Europlanet Science Congress 2021
Virtual meeting
13 – 24 September 2021
Europlanet Science Congress 2021
Virtual meeting
13 September – 24 September 2021
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EXO1

Zooming In On Planet Formation

The inner regions of planet forming disks surrounding young stars are key to our understanding of the formation of rocky, Earth-like planets and super-Earths. We know from exoplanet surveys that such planets are abundantly present around low mass stars. Rocky planets are essential ingredients in the quest for life outside the solar system. Understanding their properties and formation history is key to our efforts to put the solar system in perspective.

Investigations of the outer regions of the accretion disk provide us with information on the distribution of volatile material and ices in planetary systems, and studies on disk properties, on evolved cold, gaseous or sub-Neptune planets, as well as migration studies of planets leading to various different system architectures (e.g. to hot Jupiters close to their host star) help us to better understand the evolution of our own solar system.

We invite abstracts from different disciplines working on planet formation, including for example observations of planet forming disks, recent or on-going exoplanet surveys, theoretical and computational models, as well as comparative studies using solar system data from exploration missions, meteorite analysis and remote sensing.

Co-organized by TP
Convener: Lena Noack | Co-conveners: Myriam Benisty, Mario Flock, Inga Kamp, Yamila Miguel, Rens Waters

Thu, 16 Sep, 10:40–11:25

Chairpersons: Lena Noack, Inga Kamp, Mario Flock

EPSC2021-861
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solicited
Jacques Kluska
Spatially resolved observations from ALMA or direct imaging instruments revealed an extreme diversity and complexity of structures and substructures in the outer parts of protoplanetary disks.
However, these techniques do not resolve the inner regions of protoplanetary disks, typically at less than 5 astronomical units from the star.
These inner regions are crucial to understand the formation of telluric planets.
They are also the theatre of strong interactions between the star and the disk that can influence planet formation.
Thanks to infrared interferometry we can reach an angular resolution of ~1mas reaching sub-astronomical unit physical scales.
We can, therefore use infrared interferometry to reveal and study the structure, composition, and dynamics of the inner parts of protoplanetary disks.
In the past few years, the advent of infrared interferometers combining four telescopes such as PIONIER, MATISSE or GRAVITY enabled us to study these disks with an unprecedented detail.
In this talk, I will review the recent results of near and mid-infrared interferometric observations of protoplanetary disks.

How to cite: Kluska, J.: Zooming in on the place of rocky planet formation: infrared interferometric observations of protoplanetary disks, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-861, https://doi.org/10.5194/epsc2021-861, 2021.

EPSC2021-70
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ECP
Marija Jankovic et al.

Short-period super-Earths and mini-Neptunes have been shown to be common, yet it is still not understood how and where inside protoplanetary discs they could have formed. To form these planets at the short periods at which they are detected, the inner regions of protoplanetary discs must be enriched in dust. Dust could accumulate in the inner disc if the innermost regions accrete via the magneto-rotational instability (MRI). We developed a model of the inner disc which includes MRI-driven accretion, disc heating by both accretion and stellar irradiation, vertical energy transport, dust opacities, dust effects on disc ionization, thermal and non-thermal sources of ionization. The inner disc is assumed to be in steady state, and the dust is assumed to be well-mixed with the gas. Using this model, we explore how various disc and stellar parameters affect the structure of the inner disc and the possibility of dust accumulation. We show that properties of dust strongly affect the size of the MRI-accreting region and whether this region exists at all. Increasing the dust-to-gas ratio increases the size of this region, suggesting that dust may accumulate in the inner disc without suppressing the MRI. Overall, conditions in the inner disc may be more favourable to planet formation earlier in the disc lifetime, while the disc accretion rate is higher.

How to cite: Jankovic, M., Mohanty, S., Owen, J., and Tan, J.: MRI-accreting inner regions of protoplanetary discs, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-70, https://doi.org/10.5194/epsc2021-70, 2021.

EPSC2021-514
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ECP
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Tabea Bogdan et al.

