Research

My research focuses on the formation and evolution of (extrasolar) planets. Below, I will describe some recent projects.

Planetesimal and gas dynamics in binaries
Evolution of low-mass planets in non-isothermal discs

Planetesimal and gas dynamics in binaries

The majority of stars in the Milky Way are part of a multiple system, in which two or more stars orbit each other. This work focuses on planet formation in a system with two stars on a relatively close orbit. In particalar, we are interested in relative velocities between planetesimals (the builing blocks of terrestrial planets) in a circumprimary disc for such a system. If we want to grow planets from these building blocks, relative velocities had better be small, otherwise collisions between planetesimals would lead to their destruction rather than growth. This is an interesting problem, because we do find planets in these highly perturbed systems.

The gravitational perturbation of the (eccentric) binary puts the planetesimals on eccentric orbits. At first, neighbouring planetesimals will be on almost similar orbits, which leads to small relative velocities. At a later stage, orbital crossing may occur. Gas drag plays an important role in this problem, because the strength of the drag depends on the size of the planetesimal. This leads to differential orbital phasing: although at first, neigbouring planetesimals of equal size are on almost similar orbits, this will not be the case for different sized bodies. This leads to high relative velocities even before orbital crossing occurs.

Previous studies treated the gas disc as being staic and circular. In reality, the gas disc is also perturbed by the binary. We show that it is the eccentricity of the gas disc that plays a major role in determining the relative velocities between planetesimals. For a favourable gas eccentricity, there may be no differential orbital phasing at all. This would make planet formation in a close binary system relatively easy. However, our hydrodynamical simulations show that this situation does not occur in practice. In fact, the full non-linear evolution of the gas disc leads to even higher encounter velocities between planetesimals. It is therefore not yet clear how planets can form in close binary systems.

Further reading:

Paardekooper, S.-J., Thebault, P. and Mellema, G.
Planetesimal and gas dynamics in binaries
2008, MNRAS, in press

Thebault, P., Marzari, F. and Scholl, H.
Relative velocities among accreting planetesimals in binary systems: The circumprimary case
2006, Icarus, 183, 193

Evolution of low-mass planets in non-isothermal discs

Planets are formed in circumstellar discs of gas and dust around young stars. During the early stages of their lifes, these discs are still around and planets interact gravitationally with them. This interaction may lead to large changes in the mass and orbit of the planet, and is therefore crucial in linking the observed, present-day orbital distribution of planets to the process of planet formation.

For low-mass planets, the interaction between planet and disc is linear, and it is usually found that in this case planets move inward, at a rate proportional to their mass. This is called Type I migration, and may well prove fatal for planets of a few times the mass of the Earth, because Type I migration rapidly takes them into the central star.

One aspect that is usually ignored is the heating and cooling balance in the disc. A locally isothermal equation of state is then adopted, which makes the temperature a constant function of the distance to the central star. This equation of state is appropriate when the disc is able to radiate away all excess heat very efficiently. However, this assumption may not hold in the region where planets are supposed to form, because the disc is very optically thick from typically 1-10 AU. This makes it hard for the disc to cool efficiently.

If we want to release the locally isothermal assumption, it becomes necessary to perform radiation-hydrodynamical simulations in order to account for the heating and cooling balance. Surprisingly, simulations then show a torque reversal when cooling is inefficient. Planets start to move outward! Only in regions of low density, where the disc can cool efficiently, does one recover inward Type I migration.

Further reading:

Paardekooper, S.-J. and Mellema, G.
Growing and moving low-mass planets in non-isothermal disks
2008, A&A, 478, 245

Paardekooper, S.-J. and Mellema, G.
Halting Type I migration in non-isothermal disks
2006, A&A, 459, L17