For a full up-to-date list, see ADS. Some recent results below.

Hydrodynamics on Triangles

The vast majority of visible matter in the Universe is in gaseous form, and its dynamics is therefore governed by the equations of hydrodynamics. In many cases, solutions to the equations can only be obtained by numerical simulations. One would like the numerical method to be as flexible as possible. For mesh-based methods, unstructured triangular meshes offer a lot of freedom, and have the benefit of allowing a multidimensional extension to Roe's approximate Riemann solver. I have implemented these ideas into an open source package ASTRIX, which is targeted to run on Graphics Processing Units.

Paardekooper, S.-J., 2017, MNRAS, 469, 4306 (arXiv)


Depth of planetary gaps

Massive planets carve out gaps in protoplanetary discs. This is one of these weird disc situations where gravity acts as a repulsive force: the planet pushes material away from its orbit, leaving a low-density gap. This has been known since the 70s, but what exactly sets the depth of these gaps? In simple 1D calculations, the gaps are completely empty. In more realistic 2D simulations, they are far from empty, although the density is reduced by a few orders of magnitude. Why this difference? Paul Hallam and myself tried to shed some light on this issue by looking at simulations where we put the 1D approximation for the gravitational field of the planet into a 2D simulation. As long as the disc is not perfectly axisymmetric to begin with, the steep gap edges become unstable and these instabilities keep refilling the gap, leading to gap depths that come close to the 2D results. Therefore, it seems that gap edge instabilities play a role in determining the depths of planetary gaps.

Hallam, P.D., Paardekooper, S.-J., 2017, MNRAS, 469, 3813 (arXiv)

We have a neighbour!

Our nearest neighbour star Proxima Centauri has a planet! It may even be habitable...

Anglada-Escude, G., et al. 2016, Nature, 536, 437 (arXiv)

Retrograde binary black holes

Supermassive black hole binaries may form as a consequence of galaxy mergers. Interestingly, both prograde and retrograde orbits are possible. We study a binary of small mass ratio immersed in and interacting with a gaseous accretion disc in order to estimate time scales for inward migration. Movies on the left and right show the evolution of the surface density with a companion mass ratio of 0.01. Top panels show azimuthally averaged values ov the surface density (solid line) and disc eccentricity (dotted line). Bottom panels show the 2D surface density evolution. The left movie shows the initial interaction at high cadence, while the right movie shows the long term evolution and gap formation.

Ivanov, P. B., Papaloizou, J.C.B., Paardekooper, S.-J. and Polnarev, A.G., 2015, A&A, 576, 29 (arXiv)

The curious case of Kepler-36

Exotic planetary systems can be found around other stars. One example is Kepler-36, where two planets orbit extremely close to one another. The planet closest to the star is a Super-Earth, while just slightly further away a Neptune-type planet can be found. If London was located on the Super-Earth, the other planet would, at closest approach, appear twice as big as our full moon! It turns out to be very difficult to form such a planetary system. How can we get two such very different planets extremely close together? We found that convergent planet migration in a turbulent protoplanetary disc can do the job. Because the outer planet is more massive than the inner one, it migrates faster towards the star, bringing the planets close together. Turbulence in the disc helps to break low-order resonances, while damping caused by the disc keeps the system stable. 

Paardekooper, S.-J., Rein, H. and Kley, W. 2013, MNRAS, 434, 3018 (arXiv)

Planet or brown dwarf?

Massive planets open up gaps in protoplanetary discs. Gaps, or even inner holes, are commonly observed in discs around young stars. It would of course be very interesting to link such a gap to a planet. It is possible, using interferometric observations, to get information on the shape of the gap. This can then be linked, using hydrodynamic simulations, to the possible range of masses for the planet. In the particular case of HD 100546, we found that these observations can only be explained by a very massive planet, more like a Brown Dwarf.

Mulders, G., Paardekooper, S.-J., Panic, O., Dominik, C., van Boekel, R. and Ratzka, T. 2013, A&A, 557, A68 (arXiv)

How not to build Tatooine

A recently discovered class of extreme planets resembles Tatooine from Star Wars: these planets do not orbit just one star, no, they have two! These circumbinary planets are important test cases for planet formation theory. Close to the two stars, it is very difficult to form planets: the gravitational pull from the two stars make for a very hostile environment. Even in the most favourable circumstances, we have not been able to account for these planet at the location where they are observed right now. We therefore conclude that it is more likely that such planets were formed further away from the two stars, and subsequently migrated inward to their current location.

Paardekooper, S.-J., Leinhardt, Z. M., Thebault, P. and Baruteau, C. 2012, ApJL, 754, L16 (arXiv)