Orals: Mon, 19 Sep | Room Andalucia 3
Planets form in protoplanetary discs and their interactions with the gas give rise to migration. For a long time, discs were believed to have a non-negligible viscosity to justify the high accretion rates of gas onto the central star. However, it has recently been shown observationally and theoretically that protoplanetary discs are probably much less viscous than previously thought. In our study, we use a new paradigm for the theoretical modelling of discs where the accretion onto the central star is done through the superficial layers while the mid-plane has a close to zero viscosity (Lega et al. 2022). In such discs, the migration of a single giant planet differs from the classical Type-II migration regime and depends on the thickness of the accretion layer. It is therefore interesting to consider the migration of a pair of giant planets in this new model. We have started this project, in the simplified framework of 2D hydrodynamical simulations (using the code FARGOCA) with an α viscosity parameter of 10−5 (in the standard Shakura & Sunyaev 1973 viscosity parametrization). We first consider a pair of Jupiter and Saturn mass planets, then extend our study to a wider range of planetary masses.
In classical viscous discs (corresponding to an α=10−3), Jupiter and Saturn systems are most often locked in the 3:2 mean motion resonance and may migrate outwards. Instead in our case (α=10−5), we find that the pair of planets gets locked in the 2:1 resonance and has a stalled or slightly inward migration. We confirmed this result for a range of disc masses and thicknesses as well as different starting positions of Saturn. This result is also independent of the mass of the outer planet. In order to explain our result, we have a used a criterion for resonance crossing based on Batygin, 2015 . Unlike in classical discs, a planet growing and migrating in a low viscosity disc does not reach the migration speed required to cross the 2:1 MMR. The only case in which outward migration is observed, is the "ad-hoc" scenario where Saturn would form inside the 2:1 resonance and get locked in the 3:2. However, owing to the large width of Jupiter's gap, this scenario seems unlikely.
If the Solar System formed from such a low-viscosity disc, this result has strong implications for the Grand Tack and Nice models, which both assume Jupiter and Saturn to be inside the 2:1 resonance. The stalled migration could, however, explain the so called warm-Jupiters population among the detected exoplanets, providing that these are in multi-planet systems. Additionally, we remark that the only system with two giant planets observed in a disc of gas, namely PDS70, occurs to be close to the 2:1 resonance.
Figure 1: Surface density of a 2D simulation after nearly 300 000 years of evolution, displaying Jupiter (filled circle) and Saturn (empty circle) in their common gap. The planets are stably locked in the 2:1 mean motion resonance and are following a very slow inward migration at a speed of one a.u. per million years.
References:
E. Lega et al., “Migration of Jupiter Mass Planets in Discs with Laminar Accretion Flows,” Astronomy & Astrophysics 658 (2022)
Konstantin Batygin, “Capture of Planets into Mean-Motion Resonances and the Origins of Extrasolar Orbital Architectures,” Monthly Notices of the Royal Astronomical Society 451, no. 3 (August 11, 2015)
How to cite: Griveaud, P., Crida, A., and Lega, E.: Minimal viscosity discs lock pairs of giant planets in 2:1 resonance with stalled migration., Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-464, https://doi.org/10.5194/epsc2022-464, 2022.
We aim to develop a simple prescription for migration and accretion in 1D disc models, calibrated with results of 3D hydrodynamic simulations [1,2]. Our focus lies on non-self-gravitating discs, but we also discuss to what degree our prescription could be applied when the discs are self-gravitating.
We study migration using torque densities. Our model for the torque density is based on existing fitting formulas, which we subsequently modify to prevent premature gap-opening. At higher planetary masses, we also apply torque densities from hydrodynamic simulations directly to our 1D model [3]. These torque densities allow modelling the orbital evolution of an initially low-mass planet that undergoes runaway-accretion to become a massive planet. The two-way exchange of angular momentum between disc and planet is included. This leads to a self-consistent treatment of gap formation that only relies on directly accessible disc parameters.
We present a formula for Bondi- and Hill- gas accretion in the disc-limited regime. This formula is self-consistent in the sense that mass is removed from the disc in the location from where it is accreted. Fig. 1 shows an exampe of the time evolution of semi-major axis and mass of a growing, migrating planet. Our proposed model "High mass torque" is shown as purple dash-dotted line.
We find that the resulting evolution in mass and semi-major axis in the 1D framework is in good agreement with those from 3D hydrodynamical simulations for a range of parameters.
Our prescription is valuable for simultaneously modelling migration and accretion in 1D-models. We conclude that it is appropriate and beneficial to apply torque densities from hydrodynamic simulations in 1D models, at least in the parameter space we study here. More work is needed to in order to determine whether our approach is also applicable in an even wider parameter space and in situations with more complex disc thermodynamics, or when the disc is self-gravitating.
