Planet Formation Page

My planet formation research has focused on the growth and dynamics of solid bodies with sizes of order 1 km. I have also done work looking at late stage (>1000 km) growth which is summarized on my Astrobiology page. To study 1 km "planetesimal" growth, I use an N-body code (which calculates the gravitational interaction among all particles) called PKDGRAV, written by Joachim Stadel, Thomas Quinn, and Derek Richardson. This code is designed to run in parallel, and I therefore use supercomputers like Lemeiux at the Pittsburgh Supercomputer Center and Columbia at the NASA Advanced Supercomputing Division. I am also collaborating with Jack Lissauer.

Direct simulations of 1 km planetesimal growth is tricky because there are over 3 trillion of them in the region that now spans the orbits of Mercury to Mars. Derek and colleagues completed the largest simulation to date with 1 million 100 km particles. That's a LOT less than 3 trillion, so we examine small pieces of the disk that contain about 100,000 particles. Ideally these patches are representative of the whole disk, but variations may well be present. However we are confident that our results are accurate until the total number of particles has been halved. So far we have looked only at patches located at 0.4 AU and 1.0 AU.

At 0.4 AU we ran trials with a few different initial conditions. Our nominal simulation begins with 1 km particles that have a random velocity equal to the escape velocity. Two others have random velocities equal to 1/2 and 2 times the escape speed. We call these simulations P₁, P_0.5, and P₂, respectively. The P stands for "Perfect accretion", which means that when two particles touch they instantly turn into a sphere that has a mass equal to the sum of the two colliders. P₁ begins with ~100,000 particles, but the others begn with ~25,000.

In Fig. 1 we plot the mass distribution of particles for the three simulations at the time that the number of bodies was halved. Fig. 2 shows the evolution of the growth of the largest body. Note that the time to halve the number of particles also correlates with the initial mean velocity of the particles. In Fig. 3 we follow the evolution of the escape speed of the largest body and the typical random velocity. The random velocities increase, but not as fast as the largest escape speed.

Fig. 1 - The mass spectrum of particles at 0.4 AU when the total number of particles had been halved. For lower velocity distribution, more massive bodies appear. N(m) is the number of particles of a given mass, and m₁ is the mass of a 1 km planetesimal.

Fig. 2 - Growth rate of the largest particle in each simulation. For smaller random velocities, growth proceeds more quickly (consistent with Fig. 1). Note that the curves end when the total number of particles has been halved. Therefore the growth timescale seems to correlate with initial random velocities as well.

Fig 3. - Evolution of the largest particle's escape speed relative to the typical random velocity (v_RMS). In all cases the two curves are diverging, suggesting that the largest particle's growth rate will accelerate, since growth rate is proportional to (v_esc/v_RMS)².

Results at 1 AU are coming.

So what does all this mean? We are now capable of realistically modeling the growth of 1 km bodies. This represents a resolution increase of 1,000,000 (the ratio of masses of 100 km to 1 km bodies). Therefore we can go back to a much earlier epoch than any other simulation of planet formation. Additionally we have demonstrated that the patch framework is a viable method to simulate planet growth. In the future we can use it to tackle related problems in planet formation, focusing on small regions of the protoplanetary disk.


Last Update: 1 Aug 2007