On the likely effect of disk self-gravity on low mass planet migration |
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On the likely effect of disk self-gravity on low mass planet migration
Since the discovery of Jupiter-like planets around nearby stars, it is commonly believed that planets form far away from their host star and migrate inwards, as a consequence of gravitational torques exerted by a gaseous disk. Spiral density waves are excited in the disk at Lindblad resonances, leading to angular momentum exchange and making the planet drift in a time much shorter than the planet formation timescale.
Two researchers (among whom A. Pierens from Paris Observatory) have for the first time determined analytically the possible effet of the disk gravity on the orbital motion of the planet, and conclude that that migration should be accelerated ! Will very high resolution numerical simulations confirm this issue ?
The first extrasolar planet was discovered ten years ago at the Observatoire de Haute Provence (Mayor et Queloz 1995,Nature 378, 355). Today, more than a hundred of planets are known (Schneider 2005, The Extrasolar Planets Encyclopaedia), and many of them rotate on a tight orbit (their semi-major axis lies between 0.01 and 1 AU). So, in comparison with planets in the Solar System, extrasolar planets have very different orbital properties. These observations are commonly explained thanks to planetary migration. In this scenario, planets and planetesimals form in the outer regions of the circumstellar disk and then migrate inwards because of the gravitational interaction with the disk (see figure 1). In the framework of the standard theory (Ward 1997, Icarus, 126, 261), migration is caused by a slight imbalance of the gravity field created by the spiral density waves. When the gravitational force exerted by the outer disk is greater than the one created by the inner disk, the planet looses angular momentum and drifts inwards. However, the migration timescale is very short and that is the reason why people seek for a mechanism able to slow down (or even stop) the migration. Several mechanisms have been proposed like the effect of the magnetic field, tri-dimensional effects, torques at corotation (where the planet rotates at the same speed as the disk particles), eccentricity effets, interaction between several planets, and so on.
Figure 1: The mechanism for type-I migration (planets much less massive than Jupiter). In this case, the interaction between the planet and the disk is linear (unlike type-II migration, which occurs when a planet can open a gap in the disk). Image © A. Pierens. Numerical simulations are a useful tool to understand planetary migration. These have confirmed that planets tend to migrate inwards in about a few hundreds of thousand years (Nelson et al. 2000, MNRAS 318, 18). Recently, the remarkable simulations by Nelson & Benz (2003, ApJ 589, 556) have recently pointed out the effect of the disk mass. Because of a lack of numerical resolution, the real effect of the disk gravity can not be clearly identified yet, and is still an unsolved problem. The main problem is that self-gravity is very time consuming, precludind high resolution numerical simulations and reliable conclusions.
Figure 2: Relative shift of Inner Lindblad resonances (ILRs) and outer Lindblad resonances (OLRs) in a homogeneous disk.
Click on the image to enlarge itTwo researchers, Arnaud Pierens (LUTh/Observatoire de Paris-Meudon) and Jean-Marc Huré (Université Bordeaux 1 and Observatoire Astronomique de Bordeaux) have shown by analytical means that, in the end, the gaseous disk should accelerate the migration of low mass planets (planets ten times less massive than Jupiter, corresponding to type-I migration). They also conclude that this result does not really depend upon the surface density profile. The effect of the disk gravity is twofold: on the one hand, the angular velocity of the planet is enhanced; on the other hand, the position of Lindblad resonances (where the amplitude of the waves is formally infinite) are shifted in comparison with the keplerian case. This analytical prediction should, hopefully, be confirmed by high resolution numerical simulations, which should take some time...
Figure 3: Lindblad torques exerted at the inner (ILRs) and outer (OLRs) Lindblad resonances in a homogeneous disk, with and without disk gravity.
Click on the image to enlarge itIn brief, if one wish to explain the presence of planets on tight orbits, a mechanism able to slow down migration must exist. It seems that the the disk mass (even small) is not the good candidate!
Reference
How does disk gravity really influence type-I migration ?
Arnaud Pierens (1), Jean-Marc Huré (2)
(1) Paris Observatory (LUTH), (2) Bordeaux Observatory
Astronomy and Astrophysics Letters, 433, L37 astro-ph/0503238
Contact
Arnaud Pierens (Observatoire de Paris, LUTH)