Fig. 1: Time evolution of an initially low-mass planet (5 Mearth), starting at 5.2 au in a disc with an initial surface density of 100 g cm-2. Left: Semi-major axis. Right: Planetary mass. The figure shows different models for the torque density and the feeding zone radius we studied in [4].
References:
[1] D’Angelo, G. & Lubow, S. H. 2008, Astrophysical Journal, 685, 560
[2] D’Angelo, G. & Lubow, S. H. 2010, Astrophysical Journal, 724, 730
[3] Schib, O., Mordasini, C., Wenger, N., Marleau, G. D., & Helled, R. 2021, Astronomy and Astrophysics, 645, A43
[4] Schib, Mordasini & Helled 2022, Astronomy and Astrophysics accepted
How to cite: Schib, O., Mordasini, C., and Helled, R.: Calibrated Gas Accretion and Orbital Migration of Protoplanets in 1D Disc Models, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-46, https://doi.org/10.5194/epsc2022-46, 2022.
The early stages of the formation of binary stellar systems are still rather poorly understood observationally, which contrasts with some significant recent improvements in numerical simulations. We present a comprehensive study with the VLA and ALMA of the close (separation = 90 au) proto-binary system SVS 13. Our very high sensitivity and spatial resolution observations trace the dust as well as the ionized and molecular gas in this system, reaching scales as small as ~10 au. We infer the orbital motion and masses of the two protostars. We image two circumstellar disks and a still-forming circumbinary disk with prominent spiral arms extending ~500 au. We study the 3D kinematics of the system and measure the physical properties of the disks. We also find evidence for variation of chemical properties on scales of a few tens of au. Finally, we will discuss on how the properties of the SVS 13 system compare with those of a few other protobinary systems that have been observed with a similar degree of detail, and with the predictions of numerical simulations. This kind of information provides some clues on the final configuration of planetary systems in binary systems.
ALMA observation of dust in the disks around SVS 13 (credit: A.K. Diaz-Rodriguez, G. Anglada 2022).
Cartoon model of the system. The red-blue colours indicate the motion of the gas. Red – away from us, blue – towards us. The peculiar yin-yang shape results from the combination of infalling and rotation motions (credit: A. K. Diaz-Rodriguez et al. 2022).
How to cite: Anglada, G., Diaz-Rodriguez, A. K., Blázquez-Calero, G., Osorio, M., Gómez, J. F., Fuller, G. A., Estalella, R., Torrelles, J. M., Cabrit, S., Rodríguez, L. F., Macías, E., Carrasco-González, C., Zapata, L. A., de Gregorio-Monsalvo, I., and Ho, P. T. P.: Observing the very early stages of the formation of a circumbinary planetary system in SVS 13, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-1031, https://doi.org/10.5194/epsc2022-1031, 2022.
The discovery of multi-planet resonant chains such as those in TRAPPIST-1 and Kepler-90, where adjacent planets are in different commensurabilities, has raised questions on the formation of these systems and the reason for the diversity of their resonances. It is widely accepted that these systems formed through the combination of migration and resonance-capture where migrating planets capture each other in resonances. However, this scenario cannot explain why adjacent planets have different period-ratios. The reason is that migrating planets tend to capture each other in the same resonances (e.g., the three giant planets in the four-planet system of GJ 876 are in a 4:2:1 Laplace resonance).
To overcome this difficulty, it has been suggested that the diversity of resonances in resonant-chain systems is a post-capture phenomenon that has roots in the mutual tidal interactions of these bodies. That is, after planets have been captured in the same resonance, tidal forces cause the planets to leave their commensurabilities until they are captured in a different resonance. The latter motivated us to examine the validity of this scenario, both during the formation of resonant chains and also as a post-formation phenomenon.
To determined the probability of forming resonant chains and capture in different resonances, we carried out more than 2700 simulations of multiple-planet migration, where fully formed planets were migrating while interacting with one another, and more than 60 simulations of planet formation in a protoplanetary disk subject to the perturbation of migrating planets. Simulations were carried out for different values of planets’ masses and migration rates, and the number of migrating planets.
Figure 1 shows the results. As shown here, from all our simulations, only 130 (~5%) resulted in captures into resonances suggesting that multi-planet resonances are not a common occurrence. The largest number of captures appears for 5:3 (a new finding) followed by 3:2 and 2:1 resonances. Results also showed that the probability of capture (and, therefore, the final commensurabilities) is highly depended on the characteristics of the systems, especially the planets’ mass-ratio and migration speed. Figure 2 shows a sample of our planet formation simulations in which planets form in a protoplanetary disk that is subject to the perturbation of three migrating giant planets. As shown here, after 1 Myr, super-Earth and larger planet are formed with some being mutually captured in resonances (i.e., forming a resonant chain).
