Theoretical models of planetary system formation: mass vs. semi-major axis

Abstract

Context. Planet formation models have been developed during the past years to try to reproduce what has been observed of both the solar system and the extrasolar planets. Some of these models have partially succeeded, but they focus on massive planets and, for the sake of simplicity, exclude planets belonging to planetary systems. However, more and more planets are now found in planetary systems. This tendency, which is a result of radial velocity, transit, and direct imaging surveys, seems to be even more pronounced for low-mass planets. These new observations require improving planet formation models, including new physics, and considering the formation of systems. Aims. In a recent series of papers, we have presented some improvements in the physics of our models, focussing in particular on the internal structure of forming planets, and on the computation of the excitation state of planetesimals and their resulting accretion rate. In this paper, we focus on the concurrent effect of the formation of more than one planet in the same protoplanetary disc and show the effect, in terms of architecture and composition of this multiplicity. Methods. We used an N-body calculation including collision detection to compute the orbital evolution of a planetary system. Moreover, we describe the effect of competition for accretion of gas and solids, as well as the effect of gravitational interactions between planets. Results. We show that the masses and semi-major axes of planets are modified by both the effect of competition and gravitational interactions. We also present the effect of the assumed number of forming planets in the same system (a free parameter of the model), as well as the effect of the inclination and eccentricity damping. We find that the fraction of ejected planets increases from nearly 0 to 8% as we change the number of embryos we seed the system with from 2 to 20 planetary embryos. Moreover, our calculations show that, when considering planets more massive than ∼5 M ⊕ , simulations with 10 or 20 planetary embryos statistically give the same results in terms of mass function and period distribution.

Characterization of exoplanets from their formation

“…An important idealization of the syntheses presented here is that they assume that only one embryo per disk forms (see Alibert et al 2013 for the impact of the concurrent formation of many embryos). While this should not usually affect the thermodynamics of the accretion process itself, it can change the formation tracks in particular in systems where several giant planets form.…”

“…One important constraint can clearly not be met by the synthetic planets: the semimajor axes are just 0.2-16 AU, much less than the 53 AU in the observation. Here, mechanisms currently not included in the formation model must be invoked, which could be scattering (Alibert et al 2013) or a faster core growth for example via pebbles (Ormel & Klahr 2010;Bitsch et al 2015).…”

“…This will lead to a direct prediction of the magnitudes instead of the total luminosity only. Also, considering multiple embryos per disk to take their dynamical interactions into account (Alibert et al 2013) will enable us to also look at the luminosity-separation diagram, of crucial importance for direct detections. Finally, it will be interesting to perform dedicated simulations for specific recently discovered systems, tuning in particular the stellar mass and metallicity, as was done for β Pic b (Bonnefoy et al 2013).…”

Constraining the volatile fraction of planets from transit observations

“…Considering such a high amount of volatiles is probably unrealistic, but it is important to note that depending on the formation scenario of hot Neptunes, very different amounts of volatiles are expected. For a formation with migration (see, e.g., Alibert et al 2013), we expect a very high percentage of volatiles, whereas for in situ formation (e.g., Chiang & Laughlin 2013), hot Neptunes are predicted to be dry. The two considered planets do not have the same radius at any time, since the non-gaseous part of the planet has itself a different radius.…”

“…We finally considered four volatile fractions for the second population, namely 10%, 30%, 50%, and 70%. We note that some of the planets considered in these two figures may not exist in nature because no formation path leads to such an interior structure (see, e.g., Fortier et al 2013;Alibert et al 2013). …”