The late stage formation of planetary systems has a crucial impact on the final system configuration. A deep understanding of the architecture of both RV-detected systems and transit-detected systems is particularly important to get a unified vision of planetary system formation.
In this session we address the question of the formation, dynamical evolution and stability of planetary systems in a broad sense, including the effects of planet-disc interactions, resonances, high eccentricity migration, binary stars,...
Observations of the Rossiter-McLaughlin effect have revealed that the orbits of many exoplanets are misaligned with respect to the stellar rotation axis. Various scenarios have been proposed that associate the orbit obliquity either with multi-body interactions or dynamical processes in the disc during the planet formation process. In this talk, I will present how infrared interferometry allows us to study the origin of the planet obliquity:
In the first part of the talk I will present observations that reveal the recently-posted disc tearing effect, where the gravitational torque of companions on misaligned orbits can tear the disc apart into distinct rings that precess independently around the central objects. We imaged the triple system GW Orionis using VLTI, CHARA, ALMA, SPHERE, and GPI and discover three rings in thermal light and an asymmetric structure with radial shadows in scattered light. The inner-most ring is eccentric (e=0.3; 43 au radius) and strongly misaligned both with respect to the orbital planes and with respect to the outer disc. Modelling the scattered light signatures and the shape of the shadows cast by the misaligned ring allows us derive the shape and 3-dimensional orientation of the disc surface, revealing that the disc is strongly warped and breaks at a radius of about 50 au. Based on the measured triple star orbits and disc properties, we conducted smoothed particle hydrodynamic simulations which show that the system is susceptible to the disc tearing effect. The ring offers suitable conditions for planet formation, providing a mechanism for forming wide-separation planets on highly oblique orbits. Our results imply that there may exist a significant, yet undiscovered population of long-period planets on highly oblique orbits that has formed around misaligned multiple systems.
In the second part I will show how infrared interferometry can be used to search for this predicted population of wide-separation planets on oblique orbits, probing a highly complementary regime to the parameter space accessible with the Rossiter-McLaughlin effect. I will present the first study where the spin-orbit alignment has been measured for a directly-imaged exoplanet, namely on Beta Pictoris b. We used VLTI/GRAVITY spectro-interferometry with an astrometric accuracy of 1 microarcsecond to measure the photocenter displacement associated with the stellar rotation. Taking inclination constraints from astroseismology into account, we constrain the 3-dimensional orientation of the stellar spin axis and find that Beta Pic b orbits its host star on a prograde orbit with a small obliquity angle.
I will conclude by offering a near-term perspective on how infrared interferometry with the proposed BIFROST beam-combination instrument could advance our understanding of the planet formation process and of the early dynamical evolution of exoplanetary systems.
How to cite:
Kraus, S.: The origin of the obliquity in planetary systems studied with infrared interferometry, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-61, https://doi.org/10.5194/epsc2020-61, 2020.
Stars born in clusters are subject to frequent stellar flybys and so are their planets. The influence of an encounter reaches beyond the brief flyby itself in that the mutual forcing between the planets will continue to shape the planetary system in the long term and in a way that is impossible without the encounter in the first place. As a consequence, different planetary systems of different orbital scales and mass ranges behave differently as a result of the encounters.
Here we study the encounters between two planetary systems where each star has its own planets using N-body simulations. Besides the immediate effect of the encounter, we have also propagated the systems post-encounter for up to 10^8 yr. See Figure 1 for an illustration.
We find that immediately during the encounter, a planet can be ejected from its original host star. Here, the interplanetary interactions are negligible and a planet’s stellar-centric distance is a key factor. Only encounters closer than a few times that distance can cause strong disturbances, e.g., to eject the planet or to break the resonance in multi-planet systems. This means that close-in (<1 au) planets are, to a large extent, immune to such flybys and so are the orbital resonances among these planets because encounters as close as a few au are very rare. Wide-orbit planets, in contrast, are especially susceptible. Take the HR 8799 system for example; the odds for an encounter at 100s of au to disrupt the systems are still about 50%. Hence, wide-orbit multi-planet systems probably do not originate in dense clusters.
Then, during the long-term post-encounter evolution, the interplanetary forcing takes control and the planets’ masses, intertwined with orbital spacing, play an important role. In general, the larger the angular momentum deficit (AMD) a system acquires immediately during the encounter, the more likely and the earlier it becomes unstable in this later phase. The eccentricity change during the encounter is not related to the planetary mass. Hence, if a multi-planet system has the more massive planets farther-out, this system gains more AMD during the encounter and is more prone to later instability than one with massive planets closer-in.
