our numerical examples indicate that the overall behavior of our model is in line with several known properties of collisional events, like the energy and angular momentum partition during high velocity impacts. Therefore, it may be considered as a well defined minimal model.  相似文献   

8.
《Icarus》1998,132(1):113-124
We present results of two-dimensional gravitationalN-body simulations of the late stage of planetary formation. This stage is characterized by the direct accretion of hundreds of lunar-sized planetesimals into planetary bodies. Our simulation code is based on the Hermite Individual Timestep integration algorithm, and gravitational interactions among all bodies are included throughout the simulations. We compare our simulation with earlier works that do not include all interactions, and we find very good agreement. A previously published collisional fragmentation model is included in our simulation to study the effects of the production of fragments on the subsequent evolution of the larger planetary bodies. It is found that for realistic two-body collisions that, according to this model, both bodies will suffer fragmentation, and that the outcome of the collision will be a relatively large core containing most of the mass and a few small fragments. We present the results of simulations that include this simple fragmentation model. They indicate that the presence of small fragments have only a small effect on the growth or orbital evolution of the large planet-sized bodies.  相似文献   

9.
Numerical simulations of asteroid breakups, including both the fragmentation of the parent body and the gravitational interactions between the fragments, have allowed us to reproduce successfully the main properties of asteroid families formed in different regimes of impact energy, starting from a non-porous parent body. In this paper, using the same approach, we concentrate on a single regime of impact energy, the so-called catastrophic threshold usually designated by , which results in the escape of half of the target’s mass. Thanks to our recent implementation of a model of fragmentation of porous materials, we can characterize for both porous and non-porous targets with a wide range of diameters. We can then analyze the potential influence of porosity on the value of , and by computing the gravitational phase of the collision in the gravity regime, we can characterize the collisional outcome in terms of the fragment size and ejection speed distributions, which are the main outcome properties used by collisional models to study the evolutions of the different populations of small bodies. We also check the dependency of on the impact speed of the projectile.In the strength regime, which corresponds to target sizes below a few hundreds of meters, we find that porous targets are more difficult to disrupt than non-porous ones. In the gravity regime, the outcome is controlled purely by gravity and porosity in the case of porous targets. In the case of non-porous targets, the outcome also depends on strength. Indeed, decreasing the strength of non-porous targets make them easier to disrupt in this regime, while increasing the strength of porous targets has much less influence on the value of . Therefore, one cannot say that non-porous targets are systematically easier or more difficult to disrupt than porous ones, as the outcome highly depends on the assumed strength values. In the gravity regime, we also confirm that the process of gravitational reaccumulation is at the origin of the largest remnant’s mass in both cases. We then propose some power-law relationships between and both target’s size and impact speed that can be used in collisional evolution models. The resulting fragment size distributions can also be reasonably fitted by a power-law whose exponent ranges between −2.2 and −2.7 for all target diameters in both cases and independently on the impact velocity (at least in the small range investigated between 3 and 5 km/s). Then, although ejection velocities in the gravity regime tend to be higher from porous targets, they remain on the same order as the ones from non-porous targets.  相似文献   

10.
The origin of asteroid families in terms of collisional breakup is analyzed using the data by Williams (1979, in Asteroids (T. Gehrels, Ed.), pp. 1040–1063, Univ. of Arizona Press, Tucson). The distributions of mass and relative velocity of the minor family members with respect to the largest body are derived. These ditributions are then compared with the outcomes of catastrophic impacts, predicted from theoretical arguments and observed from laboratory experiments. The general features of the mass distributions can be interpreted in terms of collisional disruption of a parent body followed by self-gravitational reaccumulation on the largest remnant; no decisive evidence for multiple reaccumulations is found. The typical ejection velocities of the family members are of the same order as those of laboratory fragments; since the definition of families is based on purely dynamical arguments, this results gives direct observational support to the collisional formation hypothesis. The transition between collisional outcomes dominated by solid-state forces and by self-gravitatation, expected to occur at diameters D ~ 100 km on the basis of rotational studies and of theoretical estimates, is clearly confirmed by the present analysis. A “morphological” classification into three broad classes (asymmetric, dispersed, and intermediate) is introduced; it is based on the distribution of mass vs relative velocity, taking also into account the parent body's (and the largest remnant's) escape velocity. Finally some results are outlined which apparently do not fit the theoretical predictions: (1) the degree of fragmentation in real families is generally lower than that observed for experimental targets and (2) when the relative velocities are computed, including also proper eccentricity and inclination differences, values higher by about a factor 4 than those derived from semiaxes differences only are found. Further studies are proposed, including more observations, better proper elements computation and classification methods, and new investigations on the physics of hypervelocity impacts.  相似文献   

11.
Numerical simulations have been used to study high velocity two-body impacts. In this paper a two-dimensional Lagrangian finite difference hydrocode and a three-dimensional smooth particle hydrocode (SPH) are described and initial results reported.

