O. M. Guilera

The diversity of planetary system architectures: contrasting theory with observations

In order to explain the observed diversity of planetary systems architectures and relate this primordial diversity with the initial properties of the disc where they were born, we develop a semi-analytical model for computing planetary system formation. The model is based on the core instability model for the gas accretion of the embryos and the oligarchic growth regime for the accretion of the solid cores. Two regimes of planetary migration are also included. With this model, we consider different initial conditions based on recent results in protoplanetary discs observations, to generate a variety of planetary systems. These systems are analyzed statistically, exploring the importance of several factors that define the planetary systems birth environment. We explore the relevance of the mass and size of the disc, metallicity, mass of the central star and time-scale of gaseous disc dissipation, in defining the architecture of the planetary system. We also test different values of some key parameters of our model, to find out which factors best reproduce the diverse sample of observed planetary systems. We assume different migration rates and initial disc profiles, in the context of a surface density profile motivated by similarity solutions. According to this, and based on recent protoplanetary discs observational data, we predict which systems are the most common in the solar neighbourhood. We intend to unveil, whether our Solar System is a rarity or more planetary systems like our own are expected to be found in the near future. We also analyze which is the more favourable environment for the formation of habitable planets. Our results show that planetary systems with only terrestrial planets are the most common, being the only planetary systems formed when considering low metallicity discs and which also represent the best environment for the developing of rocky, potentially habitable planets. We also found that planetary systems like our own are not rare in the solar neighbourhood, being its formation favoured in massive discs where there is not a large accumulation of solids in the inner region of the disc. Regarding the planetary systems that harbor hot and warm Jupiter planets, we found that this systems are born in very massive, metal-rich discs. Also a fast migration rate is required in order to form these systems. According to our results, most of the hot and warm Jupiter systems are composed by only one giant planet, which is also a tendency of the current observational data.

Consequences of the simultaneous formation of giant planets by the core accretion mechanism

Context. The core accretion mechanism is presently the most widely accepted cause of the formation of giant planets. For simplicity, most models presently assume that the growth of planetary embryos occurs in isolation. Aims. We explore how the simultaneous growth of two embryos at the present locations of Jupiter and Saturn affects the outcome of planetary formation. Methods. We model planet formation on the basis of the core accretion scenario and include several key physical ingredients. We consider a protoplanetary gas disk that exponentially decays with time. For planetesimals, we allow for a distribution of sizes from 100 m to 100 km with most of the mass in the smaller objects. We include planetesimal migration as well as different profiles for the surface density Σ of the disk. The core growth is computed in the framework of the oligarchic growth regime and includes the viscous enhancement of the planetesimal capture cross-section. Planet migration is ignored. Results. By comparing calculations assuming formation of embryos in isolation to calculations with simultaneous embryo growth, we find that the growth of one embryo generally significantly affects the other. This occurs in spite of the feeding zones of each planet never overlapping. The results may be classified as a function of the gas surface density profile Σ :i fΣ ∝ r −3/2 and the protoplanetary disk is rather massive, Jupiter’s formation inhibits the growth of Saturn. If Σ ∝ r −1 isolated and simultaneous formation lead to very similar outcomes; in the the case of Σ ∝ r −1/2 Saturn grows faster and induces a density wave that later accelerates the formation of Jupiter. Conclusions. Our results indicate that the simultaneous growth of several embryos impacts the final outcome and should be taken into account by planet formation models.

Planetesimal fragmentation and giant planet formation

Context. In the standard scenario of planet formation, terrestrial p lanets and the cores of the giant planets are formed by accretion of planetesimals. As planetary embryos grow the planetesimal velocity dispersion increases due to gravitational excita tions produced by embryos. The increase of planetesimal relative velocities causes the fragmentation of them due to mutual collisions. Aims. We study the role of planetesimal fragmentation on giant planet formation. We analyze how planetesimal fragmentation modifies the growth of giant planet’s cores for a wide range of plan etesimal sizes and disk masses. Methods. We incorporate a model of planetesimal fragmentation into our model of in situ giant planet formation. We calculate the evolution of the solid surface density (planetesimals plus fragments) due to the accretion by the planet, migration and fragmentation. Results. The incorporation of planetesimal fragmentation significa ntly modifies the process of planetary formation. If most of t he mass loss in planetesimal collisions is distributed in the s maller fragments, planetesimal fragmentation inhibits the growth of the embryo for initial planetesimals of radii lower than 10 km. Only for initial planetesimals of 100 km of radius, and disks greater than 0.06 M⊙, embryos achieve masses greater than the mass of the Earth. However, even for such big planetesimals and massive disks, planetesimal fragmentation induces the quickly formation of massive cores only if most of the mass loss in planetesimal collisions is distributed in the bigger fragments. Conclusions. Planetesimal fragmentation seems to play an important role in giant planet formation. The way in which the mass loss in planetesimal collisions is distributed leads to different results, inhibiting or favoring the formation of mass ive cores.