Sticking properties are of great importance for planetesimal formation in protoplanetary disks. During the early phases of pebble growth, grains regularly travel from cold, water-rich regions to the warm inner part of the disk, experiencing ever higher temperatures. This drift leads to changes in composition, grain size, morphology, and water content. To follow the evolution that the dust might go through, we milled a meteorite to micrometer dust and tempered it under vacuum at increasing temperatures up to 1400 K. For each tempered sample we measured the splitting tensile strength of millimeter-sized dust aggregates using a well-established method known as the Brazilian test. To link the evolution of surface energy with temperature to compositional changes, we additionally measured the (ferric) composition of the samples by Mössbauer spectroscopy. 

At the low pressure of protoplanetary disks and at moderate temperatures, grains presumably hold only a monolayer of surface water and can thus be considered as dry. As the dust drifts further inwards towards higher temperature regions even this monolayer of water may evaporate completely and grains are super dry. In the laboratory, contacts between grains in cylinders are dry and remain dry for measurement if they are prepared for the Brazilian test before tempering. If cylinders are prepared after tempering but from the tempered dust, contacts are wet contacts but the influence of the composition can be traced.

For wet samples, we measured an effective surface energy which monotonously decreases by a factor of 5 from room temperature to about 1300 K due to compositional changes [1]. This reduction of surface energy still holds for dry samples but with an increase in the sticking force by a factor of ~ 10 over the wet samples. Super dry samples deviate strongly from this starting at about 900 K. Above this temperature, the surface energy is boosted and increases exponentially up to another factor of ~ 100 at about 1200 K [2].

Exceeding temperatures of 1300 K, grain sizes microscopically change (increase) for all samples, leading to an instability of aggregates and therefore making growth challenging. Beyond 1400 K no classical collisional growth is possible. 

As consequence, there is a spatial region in protoplanetary disks with temperatures around 1200 K which favors aggregation and, therefore, will likely be a sweet spot for planetesimal formation as indicated in fig.1.

[1] Bogdan, T., Pillich, C., Landers, J., Wende, H., & Wurm, G. (2020). Drifting inwards in protoplanetary discs I Sticking of chondritic dust at increasing temperatures. Astronomy & Astrophysics638, A151.

[2] Pillich, C., Bogdan, T., Landers, J., Wurm, G., Wende, H. (2021). Drifting inwards in protoplanetary discs II The influence of water on sticking properties at increasing temperatures. Astronomy & Astrophysics, (accepted).

 

How to cite: Bogdan, T., Pillich, C., Landers, J., Wende, H., and Wurm, G.: The influence of water and mineralogy on sticking properties at increasing temperatures, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-514, https://doi.org/10.5194/epsc2021-514, 2021.

EPSC2021-721
Helmut Lammer et al.

Here we discuss terrestrial planet formation by using Earth and our knowledge from various isotope data such as 182Hf-182W, U-Pb, lithophile-siderophile elements, atmospheric 36Ar/38Ar, 20Ne/22Ne, 36Ar/22Ne isotope ratios, the expected solar 3He abundance in Earth’s deep mantle and Earth’s D/H sea water ratios as an example. By analyzing the available isotopic data one finds that, the bulk of Earth’s mass most likely accreted within 10 to 30 million years after the formation of the solar system. Proto-Earth most likely accreted a mass of 0.5 to 0.6 MEarth during the disk lifetime of 3 to 4.5 million years and the rest after the disk evaporated (see also Lammer et al. 2021; DOI: 10.1007/s11214-020-00778-4). We also show that particular accretion scenarios of involved planetary building blocks, large planetesimals and planetary embryos that lose also volatiles and moderate volatile rock-forming elements such as the radioactive decaying isotope 40K determine if a terrestrial planet in a habitable zone of a Sun-like star later evolves to an Earth-like habitat or not. Our findings indicate that one can expect a large diversity of exoplanets with the size and mass of Earth inside habitable zones of their host stars but only a tiny number may have formed to the right conditions that they could potentially evolve to an Earth-like habitat. Finally, we also discuss how future ground- and space-based telescopes that can characterize atmospheres of terrestrial exoplanets can be used to validate this hypothesis.   