The 2D hydrocode has successfully reproduced both the fragment size distribution and the mean fragment velocities from laboratory impact experiments using basalt and cement mortar. Further, the hydrocode calculations have determined that the energy needed to fracture a body has a much stronger dependence on target size than predicted from most scaling theories. In addition, velocity distributions obtained (using homogeneous targets at impact velocities around 2 km s−1) indicate that mean ejecta speeds resulting from large-body collisions do not generally exceed escape velocities.

The SPH model provides a fully three-dimensional framework for studying impacts, so that phenomena such as oblique collisions or impacts into non-spherical targets may be studied. The gridless code allows for arbitrary levels of distortion, and is hence appropriate for modeling the large-scale deformations which accompany most impact events. Because fragments are modeled explicitly, greater numerical accuracy is achieved in the regions of large fragments than with the purely statistical approach of the 2D model. Of course, this accuracy comes at the expense of significantly greater computational requirements.

These codes can be, and have been, used to make specific predictions about particular objects in our solar system. But more significantly, they allow us to explore a broad range of collisional events. Certain parameters (size, time) can be studied only over a very restricted range within the laboratory; other parameters (initial spin, low gravity, exotic structure or composition) are difficult to study at all experimentally. The outcomes of numerical simulations lead to a more general and accurate understanding of impacts in their many forms.  相似文献   


12.
The influence of partially elastic collisions, gravitational encounters, and different gravitational potentials is studied in terms of computer simulations involving a ring of 200 identical particles. If the masses of the particles are small, their mutual gravitational attraction is found to produce a decrease in the dispersion of velocities below the collisional equilibrium value, but for heavier particles the dispersion again begins to increase. The vertical component of the force which is produced by the self-gravitation of the ring reduces its thickness. The results of the simulations are in good agreement with the predictions of the collisional theory.  相似文献   

13.
In this paper, we compare the outcome of high-velocity impact experiments on porous targets, composed of pumice, with the results of simulations by a 3D SPH hydrocode in which a porosity model has been implemented. The different populations of small bodies of our Solar System are believed to be composed, at least partially, of objects with a high degree of porosity. To describe the fragmentation of such porous objects, a different model is needed than that used for non-porous bodies. In the case of porous bodies, the impact process is not only driven by the presence of cracks which propagate when a stress threshold is reached, it is also influenced by the crushing of pores and compaction. Such processes can greatly affect the whole body's response to an impact. Therefore, another physical model is necessary to improve our understanding of the collisional process involving porous bodies. Such a model has been developed recently and introduced successfully in a 3D SPH hydrocode [Jutzi, M., Benz, W., Michel, P., 2008. Icarus 198, 242-255]. Basic tests have been performed which already showed that it is implemented in a consistent way and that theoretical solutions are well reproduced. However, its full validation requires that it is also capable of reproducing the results of real laboratory impact experiments. Here we present simulations of laboratory experiments on pumice targets for which several of the main material properties have been measured. We show that using the measured material properties and keeping the remaining free parameters fixed, our numerical model is able to reproduce the outcome of these experiments carried out under different impact conditions. This first complete validation of our model, which will be tested for other porous materials in the future, allows us to start addressing problems at larger scale related to small bodies of our Solar System, such as collisions in the Kuiper Belt or the formation of a family by the disruption of a porous parent body in the main asteroid belt.  相似文献   

14.
More than a decade of dedicated experimental work on the collisional physics of protoplanetary dust has brought us to a point at which the growth of dust aggregates can-for the first time-be self-consistently and reliably modeled. In this article, the emergent collision model for protoplanetery dust aggregates, as well as the numerical model for the evolution of dust aggregates in protoplanetary disks, is reviewed. It turns out that, after a brief period of rapid collisional growth of fluffy dust aggregates to sizes of a few centimeters, the protoplanetary dust particles are subject to bouncing collisions, in which their porosity is considerably decreased. The model results also show that low-velocity fragmentation can reduce the final mass of the dust aggregates but that it does not trigger a new growth mode as discussed previously. According to the current stage of our model, the direct formation of kilometer-sized planetesimals by collisional sticking seems unlikely, implying that collective effects, such as the streaming instability and the gravitational instability in dust-enhanced regions of the protoplanetary disk, are the best candidates for the processes leading to planetesimals.  相似文献   