The role of the initial surface density profiles of the disc on giant planet formation: comparing with observations

In order to explain the main characteristics of the observed population of extrasolar planets and the giant planets in the Solar system, we need to get a clear understanding of which are the initial conditions that allowed their formation. To this end we develop a semi-analytical model for computing planetary systems formation based on the core instability model for the gas accretion of the embryos and the oligarchic growth regime for the accretion of the solid cores. With this model we explore not only different initial discs profiles motivated by similarity solutions for viscous accretion discs, but also consider different initial conditions to generate a variety of planetary systems assuming a large range of discs masses and sizes according to the last results in protoplanetary discs observations. We form a large population of planetary systems in order to explore the effects in the formation of assuming different discs and also the effects of type I and II regimes of planetary migration, which were found to play fundamental role in reproducing the distribution of observed exoplanets. Our results show that the observed population of exoplanets and the giant planets in the Solar system are well represented when considering a surface density profile with a power law in the inner part characterized by an exponent of −1, which represents a softer profile when compared with the case most similar to the minimum mass solar nebula model case.

Simultaneous formation of solar system giant planets

Context. In the last few years, the so-called “Nice model” has become increasingly significant for studying the formation and evolution of the solar system. According to this model, the initial orbital configuration of the giant planets was much more compact than the one we observe today. Aims. We study the formation of the giant planets in connection with several parameters that describe the protoplanetary disk. We aim to establish which conditions enable their simultaneous formation in line with the initial configuration proposed by the Nice model. We focus on the conditions that lead to the simultaneous formation of two massive cores, corresponding to Jupiter and Saturn, which are able to reach the cross-over mass (where the mass of the envelope of the giant planet equals the mass of the core, and gaseous runway starts), while two other cores that correspond to Uranus and Neptune have to be able to grow to their current masses. Methods. We compute the in situ planetary formation, employing the numerical code introduced in our previous work for different density profiles of the protoplanetary disk. Planetesimal migration is taken into account and planetesimals are considered to follow a size distribution between r min (free parameter) and r max = 100 km. The core’s growth is computed according to the oligarchic growth regime. Results. The simultaneous formation of the giant planets was successfully completed for several initial conditions of the disk. We find that for protoplanetary disks characterized by a power law (Σ ∝ r −p ), flat surface density profiles (p ≤ 1.5) favor the simultaneous formation. However, for steep slopes (p ∼ 2, as previously proposed by other authors) the simultaneous formation of the solar system giant planets is unlikely. Conclusions. The simultaneous formation of the giant planets – in the context of the Nice model – is favored by flat surface density profiles. The formation time-scale agrees with the estimates of disk lifetimes if a significant mass of the solids accreted by the planets is contained in planetesimals with radii < 1k m.

Terrestrial planets in high-mass disks without gas giants

Context. Observational and theoretical studies suggest that planetary systems consisting only of rocky planets are probably the most common in the Universe. Aims. We study the potential habitability of planets formed in high-mass disks without gas giants around solar-type stars. These systems are interesting because they are likely to harbor super-Earths or Neptune-mass planets on wide orbits, which one should be able to detect with the microlensing technique. Methods. First, a semi-analytical model was used to define the mass of the protoplanetary disks that produce Earth-like planets, super- Earths, or mini-Neptunes, but not gas giants. Using mean values for the parameters that describe a disk and its evolution, we infer that disks with masses lower than 0.15 Mare unable to form gas giants. Then, that semi-analytical model was used to describe the evolution of embryos and planetesimals during the gaseous phase for a given disk. Thus, initial conditions were obtained to perform N-body simulations of planetary accretion. We studied disks of 0.1, 0.125, and 0.15 M� . Results. All our simulations form massive planets on wide orbits. For a 0.1 Mdisk, 2-3 super-Earths of 2.8 to 5.9 M⊕ are formed between 2 and 5 AU. For disks of 0.125 and 0.15 M� , our simulations produce a 10-17.1 M⊕ planet between 1.6 and 2.7 AU, and other super-Earths are formed in outer regions. Moreover, six planets survive in the habitable zone (HZ). These planets have masses from 1.9 to 4.7 M⊕ and significant water contents ranging from 560 to 7482 Earth oceans, where one Earth ocean represents the amount of water on Earths surface, which equals 2.8 × 10 −4 M⊕. Of the six planets formed in the HZ, three are water worlds with 39%-44% water by mass. These planets start the simulations beyond the snow line, which explains their high water abundances. In general terms, the smaller the mass of the planets observed on wide orbits, the higher the possibility to find water worlds in the HZ. In fact, massive planets can act as a dynamical barrier that prevents the inward diffusion of water-rich embryos located beyond the snow line. Conclusions. Systems without gas giants that harbor super-Earths or Neptune-mass planets on wide orbits around solar-type stars are of astrobiological interest. These systems are likely to harbor super-Earths in the HZ with significant water contents, which missions such as Kepler and Darwin should be able to find.