In unstable planetary systems, usually the less massive planets are lost; in systems of no mass hierarchy, all planets are equally vulnerable. Both interplanetary scattering and a stellar encounter can cause the loss of a planet in a multi-planetary system (Figure 2). We find that the encounters are in general gentler in the sense that the outer planet can be instantly ejected without disturbing the inners much, leading to a lower eccentricity distribution for the survivors. On the contrary, interplanetary scattering gives rise to significantly more excited systems.
During the encounter, a planet can also be captured by the intruder. The captured planets intensify the post-encounter instability (Figure 3) of the planetary system of the intruder and they themselves are often lost. Otherwise, a massive captured planet on a wide orbit can tilt the inner tightly-packed original planets via the Kozai-Lidov mechanism. This creates a ``cold'' system with small eccentricities and low mutual-inclinations which as a whole highly is inclined with respect to the equator of the central star. Finally, the captured planets usually acquire highly-eccentric and -inclined orbits and half are retrograde.
Full details can be found in Li, Mustill & Davies (2019, MNRAS, 488, 1366; 2020, MNRAS in press, doi: 10.1093/mnras/staa1622).
The authors acknowledge financial support from Knut and Alice Wallenberg Foundation (2014.0017 and 2012.0150) and from Vetenskapsrådet (2017-04945). The authors also thank the Royal Physiographic Society of Lund.
How to cite:
Li, D., Mustill, A., and Davies, M.: Flyby encounters between two planetary systems, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-228, https://doi.org/10.5194/epsc2020-228, 2020.
Robust evidence of an ice giant planet shedding its atmosphere around the white dwarf WD J0914+1914 represents a milestone in exoplanetary science, allowing us to finally supplement our knowledge of white dwarf debris discs, minor planets and metal pollution with the presence of a major planet.
Here, I discuss the possible dynamical origins of this planet, WD J0914+1914 b. The very young cooling age of the host white dwarf (13 Myr) combined with the currently estimated planet-star separation of about 0.07 au imposes particularly intriguing and restrictive coupled constraints on its current orbit and its tidal dissipation characteristics. The planet must have been scattered from a distance of at least a few au to its current location, requiring the current or former presence of at least one more major planet in the system in the absence of a hidden binary companion. I show that WD J0914+1914 b could not have subsequently shrunk its orbit through chaotic f-mode tidal excitation (characteristic of such highly eccentric orbits) unless the planet was or is highly inflated and possibly had partially thermally self-disrupted from mode-based energy release. I also demonstrate that if the planet is currently assumed to reside on a near-circular orbit at 0.07 au, then non-chaotic equilibrium tides impose unrealistic values for the planet's tidal quality factor. I conclude that WD J0914+1914 b either (i) actually resides interior to 0.07 au, (ii) resembles a disrupted `Super-Puff' whose remains reside on a circular orbit, or (iii) resembles a larger or denser ice giant on a currently eccentric orbit. Distinguishing these three possibilities strongly motivates follow-up observations.
I will also analyse the prospects for exterior extant rocky asteroids, boulders, cobbles, and pebbles to radiatively drift inward past the planet due to the relatively high luminosity of this particularly young white dwarf, and I will place stability bounds on the gas disc formed from the planet's evaporated atmosphere.
Caption: Demonstration that WD J0914+1914 b was very unlikely to have experienced high-eccentricity chaotic tidal evolution unless the planet is or was a highly inflated Super-Puff. The solid curves represent the minimum initial semimajor axes (y-axis) for which different types of planets would have experienced chaotic tidal evolution around the white dwarf for given orbital pericentres (x-axes). The vertical dashed lines are representative white dwarf tidal disruption radii for each type of planet, ordered from left to right in the same way as the solid curves. Because Super-Puffs are particularly vunerable to self-disruption through chaotic tides, current observations may be of a partially or fully disrupted ice giant.
How to cite:
Veras, D. and Fuller, J.: The dynamical history and current orbital constraints of a milestone ice giant planet orbiting a white dwarf, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-239, https://doi.org/10.5194/epsc2020-239, 2020.