15.
Insights into collisional physics may be obtained by studying the asteroid belt, where large-scale collisions produced groups of asteroid fragments with similar orbits and spectra known as the asteroid families. Here we describe our initial study of the Karin cluster, a small asteroid family that formed 5.8±0.2 Myr ago in the outer main belt. The Karin cluster is an ideal ‘natural laboratory’ for testing the codes used to simulate large-scale collisions because the observed fragments produced by the 5.8-Ma collision suffered apparently only limited dynamical and collisional erosion. To date, we have performed more than 100 hydrocode simulations of impacts with non-rotating monolithic parent bodies. We found good fits to the size-frequency distribution of the observed fragments in the Karin cluster and to the ejection speeds inferred from their orbits. These results suggest that the Karin cluster was formed by a disruption of an ≈33-km-diameter asteroid, which represents a much larger parent body mass than previously estimated. The mass ratio between the parent body and the largest surviving fragment, (832) Karin, is ≈0.15-0.2, corresponding to a highly catastrophic event. Most of the parent body material was ejected as fragments ranging in size from yet-to-be-discovered sub-km members of the Karin cluster to dust grains. The impactor was ≈5.8 km across. We found that the ejections speeds of smaller fragments produced by the collision were larger than those of the larger fragments. The mean ejection speeds of >3-km-diameter fragments were . The model and observed ejection velocity fields have different morphologies perhaps pointing to a problem with our modeling and/or assumptions. We estimate that ∼5% of the large asteroid fragments created by the collision should have satellites detectable by direct imaging (separations larger than 0.1 arcsec). We also predict a large number of ejecta binary systems with tight orbits. These binaries, located in the outer main belt, could potentially be detected by lightcurve observations. Hydrocode modeling provides important constraints on the interior structure of asteroids. Our current work suggests that the parent asteroid of the Karin cluster may have been an unfractured (or perhaps only lightly fractured) monolithic object. Simulations of impacts into fractured/rubble pile targets were so far unable to produce the observed large gap between the first and second largest fragment in the Karin cluster, and the steep slope at small sizes (≈6.3 differential index). On the other hand, the parent asteroid of the Karin cluster was produced by an earlier disruptive collision that created the much larger, Koronis family some 2-3 Gyr ago. Standard interpretation of hydrocode modeling then suggests that the parent asteroid of the Karin cluster should have been formed as a rubble pile from Koronis family debris. We discuss several solutions to this apparent paradox.  相似文献   

16.
We have applied the algorithm developed by Petit and Farinella (Celest. Mech. 57, 1–28, 1993) to model the outcomes of impacts between asteroids of different sizes, to show that a crucial feature of these models is the assumed relationship between velocity and mass of fragments ejected after a shattering impact. Not only how the mean velocity depends upon mass is important to determine the extent of fragment reaccumulation, but also the distribution of velocities about the mean values. The available experimental evidence on this issue is still sparse, and does not constrain the collisional models well enough to allow us to make reliable predictions on the outcomes of impacts between bodies of size much larger than the laboratory targets. As a consequence, when the collisional outcome models are used as an input for simulations of the asteroid collisional history since the origin of the solar system, the results show a strong sensitivity to the assumed velocity vs mass relationship. This sensitivity is stronger in the diameter range (a few tens to a few hundreds of km) where the self-gravitational reaccumulation of fragments is most effective, but may also extend to much smaller sizes.  相似文献   

17.
Akira Fujiwara 《Icarus》1982,52(3):434-443
The fragmentation of the parent asteroids of the Themis, Eos, and Koronis families is investigated by considering mutual gravitational effects among the fragmented bodies. The masses of the parent asteroids and the kinetic and gravitational energies of the fragmented bodies are estimated. Comparison of these results and data from the laboratory impact experiments leads to the conclusion that the parent asteroids of the three families were completely fragmented at Ep/M of 108 erg/g or more (Ep, impact energy; M, parent mass). However, since most of the fragments had low relative velocities many reaccumulated through mutual gravitation. The larger members in these families should have the rubble pile structures and hydrostatic equilibrium figures.  相似文献   

