February 3, 2004 | David F. Coppedge

Accretion: The Missing Link in Planetary Evolution

Every school child has seen artwork of planets evolving from a disk of dust and gas around a star like our sun, but there’s a missing link in the story.  How did the dust particles stick together?

Once a clump of material is massive enough, it can attract more material by its own gravity.  The moon, for instance, pulls meteors in.  They stay there and don’t bounce off, except in the unusual case of a high-speed glancing blow.  From the well-understood law of gravity, a planetary body needs to be about 1-10 km in diameter to grow by accretion.  From there, this “planetesimal,” according to theory, would experience runaway growth as long as there is material around to feed it.  Getting the body to this size is the problem.  Smaller bodies do not have sufficient gravity to pull in neighboring material.  A disk around a star, however, starts out with dust and ice grains much smaller, even microscopic in size.  It is estimated that the original dust particles in the primordial solar nebula were a tenth of a micrometer in diameter, too small to see.  How could these grow into planetesimals a mile across?

This problem is not new.  Planetary evolutionists have wrestled with it repeatedly.  In the February issue of Icarus,1 Sin-iti Sirono of Nagoya University, Japan, tries to identify the requirements for colliding particles to stick together rather than bounce or smash each other apart.  He certainly respects the problem; in his introduction, he asks with a Japanese accent, “There is a immense gap of 13 orders of magnitude between the grain size and the size of a planet.  How planets are formed across this gap?”  Behold the missing link of planetary evolution.

Accretion is a complex problem with many variables.  Think of firing a bullet at a rock.  A small bullet might form a crater, catastrophically disrupt the rock, or merge with the rock, if the rock is porous and able to absorb the blow.  What physical laws govern the outcome?  Sirono, after a great deal of modeling and computation, arrives at three constraints:

  1. The target must have low compressive strength relative to shear strength and tensile strength.
  2. Impact velocity must be 0.4% the speed of sound of the medium.
  3. The bodies must be made of materials that allow the “restoration of damage” effect.  This is an automatic “repair” mechanism that occurs if a ruptured material can rebound such that interatomic forces can partially heal the breach, as if little magnets in the pieces pull them back together.

It should be evident with a little thought that other variables can also be important.  To visualize this, imagine two astronauts, Chuck and Tom, having a snowball fight in the cargo bay of a space shuttle.  Let’s say they both have good timing and aim; they always make their snowballs collide in the space between them.  Since gravity is not a factor in the weightlessness of space, what factors would make the snowballs stick together (accrete) instead of bouncing off each other or fragmenting into smithereens?  Here are a few of the variables:

  1. Temperature.  Soft, wet snowballs are more likely to stick than hard, icy ones.
  2. Density.  Low-density snowballs are more likely to stick than packed ones.  The compressive strength of snowballs can vary by a factor of 1000, Sirono says: “As the density of an aggregate goes lower, the strength becomes lower and vice versa.  For example, the strength range due to density variations is more than three orders of magnitude for a bed of snow.”  So if our astronauts tightly pack their snowballs, they well be less likely to stick, but also more subject to disruption.
  3. Relative size.  A small snowball might stick more readily to a large one, than would two of equal size.  Sirono’s simulations suggest that the threshold ratio for optimum chance of sticking is 3/10 or lower.
  4. Glancing angle.  A small impactor is more likely to stick to a target in a direct bulls-eye hit rather than a glancing blow.
  5. Differentiation.  Let’s say Chuck and Tom throw rocks coated with snow.  They might accrete if the relative velocity is low and the snow coating absorbs some of the energy.
  6. Glue.  If our astronauts have access to some kind of adhesive with which to saturate their weapons, the snowballs might glue themselves together.  Sirono thinks interstellar organic molecules might just do the trick.  He cites earlier work that suggests organics might comprise a significant fraction of the material (silicate:ice:organic mass ratio of 1:1:1.6), and that the organics might form a viscoelastic fluid between the particles.  “It may be possible that the organic materials play a role of glue which connects grains and fragments,” he suggests.

If our astronauts perfect the art of getting their snowballs to stick together, new problems arise as the wad of snowballs grows.  Earlier models often assumed that the properties of an accreting mass scaled uniformly upward, but Sirono reminds us that the aggregate of particles is subject to new forms of catastrophic rupture.  Sirono explains,

There are voids and cracks inside a large aggregate that significantly lowers the strength of an aggregate.  Tensile stress concentrates in regions around the cracks, and fracturing starts from contacts between such grains.  An aggregate will be broken by much smaller stresses than those expected by direct extrapolation from interaction forces between grains.