Alexandre Emsenhuber, Christoph Mordasini, Michel Mayor, Maxime Marmier, Stéphane Udry, Lokesh Mishra, Yann Alibert, Willy Benz, and Erik Asphaug
Understanding planetary formation is principally a theoretical task. However, the relevant processes that occur during this phase are poorly constrained, from how solids grow from dust to Earth-like planets or cores of giant planets, to how planetary migration affects the architecture of the systems. To determine if these model represent the reality, we need to compare them with observations.
Planetary formation and evolution models have many unknowns. As individual systems of extrasolar planets provide a low number of data, the comparison has to be performed at the population level to provide meaningful constraints on the models. Here, we present a framework for this purpose. It encompasses the Bern global model of planetary formation and evolution, the distribution of protoplanetary disc properties to perform planetary population synthesis, and the comparison of the synthetic planetary population with the combined Coralie-HARPS GTO survey .
The Generation III Bern model is a global model of planetary formation and evolution . It tracks the relevant processes that occur during the formation and evolution of planetary systems.
The formation stage tracks the evolution of a viscous accretion disc, whose viscosity is provided by the standard α-parametrisation. Solids are represented by planetesimals, whose dynamical state is given by the drag from the gas and the stirring from the other planetesimals and the growing protoplanets.
A fixed number of protoplanetary seeds (1-100) are placed at the beginning of the formation. These protoplanets accrete planetesimals from the disc and cores of other protoplanets core upon collision. The gaseous envelope's structure is retrieved by solving the standard 1D internal structure equations. They allow to retrieve the envelope mass and the gas accretion rate (in the attached phase), or the radius (in the detached phase). The formation stages also include gas-driven planetary migration and the gravitational interactions between the protoplanets by means on an N-body.
Once the formation stage is finished, the model transitions to the evolutionary phase, where planets are followed individually to 10 Gyr. The planetary evolution model includes thermodynamical evolution (cooling and contraction), atmospheric escape, bloating, and migration due to tides raised on the star.
This model is used to compute a synthetic population of planetary systems. Observational data are used to constrain the initial conditions of the protoplanetary disc: their mass, metallicities (i.e. dust to gas ratio), radial extend and life times . We selected the same number of systems as in the combined Coralie-HARPS GTO survey sample (822) so that we can also compare the absolute number of planets. We assume that each system is observed from a random direction to compute the inclination of the orbit of each planet. This enables to compute the effective mass Msin(i) of the planet. The detection probability of each planet is computed from completeness curves of the survey .
In the synthetic population, we detect 317 planets while 161 planets were detected in the actual combined Coralie-HARPS sample. Hence, the model forms about twice the number of planets that are observed. Nevertheless, the multiplicity (i.e. the mean number of planets per system) is similar in the two populations: The 317 synthetic planets are found around 204 stars, while the actually observed 161 planets are distributed in 102 systems. this indicates that the system architectures are more similar than the absolute frequencies.
The mass-period diagram (Figure 1) shows the planets in the synthetic population (black circles) and the ones found in the Coralie-HARPS survey (red circles). The two populations have similar clusters on super Earths at about 10 days and giant planets at about 1000 days. However, the synthetic planets are more concentrated in these regions and there are relatively few synthetic planets in between or hot-Jupiters.
The mass histogram (Figure 2) shows for the synthetic population (black), the observed sample (red), and the synthetic population scaled so that it has the same total value as the observed sample (blue). It reveals that both super-Earths and giant are too numerous in the synthetic population. However, there is disproportionately more giant planets coupled to a lack of Saturn-mass planets in the synthetic population.
The whole framework provides a powerful framework to quantitatively constrain models of planetary formation and evolution. We obtained that our model  is too efficient by a factor two in absolute terms, although the mean multiplicity is similar in the two samples (synthetic and observed). This excess of planets is caused by an overabundance of giant planets coupled with a relative lack of planets at intermediate masses (20 to 200 MEarth), which suggest that the gas accretion rate in our model is too high.
It is possible to statistically compare many more quantities, such as eccentricity or stellar parameter like its metallicity to see if the metallicity effect (e.g., ) is retrieved in the synthetic population. Also, different system architectures or (anti)correlated occurrence of different planet types can be compared. We will present these results during the conference.
In case the synthetic population does not retrieve the trends of the observed sample, it means that the formation model needs to be modified. Once the observed population can be satisfactorily reproduced, we can 1) determine how the physical processes work to form exoplanetary systems and 2) make predictions about the underlying population.