Our simulations also demonstrated that capture in a resonance never occurs at the resonance’s exact commensurability and there is always some deviation (Figure 3). The extent of this deviation also depends on the mass-ratio and orbital characteristics of the planets and the mechanism through which migrating planets lose energy.
Collectively, our results confirm that, 1) migrating planets can be captured in different resonances and that the diversity of resonances observed in resonant chains is a natural consequence of the formation and resonance capture mechanism, and does not require a secondary, post-formation process, and 2) no post-capture mechanism is needed to explain the deviation from exact commensurabilities observed in Kepler (and RV) planet pairs.
How to cite: Haghighipour, N.: Size and resonance diversity of multi-planet resonant chains is a natural outcome of their formation, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-303, https://doi.org/10.5194/epsc2022-303, 2022.
Posters: Mon, 19 Sep, 18:45–20:15 | Poster area Level 2
Abstract
High-precision measurements of isotopes in meteorites suggest that the early population of small bodies in the Solar System has been separated into two reservoirs by the forming Jupiter, acting as a radial barrier for these 'planetesimals' [1]. In a proposed Jupiter formation scenario [2], the solid core must grow within 1 Myr to around 20 Earth masses, then stagnate its growth for 2-3 Myr and thus separating the planetesimal reservoirs, and finally grow to the final Jupiter mass stirring and mixing the inner and outer planetesimals. The fast and early core growth is efficiently facilitated by the accretion of small 'pebble-like' objects. In order to delay the otherwise inevitable rapid runaway gas accretion for an extended period of time after the pebble accretion stops, Jupiter is proposed to be heated by slower planetesimal accretion before finally becoming massive enough to accrete a large amount of gas, reaching its present day mass.
Motivated by this proposed formation scenario of Jupiter, we investigate the consequences of a combined pebble and planetesimal accretion model for the formation of giant planets and planet formation in general [3]. We modify the Bern model of planetary population synthesis [4] with a simple model of pebble formation and accretion [5]. In a single-planet population synthesis approach, we run the model on a thousand different initial protoplanetary disks in order to probe the effects of the two solid accretion mechanisms on a population level. To uncover the interplay of the two models, we vary the amount of pebbles with respect to planetesimals.
As shown in figure 1, it proves to be difficult to form giant planets from the accretion of pebbles and planetesimals whereas both mechanisms individually are able to form giants in suitable disks. We identify the remaining accretion of planetesimals after the stop of pebble accretion to be crucial for the formation pathway of a growing planet. The envelope heating due to the accretion of solids is shown to play a critical role for the accretion of gas. A combination of enhanced inward orbital migration and delayed runaway gas accretion strongly suppresses the formation of giants in disks containing both pebbles and planetesimals.
Figure 1: Planet mass over semi-major axis snapshot after 2 Gyr of evolution for populations of one thousand disks, containing one planet. The four, otherwise identical, populations start with either only planetesimals (left), 30% pebbles (middle left), 70% pebbles (middle right), or only pebbles (right).
References
[1] Kruijer T. S., Burkhardt C., Budde G., Kleine T., 2017, Proc. Natl. Acad. Sci., 114, 6712
[2] Alibert Y., Venturini J., Helled R., et al., 2018, Nature Astronomy, 2, 873
[3] Kessler A., et al., in prep.
[4] Emsenhuber A., Mordasini C., Burn R., et al., 2021, A&A, 656, A 69
[5] Bitsch B., Lambrechts M., Johansen A., 2015b, A&A, 582, A 112
How to cite: Kessler, A., Alibert, Y., Mordasini, C., Emsenhuber, A., and Burn, R.: Giant Formation with Pebbles and Planetesimals, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-114, https://doi.org/10.5194/epsc2022-114, 2022.
The size distribution of solids in the protoplanetary disk is still ill constrained [1] but is a vital parameter that influences planetary growth [2]. The typical size and spatial distribution of solids evolves throughout the planet formation process via collisions and radial drift. As the planets grow, they excite the mutual random velocities among planetesimals making their mutual collisions destructive which leads to fragmentation, reducing their typical size. This effect of self-interacting planetesimals has been found to inhibit or favor the formation of planets due to competing effects of easier accretion of smaller fragments and depletion by gas-drag induced drift [3-4]. However, previous studies have either focused on single planets and systems or have neglected concurrent effects like migration.
