Planetary systems in stellar clusters
Most stars in the solar neighborhood formed in some sort of cluster or association. Using N-body simulations we have measured the rate of close encounters between stars in such clusters. This is important as close encounters and also exchange encounters, where an initially single star is exchanged into a binary system, can have significant effects on the orbits of planets orbiting the stars.
By monitoring the interaction histories of each star we measure the singleton fraction in the solar neighborhood. A singleton is defined by us as
- a star which has not formed in a binary,
- a star which has not later spent time within a binary system,
- a star which has not suffered close encounters with other stars.
Here we define a close encounter as when two stars pass within 1000 au of each other. This limit roughly corresponds to the hard-soft boundary in a typical stellar cluster in the solar neighborhood. The latter terms refer to binary systems: binaries which are soft will most likely be broken up when encountering another star or binary, while a hard binary will on average become harder (i.e. more tightly bound) when encountering other stars.
From our simulations we find that out the stars which formed single in the solar neighborhood; a significant fraction are not singletons once the cluster in which they formed has dispersed. For example, the singleton fraction for stars with mass between 0.8 and 1.2 times that of the Sun's is lower than 0.9. Hence, at least 10 per cent of all solar-mass stars which formed single in the solar neighborhood has spent at least some time in a binary and/or suffered one or more close encounters with other stars.
The orbits of any planets around such stars may have been altered by the perturbing force of the other star(s). If the perturbing force is very strong (such as in a very tight binary or close encounter) one or more planets may have been ejected immediately. However, taking the example of binaries, we find from our simulations that most of the binary systems formed through exchange encounters in young stellar clusters have semi-major axes in the range 100 to 1000 au. If so the companion star is to distant to directly eject planets in a planetary system resembling the solar system. However, it is strong enough to induce strong planet-planet interactions, by perturbing the orbits of the planets slightly. Such planet-planet interactions can then lead to the ejection of one or more planets. Those planets remaining in the planetary system are then left on tighter and more eccentric orbits.
In conclusion, dynamical processes in young stellar clusters can significantly alter the planet population around the stars. Beginning with a population of solar-system-like planetary system, dynamical interactions in stellar clusters can produce at least some of the extrasolar planetary systems observed around other stars in the solar neighborhood. You can read more about this study in the refereed article Malmberg et al. 2007.
Figure 1
Venn diagram of the interaction histories for stars in a stellar cluster with
initially 700 stars and an initial half-mass radius of 0.38
pc. Only those stars which were initially single in the cluster
(468) are included. The cluster had a lifetime of about 700 Myr.
The values are the average values from the 10 realizations which
we ran for this specific cluster. As can be noted only 26 per cent of all the initially
single stars in this cluster were singletons when the cluster had dispersed. Furthermore,
about 4 per cent of the initially single stars were in a binary at some point during the
lifetime of the cluster, and 1 percent of all initially single stars were left in
binaries once the cluster had dispersed.
Figure 2
The semi-major axis, a, in au and eccentricity, e, of the binaries containing initially
single stars (crosses) formed during the lifetime of a stellar cluster with
initially 700 stars (468 initially single) and an initial half-mass radius of 0.38
pc. Those binaries which are also labeled with a circle remained bound once the cluster
had dispersed and could thus be observed in the solar neighborhood today.