Our global model predicts the quantities necessary for comparison with different observational techniques, such as radius for transits and luminosity for direct imaging. We have parallel efforts to perform comparison with other surveys, such as Kepler [5,6] or SPHERE .
 Mayor, M. et al. arXiv:1109.2497 (2011)
 Emsenhuber, A., Mordasini, C., Burn, R., Alibert, Y., Benz, W., and Asphaug, E.: NGPPS I. A&A (subm.)
 Emsenhuber, A., Mordasini, C., Burn, R., Alibert, Y., Benz, W., and Asphaug, E.: NGPPS II. A&A (in prep.)
 Adibekyan, V. Geosciences, 9, 105 (2019).
 Mulders, G. D. et al. ApJ, 887, 157 (2019).
 Mishra, L. et al. EPSC abstract (2020)
 Vigan, A. et al. A&A (subm.)
How to cite:
Emsenhuber, A., Mordasini, C., Mayor, M., Marmier, M., Udry, S., Mishra, L., Alibert, Y., Benz, W., and Asphaug, E.: The New Generation Planetary Population Synthesis (NGPPS): Comparison with the HARPS GTO survey, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-339, https://doi.org/10.5194/epsc2020-339, 2020.
About half of the Sun-like stars are part of multiple-star systems. To date more than 100 planets are known moving around one stellar component of a binary star (S-type planets), with diverse eccentricities. These discoveries raise the question of their formation and long-term evolution, since the stellar companion can strongly affect the planet formation process. Here we study the dynamical influence of a wide binary companion on the (Type-II) migration of a single giant planet in the protoplanetary disk. Using a modified version of an N-body integrator adapted for binary star systems and adopting eccentricity and inclination damping formulae (derived from hydrodynamical simulations) to properly model the influence of the disk, we carried out more than 3500 numerical simulations with different initial configurations and study the dynamics of the systems up to 100 Myr. Particular attention is paid to the Lidov-Kozai resonance whose role is determinant for the evolution of the giant planet, although initially embedded in the disk, when the stellar companion is highly inclined. We highlight the high probability for the planet of experiencing, during the disk phase, a scattering event or an ejection due to the presence of the binary companion. We also show that a capture of the migrating planet in the Lidov-Kozai resonance is far from being automatic even when the binary companion is highly inclined, since only 10% of the systems actually end up in the resonance. Nevertheless, using a simplified quadrupolar hamiltonian approach, we point out that, for highly inclined binary companions, the dynamical evolutions are strongly affected by the Lidov-Kozai resonance islands, which create the pile-ups observed around – but not centred on – the pericenter values of 90° and 270° in the final distribution of the giant planets. The influence of the self-gravity of the disk on the previous results is finally discussed.
How to cite:
Roisin, A. and Libert, A.-S.: Dynamical influence of a wide binary companion on giant planet migration, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-372, https://doi.org/10.5194/epsc2020-372, 2020.
The characterization of the interplay between the inner and outer parts of planetary systems has long been impractical due to the separated detection ranges of the corresponding observation techniques. However, this gap is closing thanks to the technical improvements of the instruments and the longer observational baselines, and statistical insights are already within reach on the impact of cold Jupiters on super Earths. In this talk, I would like to present a theoretical study on the influence of an external giant planet misaligned with inner resonant planets, within the circular restricted problem. The behavior of the system depends on the relative strength between the coupling of the planets and the perturbations from the outer body. We demonstrated that mean-motion resonance strengthens the inner coupling and is very resilient to the perturbation, surviving periodic relative inclination increases of tens of degrees between the inner planets. This study has applications for the indirect detection of exoplanets, as well as the understanding of their formation and evolution, in particular the role of mean-motion resonance and relative inclinations.
How to cite:
Rodet, L. and Lai, D.: Hiding resonant planets behind a big friend, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-466, https://doi.org/10.5194/epsc2020-466, 2020.
Super-Earths are by far the most dominant type of exoplanet, yet their formation is still not well understood. In particular, planet formation models predict that many of them should have accreted enough gas to become gas giants. Here we examine the role of the protoplanetary disk in the cooling and contraction of the protoplanetary envelope. In particular, we investigate the effects of 1) the thermal state of the disk as set by the relative size of heating by accretion or irradiation, and whether its energy is transported by radiation or convection, and 2) advection of entropy into the outer envelope by disk flows that penetrate the Hill sphere, as found in 3D global simulations. We find that, at 0.1 AU, the envelope quickly becomes fully radiative, nearly isothermal, and thus cannot cool down, stalling gas accretion. This effect is significantly more pronounced in convective disks, leading to envelope mass or- ders of magnitude lower. Entropy advection at 0.1 AU in either radiative or convective disks could therefore explain why super-Earths failed to undergo runaway accretion.