Terrestrial planets and water delivery around low-mass stars

Context. Theoretical and observational studies suggest that protoplanetary disks with a wide range of masses could be found around low-mass stars. Aims. We analyze planetary formation processes in systems without gas giants around M3- and M0-type stars of 0.29 M ⊙ and 0.5 M ⊙ , respectively. In particular, we assume disks with masses of 5% and 10% of the mass of the star. Our study focuses on the formation of terrestrial-like planets and water delivery in the habitable zone (HZ). Methods. First, we use a semi-analytical model to describe the evolution of embryos and planetesimals during the gaseous phase. Then, a N -body code is used to analyze the last giant impact phase after the gas dissipation. Results. For M3-type stars, five planets with different properties are formed in the HZ. These planets have masses of 0.072 M ⊕ , ~0.13 M ⊕ (two of them), and 1.03 M ⊕ , and have water contents of 5.9%, 16.7%, 28.6%, and 60.6% by mass, respectively. Then, the fifth planet formed in the HZ is a dry world with 0.138 M ⊕ . For M0-type stars, four planets are produced in the HZ with masses of 0.28 M ⊕ , 0.51 M ⊕ , 0.72 M ⊕ , and 1.42 M ⊕ , and they have water contents of 26.7%, 45.8%, 68%, and 50.5% by mass, respectively. Conclusions. M3- and M0-type stars represent targets of interest for the search of exoplanets in the HZ. In fact, the Mars-mass planets formed around M3-type stars could maintain habitable conditions in their early histories. Thus, the search for candidates around young M3-type stars could lead to the detection of planets analogous to early Mars. Moreover, Earth-mass planets should also be discovered around M3-type stars and, sub- and super-Earths should be detected around M0-type stars. Such planets are very interesting since they could maintain habitable conditions for very long.

Giant planet formation at the pressure maxima of protoplanetary disks

Context. In the classical core-accretion planet formation scenario, rapid inward migration and accretion timescales of kilometer size planetesimals may not favour the formation of massive cores of giant planets before the dissipation of protoplanetary disks. On the other hand, the existence of pressure maxima in the disk could act as migration traps and locations for solid material accumulation, favoring the formation of massive cores. Aims. We aim to study the radial drift of planetesimals and planet migration at pressure maxima in a protoplanetary disk and their implications for the formation of massive cores as triggering a gaseous runaway accretion phase. Methods. The time evolution of a viscosity driven accretion disk is solved numerically introducing a a dead zone as a low-viscosity region in the protoplanetary disk. A population of planetesimals evolving by radial drift and accretion by the planets is also considered. Finally, the embryos embedded in the disk grow by the simultaneous accretion of planetesimals and the surrounding gas. Results. Our simulations show that the pressure maxima generated at the edges of the low-viscosity region of the disk act as planet migration traps, and that the planetesimal surface densities are significantly increased due to the radial drift towards pressure maxima locations. However, our simulations also show that migration trap locations and planetesimal accumulation locations are not exactly at the same positions. Thus, a planets semi-major axis oscillations around zero torque locations, predicted by MHD and HD simulations, are needed for the planet to accrete all the available material accumulated at the pressure maxima. Conclusions. Pressure maxima generated at the edges of a low-viscosity region of a protoplanetary disk seem to be preferential locations for the formation and trap of massive cores.

Planetary Systems formation and the diversity of Extrasolar Systems

With the end of answer questions as, how common are planetary systems like our own in the Universe? and What is the diversity of planetary systems that we could find in the universe?, we develop a semi-analytical model for computing planetary systems formation and consider different initial conditions for generating a large sample of planetary systems, which is analysed statistically. We explore the effects in the planetary system architecture of assuming different initial disc profiles and planetary migration rates.

Simultaneous formation of Jupiter and Saturn

At present, the core instability mechanism is usually considered as the way giant planets formation proceeds. There are available complex models to describe the formation of Jupiter and Saturn; however, all this models assume the isolated formation for each planet. We developed a model to describe the simultaneous formation of giant planets by the core instability mechanism and considering the oligarchic growth regime for the accretion of planetesimals. We consider a density distribution for the size of planetesimals, with radii between 100 m and 100 km, for which most of the mass of solids is in the small ones. Also, we consider planetesimals migration. The planets are immersed in a realistic protoplanetary disk that evolves in time. The evolution of the disk affects the growth capacity of the immersed planets in it. Furthermore, the same disk is the physical system through which the “planetplanet” interaction is produced. Here we not refer merely to the gravitational interaction but to the modification of the populations of planetesimals due to the presence of several planetary masses. These masses force the migration of the planetesimals modifying its surface densities, so a planet will affect the availability of material from which the remaining planets may feed in a formation system. We present the most important results of our model applied to the case of the simultaneous formation of Jupiter and Saturn. We found that, within the classical model of solar nebula (Hayashi, 1981), the isolated formation of Jupiter and Saturn undergoes significant change when it occurs simultaneously.