Numerical Simulation of Density Evolution of Dust Aggregates in Protoplanetary Disks. I. Head-on Collisions

The bulk density of dust aggregates is an important factor in collisional growth of dust in protoplanetary disks. The density of aggregates changes the coupling with the disk gas, which governs the motion of aggregates in disks. Collisional outcomes also depend on the aggregate density. We perform three-dimensional N-body simulations of sequential collisions of aggregates composed of a number of submicron-sized icy particles in order to investigate the density evolution of dust aggregates growing in protoplanetary disks. In the present simulation of sequential collisions, as the initial aggregates at each collision, we use the resultant aggregate obtained at the previous collision. By repeating N-body calculations of aggregate collisions, we examined the density evolution of aggregate collisions. At an early stage of dust growth, aggregates stick to each other without restructuring, and the density of these aggregates decreases. At a later stage, in which the impact energy exceeds a critical energy, aggregates are gradually compressed. The compressed aggregates have a fractal dimension of 2.5. Because of this small fractal dimension, their density remains very low even at this compression stage. We also derive an equation describing the density evolution of growing aggregates. Applying this equation to dust growth in protoplanetary disks, we find that dust aggregates have an extremely low density (<0.1 kg m−3). In the simulation of the present study, we consider only head-on collisions. The effect of oblique collisions would further reduce the aggregate density.

[1]  V. Safronov,et al.  Evolution of the protoplanetary cloud and formation of the earth and the planets , 1972 .

[2]  S. Weidenschilling,et al.  Dust to planetesimals: Settling and coagulation in the solar nebula , 1980 .

[3]  J. Blum,et al.  Experiments on Sticking, Restructuring, and Fragmentation of Preplanetary Dust Aggregates , 2000 .

[4]  Koji Wada,et al.  Numerical Simulation of Dust Aggregate Collisions. I. Compression and Disruption of Two-Dimensional Aggregates , 2007 .

[5]  C. Dominik,et al.  The influence of grain rotation on the structure of dust aggregates , 2006 .

[6]  S. Ida,et al.  Dust Growth and Settling in Protoplanetary Disks and Disk Spectral Energy Distributions. I. Laminar Disks , 2005, astro-ph/0502287.

[7]  J. Cuzzi,et al.  Closed-form expressions for particle relative velocities induced by turbulence , 2007, astro-ph/0702303.

[8]  J. Blum,et al.  Growth and form of planetary seedlings: results from a sounding rocket microgravity aggregation experiment. , 2004, Physical review letters.

[9]  T. Henning,et al.  N-Particle-Simulations of Dust Growth: I. Growth Driven by Brownian Motion , 1999 .

[10]  A. Tielens,et al.  Dust coagulation in protoplanetary disks: porosity matters , 2006, astro-ph/0610030.

[11]  C. Hayashi,et al.  The Gas Drag Effect on the Elliptic Motion of a Solid Body in the Primordial Solar Nebula , 1976 .

[12]  J. W. Humberston.  Classical mechanics , 1980, Nature.

[13]  C. Hayashi.  Structure of the Solar Nebula, Growth and Decay of Magnetic Fields and Effects of Magnetic and Turbulent Viscosities on the Nebula , 1981 .

[14]  C. Dominik,et al.  Resistance to rolling in the adhesive contact of two elastic spheres , 1995 .

[15]  S. Weidenschilling,et al.  Aerodynamics of solid bodies in the solar nebula. , 1977 .

[16]  Hans-Jürgen Butt,et al.  Adhesion and Friction Forces between Spherical Micrometer-Sized Particles , 1999 .

[17]  Oliver Krauss,et al.  Impacts into weak dust targets under microgravity and the formation of planetesimals , 2007 .

[18]  C. Hayashi,et al.  Settling and growth of dust particles in a laminar phase of a low-mass solar nebula , 1986 .

[19]  C. Dominik,et al.  Numerical determination of the material properties of porous dust cakes , 2008, 0802.1832.

[20]  T. Henning,et al.  Analogous Experiments on the Stickiness of Micron-sized Preplanetary Dust , 2000 .

[21]  Alexander G. G. M. Tielens,et al.  Resistance to sliding on atomic scales in the adhesive contact of two elastic spheres , 1996 .

[22]  Paul Meakin,et al.  Fractal aggregates in geophysics , 1991 .

[23]  Alexander G. G. M. Tielens,et al.  The Physics of Dust Coagulation and the Structure of Dust Aggregates in Space , 1997 .

[24]  J. Blum,et al.  Structure and mechanical properties of high-porosity macroscopic agglomerates formed by random ballistic deposition. , 2004, Physical review letters.

[25]  Koji Wada,et al.  Numerical Simulation of Dust Aggregate Collisions. II. Compression and Disruption of Three-Dimensional Aggregates in Head-on Collisions , 2008 .

[26]  K. Kendall,et al.  Surface energy and the contact of elastic solids , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[27]  G. Wurm,et al.  Growth of planetesimals by impacts at ∼25 m/s , 2005 .

[28]  P. Goldreich,et al.  The formation of planetesimals. , 1973 .