Therefore, we run planet formation simulations with the generation III Bern model [5] with a Eulerian 1D solid disks. The model tracks the growth and evolution of several planetary embryos from oligarchic growth to the final planetary system. We added to it a fragmentation toy model [6] to see the impact fragmentation has on planet formation. To see its influence on the diverse types of exoplanets we make use of a population synthesis approach to investigate larger parts of the parameter space [7]. This allows us to have a more complete picture of what influence the collisional evolution of planetesimals has on planet formation and to study the effects that arise from its interplay with the formation of multiple planets in the same system.
In figure 1, we show two exemple synthetic planet populations of 1000 systems with (right) and without (left) the added fragmentation model. We find multiple interesting features in our synthetic populations that arise from the fragmentation of planetesimals. The fragmentation lends more importance to specific locations in the disk where growth is enhanced like the ice line and the inner disk. In addition, it enhances the formation of giants.
In conclusion, there are significant differences in synthetic populations when including or neglecting fragmentation. This suggests that the addition of fragmentation to global planet formation models is important as a self-consistent solid disk description is vital to understand planet formation.
In figure 1. Comparison of a synthetic exoplanet population without (left) the added fragmentation model and one with (right). The semi major axis (in AU – log scale) is plotted on the x-axis and the planetary mass (in Earth masses – log scale) on the y-axis. Both populations are shown at an age of 5 Gyr. The Red points refer to planets with more envelope than core mass, the blue ones are icy planets (ice mass fraction larger than 1%) and the green points are rocky planets (ice mass fraction smaller than 1%).
References:
[1] Helled, R. & Morbidelli, A. 2021, in ExoFrontiers (IOP Publishing)
[2] Fortier, A., Alibert, Y., Carron, F., Benz, W., & Dittkrist, K.-M. 2012, A&A, 549, A44
[3] Guilera, O. M., de Elía, G. C., Brunini, A., & Santamaría, P. J. 2014, A&A, 565, A96
[4] Chambers, J. 2008, Icarus, 198, 256
[5] Emsenhuber, A., Mordasini, C., Burn, R., et al. 2021, A&A, 656, A69
[6] Ormel, C. W. & Kobayashi, H. 2012, The Astrophysical Journal, 747, 115
[7] Emsenhuber, A., Mordasini, C., Burn, R., et al. 2021b, A&A, 656, A70
How to cite: Kaufmann, N. and Alibert, Y.: A population level study on the influence of planetesimal fragmentation on planet formation, Europlanet Science Congress 2022, Granada, Spain, 18–23 Sep 2022, EPSC2022-135, https://doi.org/10.5194/epsc2022-135, 2022.
1. Introduction
About 50 % [1] of solar-like stars are part of binary star systems. From the nearly 5000 exoplanet candidates only about 2171 are part of a binary or multiple star systems. Inclined planets have been found in circumbinary motion, nevertheless, there are also planets in circumstellar motion which indicate inclinations. Like in the binary star systems HIP 94235 b [2] (recent) and 55 Cnc e [3].
In this study, we want to investigate the late stage of terrestrial planet formation in S-type motion in close binary star systems with a focus on the evolution of the planetesimal disk.
1https://www.univie.ac.at/adg/schwarz/multiple.html
2. Methods and Setup
To solve the equations of motion the Bulirsch-Stoer (BS) method is applied. As the n-body problem scales with O(N2) the BS method has been heavily parallelized on GPUs. As a first approximation for the collisions the so-called “perfect merging“ has been applied. In our numerical study, the interaction of some thousands disk objects are studied for 1 Myrs.
For an equal mass G-type binary star the following star parameters have been varied: ab , eb , and ib. The circumprimary disk consists of some tens of planetary embryos and 2000 planetesimals and extends between 1 and 4 au. The disk is initially dynamically cold and is within the area of stable motion [4]. The different configurations have been simulated for a time of 1 Myr each. For some selected configurations we increased the simulation time for 10 Myr.
3. Results
The wider binary (100 , 150 au) configurations show a bend in the inclination (see figure 1). The location of the bend is closer to the primary for the 100 au (∼ 2.0 au) case than in the 150 au (∼ 2.5 au) case. Additionally, in the 100 au binary star, the innermost embryos reach inclinations up to ∼ 50° compared to ∼ 30° in the 150 au binary system.
For a binary separation of 60 au the distribution of the disk objects in a and i shows some kind of wave structure within the first 200 kyrs (see figure 2). After 400 kyrs the structure is barely visible and after 600 kyrs the structure clearly disappeared.