18.
The role of catastrophic collisions in the evolution of the asteroids is discussed in detail, employing extrapolations of experimental results on the outcomrs of high-velocity impacts. We determine the range of the probable largest collision for target asteroids of different sizes during the solar system's lifetime, and we conclude that all the asteroids have undergone collisional events capable of overcoming the material's solid-state cohesion. Such events do not lead inescapably to complete disruption of the targets, because (i) for a previously unfractured target, experiments show that fragments of significant size can survive breakup, depending on the energy and geometry of the collision; (ii) self-gravitation can easily cause a reaccumulation of fragments for targets exceeding a critical size, which seems to be of the order of 100 km. In the intermediate diameter range 100?D ?300 km, where formation of gravitationally bound “rubble piles” is frequent, the transfer of angular momentum can be large enough to produce objects with triaxial equilibrium shapes (Jacobi ellipsoids) or to cause fission into binary systems. In the same size range, low-velocity escape of collisional fragments can also occur, leading to the formation of dynamical families. Asteroids smaller than ~100 km are mostly multigeneration fragments, while for D?300 km the collisional process produces nearly spheroidal objects covered by megaregoliths; whether their rotation is “primordial” or collisionally generated depends critically on the past flux of colliders. The complex and size-dependent phenomenology predicted by the theory compares satisfactorily with the observational evidence, as derived both by a classification of asteroids in terms of their size, spin rate, and lightcurve amplitude, and by a comparison between the rotational properties of family and nonfamily asteroids. The fundamental result of this investigation is that almost all asteroids are outcomes of catastrophic collisions, and that these events cause either complete fragmentation of the target bodies or, at least, drastic readjustments of their internal structure, shape, and spin rate.  相似文献   

19.
Collisions are a fundamental process in the creation of asteroid families and in satellite formation. For this reason, understanding the outcome of impacts is fundamental to the accurate modeling of the formation and evolution of such systems. Smoothed-Particle Hydrodynamics/N-body codes have become the techniques of choice to study large-scale impact outcomes, including both the fragmentation of the parent body and the gravitational interactions between fragments. It is now possible to apply this technique to targets with either monolithic or rubble-pile internal structures. In this paper we apply these numerical techniques to rubble-pile targets, extending previous investigations by Durda et al. (Durda, D.D., Bottke, W.F., Enke, B.L., Merline, W.J., Asphaug, E., Richardson, D.C., Leinhardt, Z.M. [2004]. Icarus 170, 243–257; Durda, D.D., Bottke, W.F., Nesvorný, D., Enke, B.L., Merline, W.J., Asphaug, E., Richardson, D.C. [2007]. Icarus 186, 498–516). The goals are to study asteroid–satellite formation and the morphology of the size–frequency distributions (SFDs) from 175 impact simulations covering a range of collision speeds, impact angles, and impactor sizes. Our results show that low-energy impacts into rubble-pile and monolithic targets produce different features in the resulting SFDs and that these are potentially diagnostic of the initial conditions for the impact and the internal structure of the parent bodies of asteroid families. In contrast, super-catastrophic events (i.e., high-energy impacts with large specific impact energy) result in SFDs that are similar to each other. We also find that rubble-pile targets are less efficient in producing satellites than their monolithic counterparts. However, some features, such as the secondary-to-primary diameter ratio and the relative separation of components in binary systems, are similar for these two different internal structures of parent bodies.  相似文献   

20.
The outcomes of asteroid collisional evolution are presently unclear: are most asteroids larger than 1 km size gravitational aggregates reaccreted from fragments of a parent body that was collisionally disrupted, while much smaller asteroids are collisional shards that were never completely disrupted? The 16 km mean diameter S-type asteroid 433 Eros, visited by the NEAR mission, has surface geology consistent with being a fractured shard. A ubiquitous fabric of linear structural features is found on the surface of Eros and probably indicates a globally consolidated structure beneath its regolith cover. Despite the differences in absolute scale and in lighting conditions for NEAR and Hayabusa, similar features should have been found on 25143 Itokawa if present. This much smaller, 320 m diameter S-asteroid was visited by the Hayabusa spacecraft. Comparative analyses of Itokawa and Eros geology reveal fundamental differences, and interpretation of Eros geology is illuminated by comparison with Itokawa. Itokawa lacks a global lineament fabric, and its blocks, craters, and regolith may be inconsistent with formation and evolution as a fractured shard, unlike Eros. An object as small as Itokawa can form as a rubble pile, while much larger Eros formed as a fractured shard. Itokawa is not a scaled-down Eros, but formed by catastrophic disruption and reaccumulation.  相似文献   

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