Comparing HARPS and Kepler surveys:
The alignment of multiple-planet systems

P. Figueira, M. Marmier, G. Boué, C. Lovis, N. C. Santos, M. Montalto, S. Udry, F. Pepe, M. Mayor

Abstract
Context. The recent results of the HARPS and Kepler surveys provided us with a bounty of extrasolar systems. While the two teams analyzed extensively each of their data-sets, little work has been done comparing the two.
Aims. We study a subset of the planetary population whose characterization is simultaneously within reach of both instruments. We compare the statistical properties of planets in systems with msin i >5-10M_⊕ and R>2 R_⊕, as inferred from HARPS and Kepler surveys, respectively. If we assume that the underlying population has the same characteristics, the different detection sensitivity to the orbital inclination relative to the line of sight allows us to probe the planets’ mutual inclination.
Methods. We considered the frequency of systems with one, two and three planets as dictated by HARPS data. We used Kepler’s planetary period and host mass and radii distributions (corrected from detection bias) to model planetary systems in a simple yet physically plausible way. We then varied the mutual inclination between planets in a system according to different prescriptions (completely aligned, Rayleigh distributions and isotropic) and compared the transit frequencies with one, two or three planets with those measured by Kepler.
Results. The results show that the two datasets are compatible, a remarkable result especially because there are no tunable knobs other than the assumed inclination distribution. For msin i cutoffs of 7-10M_⊕, which are those expected to correspond to the radius cutoff of 2 R_⊕, we conclude that the results are better described by a Rayleigh distribution with mode of 1° or smaller. We show that the best-fit scenario only becomes a Rayleigh distribution with mode of 5° if we assume a rather extreme mass-radius relationship for the planetary population.
Conclusions. These results have important consequences for our understanding of the role of several proposed formation and evolution mechanisms. They confirm that planets are likely to have been formed in a disk and show that most planetary systems evolve quietly without strong angular momentum exchanges such as those produced by Kozai mechanism or planet scattering.

Keywords
planetary systems – techniques: radial velocities – techniques: photometric – surveys – methods: numerical – methods: statistical

Astronomy and Astrophysics
Volume 541, Page A139_1
May 2012

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