However, the simple truth is that the observations do not bear this out, yielding a much broader distribution of
Norm Murray and I have been working on a different model for the origin of these planetary systems. We model
them as assembling in place from a population of smaller, rocky bodies. This provides a much better fit to the
observed distribution, as can be seen in the plot at left. The points show the distribution of period ratios of
neighbouring planets in multiple planet systems observed by the Kepler satellite. The histograms show the distribution
that results from a series of N-body assembly simulations we performed, to simulate the late-stage accumulation of
Although the simulations undercount some of the short period features, they
reproduce the breadth of the distribution much better than the migration model, which would predict isolated spikes
at values 1.5 and 2. The relevant paper can be found here .
The simulations were performed using the UCLA Hoffman2 shared computing cluster. The image at right shows my former student
Steve Berukoff and I in front of our contribution to the cluster.
The models reproduce most of the features of the observed distribution, including the absolute period distribution,
the distribution of planetary radii and the occurence ratios of systems of different multiplicity (i.e. how many systems
with two transiting planets are seen, relative to those with three transiting planets and so forth). This is a constraint
on the distribution of mutual inclinations in the systems, i.e. how well confined are the planets to the same orbital
One feature that is not reproduced by our models is the ratio of single transit systems to multiple transit systems, in the sense that Kepler observes far too many single transit systems relative to what is expected from the model. This has been termed the 'Kepler dichotomy' by other authors and may reflect the possibility that multiple modes of planet formation exist. Alternatively, this could indicate that some planetary systems are `stirred up' by the interactions with other planets in the system, and we are actively pursueing the investigation of this possibility.
The estimates from Kepler suggest that many, perhaps even most, M dwarfs harbour a close-in, low-mass planet. If that is true, then our simulations suggest that nearly every M dwarf has a planet in the habitable zone. M dwarfs are an order of magnitude more common in the Galaxy than G stars, so these imply that there is a large cohort of potentially habitable planets in the Galaxy. In particular, most of the nearby stars are low-mass, which then implies that many of the stars near to us may have a planet in the nearest habitable zone. This naturally leads one to speculations about the Fermi paradox, on which I have some thoughts but which are not ready for publication or advertisement yet!
The empirical success of these models raises some interesting questions about planet formation. If the planets do assemble in place, it means that the mass inventory in planetesimals is several times that inferred in the case of our own solar system, and likely cannot have simply sedimented out in the gas phase. This implies that some level of migration of solid material from large scales to small scales must still have occured, but that it likely happened at an earlier stage in the protoplanetary disk lifetime. I have recently begun to model this process as well, and have been able to demonstrate that we can reproduce the kinds of mass reservoirs required with a model in which micron-sized particles spiral in due to aerodynamic drag in the gaseous disk but are then expelled to larger radii by a protostellar outflow near the star. This circulation of solid material leads to a steady state distribution that matches well the initial conditions required for the later stage assembly. Such models also find some supporting evidence through measurements in our own solar system, because the Stardust Sample return mission to Comet Wild-2 found that much of the cometary material was processed at high temperatures, more consistent with the inner solar nebula than the distant, cold, cometary reservoir. The relevant paper can be found here .