So until the aggregate is large enough for gravity to compress and homogenize the insides, it is even more subject to disruption than were the original starting grains.  Even if a lucky aggregate forms, all Tom needs to do is lob a high-speed ice ball at it and it could splinter into small fragments again.  Better luck next time.

It seems, therefore, that many special conditions are required to keep the hopeful aggregate growing up to a size where gravitational accretion can take over.  Sirono does not estimate how likely this is to occur in a real stellar nebula.  He just points out that any accretion needs to obey the laws of physics.


1Sin-iti Sirono, “Conditions for collisional growth of a grain aggregate,” Icarus Volume 167, Issue 2, February 2004, Pages 431-452, doi:10.1016/j.icarus.2003.09.018.

Observation 1: planets around a star, with a little dust.  Observation 2: a lot of dust around a star, with no planets.  What are appropriate conclusions based on this data?

There are two possibilities.  One is that the second star is a young star with a dust disk that is on the way to becoming a new solar system, and the first is an old star with mature planets.  But there’s another possibility.  Maybe the first star has widely spaced, mature planets with stable orbits and few collisions, and the second star started out with mature planets in erratic orbits, which since collided and ground each other to dust.  The conclusion you reach has a lot to say about your world view and your respect for observation.

While no one can rule out all possibility of dust and ice grains sticking together, the probability seems rather low.  Sirono invokes several ad hoc conditions to increase the odds.  Maybe if they are as soft as silly putty and infused with some sort of organic glue, with the right angle of attack, slow enough collision speed and the right temperature, they just might stick instead of bouncing off each other.  But the organic glue cannot get too warm, because Sirono says, “It has been found that the shear modulus of the organics decreases by five orders of magnitude as temperature increases from 200 to 300 K.”  This means the glue loses its elasticity real fast as the temperature rises: “The consequence of decrease in elasticity by a factor of 10 is severe fragmentation,” he says.  For particles in the warmer parts of the nebula, this seems to be a problem, yet we observe Mercury in our solar system baking in the heat of the sun, and gas giants bigger than Jupiter in even closer orbits around other stars.  Also, even if the conditions are lucky enough for the particles to start sticking to each other, they become even more subject to disruption as the aggregate grows.

Perhaps Sinoro’s constraints don’t seem too outlandish, and one can envision scenarios in which all the right conditions might be met.  It could be argued that out of uncounted myriads of particles, some might reach the threshold of runaway gravitational accretion.  All it takes is a few to get a planetary system, right?  (Actually, our solar system is filled with many thousands of gravitationally accreting bodies, like asteroids, Kuiper Belt objects, comets, and small moons, in addition to the planets and larger moons.  Some of them appear to have been busted apart by collisions.)

Regardless, the fact remains that no one has observed grains accrete into a planetesimal, but astronomers have abundantly observed the opposite: bodies fragmenting into smaller bodies and dust.  Small bodies show abundant evidence of cratering and erosion, even the recently-photographed comet Wild-2 (see 01/02/2004), a fact that surprised scientists because this was supposed to be a pristine object from the quiet deep freeze of the outer solar system.  We observe ongoing processes of fragmentation, catastrophic collision, erosion to dust and de-evolution, but accretion exists only in the minds of theorists.  Which principle is more in accord with the second law of thermodynamics?

One would think that scientists would err on the side of conservatism, and not make claims beyond the evidence.  But the disruption view implies starting conditions that are philosophically repugnant to a naturalist: if the planets were already there, they must have been created.  So strong is the urge to have a universe that evolves upward from a bang to galaxies to planets to life, that philosophical naturalists will sneak glue and fudge and whatever else is needed to fill in the gaps.  You can believe that the dust around Vega is a young solar system in the making, but be sure your model particles obey the laws of physics.  After all, a naturalist should respect the laws of nature, by definition.  Better yet, perform realistic lab experiments.  We’ll wait till you get particles that stick before worrying you with all the other problems, such as the Kuiper capers (10/05/2003), small moon mysteries (09/29/2003), turbulent stress in planetesimals and in scientist minds (09/22/2003), the rarity of sunlike solar systems (07/21/2003), declining popularity of the planetesimal hypothesis (06/03/2003), migration woes (05/16/2003), the war of the worlds (04/17/2003), the tweak Olympics (11/22/2002), etc., and so forth, and so on.

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