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How to form planetisimals from mm-sized grains?

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Posted January 23, 2015

Sometimes I wonder: how do planets or even smaller asteroids form from an interstellar dust? Certainly, the matter aggregation process induced by gravity has a strong logic: under proper conditions, smaller particles stick together forming grains which later also clump together, consequently forming increasingly larger bodies. But the time needed to accomplish this is still perplexing to most of us.

A slice of the Allende meteorite showing circular chondrules. Image credit: Shiny Things via Flickr, CC BY-NC 2.0.

A slice of the Allende meteorite showing circular chondrules. This rock was formed along with the solar system. Image credit: Shiny Things via Flickr, CC BY-NC 2.0.

What time scale exactly are we talking about? According to scientific publication appearing on arXiv.org, you need at least ~105 (100 000) years to grow a millimeter-sized pebbles, or chondrules – as they are called by astronomers. Solids of this class may be of critical importance in the formation of planetisimals and current models of planetary formation lack a comprehensive theory clarifying how such chondrules are formed.

The authors of this study from Lund University, Sweden, used a numerical modeling to simulate a protoplanetary disk in which solar system-like planets are being formed. Their initial assumption was that disk contains a significant component of gas and solid particles that are initially micrometer-scale in size and form approximately 1% of the total disk mass. “Over time, particle sizes can grow by coagulation, and the mass ratio between gas and solids may change if particles migrate through the disk, or if the gas becomes depleted”, explain the scientists.

Location of the asteroid forming region in terms of disk mass Mdisk and semimajor axis r. In the red region (left), particle clumps cannot form for any disk model. In the yellow region (middle), particle clumps can only form if the disk turbulence is low, so that chondrule aggregate can reach R~4-5 mm in size.  In the green region (right), particle clumps can form for R  1 mm particles and low turbulence is not required. Image courtesy of the researchers.

Location of the asteroid forming region in terms of protoplanetary disk mass Mdisk and semimajor orbital axis r. In the red region (left), particle clumps cannot form for any disk model. In the yellow region (middle), particle clumps can only form if the disk turbulence is low, so that chondrule aggregate can reach R~4-5 mm in size. In the green region (right), particle clumps can form for R~1 mm particles and low turbulence is not required. Image courtesy of the researchers.

Concentrations, speeds and dimensions of dust particles, distances between them, and resulting clumping conditions were analyzed by the team. Numerical modeling revealed that dense particle clumps may form at a certain distance from the host star, because friction resulting from surrounding dust and gas slows such solids down and they migrate inwards to the star due to gravitational attraction. Therefore, larger bodies like asteroids may form only at a certain distance from the star where proper disk mass and turbulent viscosity is present.

Distribution of relative speeds for mm-sized particles. Sticking, bouncing and fragmenting regions are shown in different colors. The shape of curve is distorted by the logarithmic scale; in particular, the great majority of collisions happen in bouncing regime. Image courtesy of the researchers.

Distribution of relative speeds for mm-sized particles. Sticking, bouncing and fragmenting regions are shown in different colors. The shape of curve is distorted by the logarithmic scale; in particular, the great majority of collisions happen in bouncing regime. Image courtesy of the researchers.

Another estimate – the probability of sticking collisions between mm-sized particles – is mainly dominated by their speeds and distances between them. Even though a single collision over a course of ~105 years seems somewhat a rare event to expect, the total number of dust particles involved in this process is large. Meanwhile, the lifetime of the planetary disk which is the source of matter for the planetisimals to be built is significantly longer (~107 years) for a large multitude of such collisions to happen.

Times between sticking collisions calculated using numerical modeling. According to the study, tstick<105 years is a robust upper bound on tstick. Image courtesy of the researchers.

Times between sticking collisions calculated using numerical modeling. According to the study, tstick<105 years is a robust upper bound on sticking time of solid particles. Image courtesy of the researchers.

“A high concentration of particles is not required for this result. As the particles grow, the streaming instability becomes more effective, leading to the formation of planetisimals”, the authors say. Then asteroids may form directly from millimeter-size chondrules, particularly if weak turbulence is present in the surrounding space which facilitates the formation of solid aggregates few millimeters in size, the team concludes.

Written by Alius Noreika

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