Planets are formed in “protoplanetary disks” composed of gas and dust orbiting a central star. Once a planet has formed in the disk, the radius of its orbit can change due to gravitational forces between the planet and material in the disk. In this way, planets can migrate from their original location, a phenomenon that can explain the diversity of exoplanets (an exoplanet is a planet outside our Solar System). For more on the diversity of exoplanets, please refer to my earlier post.
In our Solar System, all the planets most likely achieved their current locations after some history of migration. Consider, for example, the migration of Uranus and Neptune, illustrated in Figure 1.
The migration of planets can be directed inward towards their star, or outwards away from their star. Planets with masses similar to Neptune and Jupiter, called Jovian planets, typically migrate inward. This inward migration of Jovian planets can explain the existence of “hot-Jupiters,” planets as massive as Jupiter with orbits smaller than that of Mercury because they are close to the sun. Similarly, other types of objects in a planetary system, such as dwarf planets and asteroids, can also migrate. Thus, planetary systems continue to evolve even after they form! This migration of objects in a planetary system appears to be an intrinsic phenomenon of planetary systems.
As a graduate student in astronomy, the focus of my work was to understand the evolution of planetary systems when the protoplanetary disk is young and still filled with gas. The younger the disk, the more gas it has; and during the disk’s early evolution, the gas strongly affects the planet’s orbit and migration. I only considered low mass objects (Saturn-mass or lower), as these are likely to be more affected by the disk environment than the high mass objects like Jupiter. To give you an idea of relative masses of these planets, 1 Saturn mass = 95 Earth masses, 1 Jupiter mass = 318 Earth masses, and 1 Earth mass = 6 trillion trillion kg (or 6*10^24 kg in scientific notation). This means that Saturn has approximately 30% of the mass of Jupiter.
To study migration of low-mass objects in a young planetary system, and to check how the initial position of the object affects its migration, I inserted 240 planets (or objects) into a simulated disk (see Figure 2). At the end of this “migration simulation,” 131 planets migrated inward and 109 planets migrated outward (see Figure 3). Figure 4 shows a toy model of what happened in the simulation. The simulations and their analyses were done on the IU supercomputers Karst and Bigred2.
We can better understand the nature of migration of low-mass planets in the young planetary system studied in this work, by applying the concepts developed in the early 1900s by Einstein. Einstein discussed the classical diffusion of particles, correlating particle diffusion with the diffusion coefficient and time . I calculated a diffusion coefficient for the planets, and obtained the typical diffusion distance of an object as a function of time in the disk. A larger diffusion coefficient would mean that planets migrate faster and vice versa. Here is a generic example of how anything can diffuse in a medium: If you add a drop of ink in water, it would “diffuse” or spread in the water as time progresses. The relevant coefficient of diffusion would determine the rate of the movement of ink in the water.
Studying the diffusion process in the disk helps us to understand the so-called “chaotic” motion of low-mass objects. Chaos in this context refers to the irregular behavior in the orbital evolution of objects (asteroids, comets, and interplanetary dust) in the Solar System . Chaotic diffusion causes dispersion of Trojan asteroids — asteroids orbiting our Sun from the same distance as Jupiter .
According to the diffusion coefficient I obtained, it takes about 500,000 years for an average low-mass object to diffuse approximately 60 astronomical units (AU), where 1 AU is the distance between Earth and the Sun. In this time a low-mass object can grow larger by accreting matter. This way once planets are born, they can move away and evolve. Therefore, solar systems evolve and change! Having a better understanding of the diffusion of objects during the early evolution of a planetary system helps us to understand the architecture of planetary systems, the diversity of exoplanets, and the nature of the universe in which we live.
- Einstein, A. 1905, Annalen der Physik, 322, 549
- Malhotra, R., Holman, M., & Ito, T. 2001, Proceedings of the National Academy of Science, 98, 12342
- Benest, D., Froeschle, C., & Lega, E., eds. 2007, Lecture Notes in Physics, Berlin Springer Verlag, Vol. 729, Topics in Gravitational Dynamics Solar, Extra-Solar and Galactic Systems