Ali-Dib, Cumming, & Lin (MNRAS 2020)
How to cite:
Ali-Dib, M., Cumming, A., and Lin, D.: Stopping Super-Earths from growing into Jupiters, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-506, https://doi.org/10.5194/epsc2020-506, 2020.
With the discovery that many exoplanetary systems harbor several closely-spaced planets, questions relating to their stability have become relevant. We have integrated closely-spaced planetary systems, with the goal of quantifying their stability times over very long time scales (up to ten billion years). Each of our systems started out with five identical, Earth-mass planets orbiting a solar-mass star, with orbits being spaced as a geometric sequence, and initial eccentricities up to e = 0.05 given to either one, or all, planets. For all planets eccentric, we ran several sets of simulations: one where the initial periapses were aligned, and others with randomized (either over all azimuths or a restricted range) initial periapse angles. In all cases, the trend in system lifetimes follows a log-linear relationship between time to close encounter and initial separation (with differing slopes). We confirmed this relationship up to initial orbit separations of approximately 10 Hill radii for small eccentricity (e=0.01), and up approximately 13 Hill radii for the largest considered eccentricity (e=0.05). toOn a more granular level, we find substantial differences in life times at resonances for low eccentricity systems, but those differences are reduced in magnitude for higher eccentricities and/or randomized periapses. For systems with just one planet eccentric, the time to close encounter depends on which planet starts out eccentric: an eccentric intermediate planet typically shortens the time to close encounter compared to the same value of eccentricity given to either the inner or outer planet. If all planets start out with the same eccentricity and aligned periapses, stability is restored — such systems are on average only slightly less stable than initially circular ones. Angular momentum deficit does not appear to influence stability times, suggesting that mean motion resonances play the dominant role over secular resonances. This was checked by comparing systems with identical total angular momentum deficit for the same initial separations. We chose to compare systems with innermost planet eccentric with their corresponding systems with outermost planet eccentric (i.e., identical AMD, implying smaller initial eccentricity). Survival times were consistent with merely initial separation and eccentricity playing the dominant roles: AMD does not appear to influence the behavior of those systems. Finally, survival probabilities are calculated for any given initial separation and given time for systems where all five planets start out with eccentricity 0.05 and randomized periapses. Here we considered batches with periapses randomly chosen within 45, 90, 135, 180, and 360 degrees, respectively. A broader choice of periapse angles is inversely correlated with the appearance of clear peaks and troughs in survival times. For periapse angles chosen within the full circle, we plot probabilities of survival at some fixed given times, as a function of initial separation. We show that their trends exhibit significantly different behaviors depending on initial system eccentricity.
How to cite:
Gratia, P.: Eccentricity and the Lifetimes of Closely-Spaced Five-Planet Systems, Europlanet Science Congress 2020, online, 21 Sep–9 Oct 2020, EPSC2020-508, https://doi.org/10.5194/epsc2020-508, 2020.
The Kepler mission revealed thousands of exoplanet candidates, providing key insights into the distributions and demographics of planetary systems. Many of these planets are in multiple-transiting planet systems, which yield additional information about the correlations within planetary systems and their architectures. However, these properties are shrouded by complex detection biases, which must be properly accounted for in order to disentangle the intrinsic system architectures from the observational biases.
In He, Ford, & Ragozzine (2019, 2020), we developed an advanced forward model (SysSim) to infer the intrinsic distributions of planetary systems around FGK dwarfs, by constructing parametric models for drawing planetary systems, simulating the Kepler detection efficiency to produce synthetic observed catalogs, and comparing these catalogs to the Kepler catalog. We show that planetary systems around FGK dwarfs are clustered in periods and in sizes, as evidenced by fitting to the observed distributions of multiplicities, period ratios, and transit depth ratios. We also find that the fraction of stars with planets (with Rp > 0.5 R⊕ and 3d < P < 300d) increases significantly towards later type (cooler) stars, rising by over a factor of two from early F to mid K dwarfs. The observed multiplicity distribution can be well matched by two populations consisting of a low and a high mutual inclination component (a Kepler dichotomy).