How to cite: Lammer, H., Scherf, M., and Erkaev, N. V.: Terrestrial planet accretion constrained by isotopes: Implications for Earth-like habitats, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-721, https://doi.org/10.5194/epsc2021-721, 2021.

EPSC2021-130
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ECP
Tim Lichtenberg and Sebastiaan Krijt

Finding and characterizing extrasolar Earth analogs will rely on interpretation of the planetary system’s environmental context. The total budget and fractionation between C–H–O species sensitively affect the climatic and geodynamic state of terrestrial worlds, but their main delivery channels are poorly constrained. We connect numerical models of volatile chemistry and pebble coagulation in the circumstellar disk with the internal compositional evolution of planetesimals during the primary accretion phase. Our simulations demonstrate that disk chemistry and degassing from planetesimals operate on comparable timescales and can fractionate the relative abundances of major water and carbon carriers by orders of magnitude. As a result, individual planetary systems with significant planetesimal processing display increased correlation in the volatile budget of planetary building blocks relative to no internal heating. Planetesimal processing in a subset of systems increases the variance of volatile contents across planetary systems. Our simulations thus suggest that exoplanetary atmospheric compositions may provide constraints on when a specific planet formed.

How to cite: Lichtenberg, T. and Krijt, S.: System-level fractionation of carbon from disk and planetesimal processing , Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-130, https://doi.org/10.5194/epsc2021-130, 2021.

EPSC2021-265
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ECP
Felix Jungmann et al.

In early phases of planet formation, bouncing and fragmentation barriers still represent major obstacles. Beginning at micrometer, dust can readily grow to sub-millimeter size in collisions due to cohesion before bouncing prevails. Later, streaming instabilities trigger further growth which might finally results into planetesimal formation by gravitational collapse. However, for streaming instabilities sub-millimeter grains might be too small, therefore there is gap of at least 1 order of magnitude in size which needs to be bridged.

Here, we present our ongoing work how to bridge this gap by charge moderated aggregation [1]. When two (dielectric) grains collide they charge. This tribocharging or collisional charging is omnipresent in nature. We designed drop tower experiments in which we generated charges on glass and basalt grains by collisions in a shaker. In microgravity, the particle trajectories and collisions were observed, and charges were measured by applying an electric field.

In early work, we analyzed millimeter-sized glass grain collisions with a copper plate. The coefficient of restitution increased with the charge on a single grain due to mirror charge forces. That means highly charged grains tend to stick more easily to surfaces than uncharged grains. The velocity where sticking is possible was increased by a factor of 100 up to several dm/s [2].
 
More recently, we used half millimeter basalt spheres and observed sticking events at several cm/s among grains themselves [3]. This is also way higher than predicted by adhesion. In a number of cases, we could observe the sequential formation of aggregates of up to ten single grains. During approach the grains are accelerated due to net charge Coulomb forces but likely also due to higher order charges on the surfaces in agreement to earlier measurements of strong permanent dipole moments [4]. Attraction increases collision cross-sections and the growth is sped up. Growth only stopped by the end of microgravity [3]. 

To observe the formation of still larger aggregates we developed a new setup, in which a dense cloud of 150 µm diameter basalt grains was continuously agitated slightly under microgravity and in vacuum. Here, the growth of a giant aggregate of centimeter size was observed collecting nearly all material in one cluster [5].

To conclude, in experiments under various conditions, we see strong evidence that electrostatic charges on grains are able to conquer the bouncing barrier. We observed the bottom-up growth tracking individual particles, stable clusters emerging from dense regions and the formation of giant clusters during agitation. These are all bricks in the wall giving evidence that collisional charging might play a crucial role in planet formation.

References:

[1] Steinpilz, T.; Joeris, K.; Jungmann, F.; Wolf, D.; Brendel, L.; Teiser, J.; Shinbrot, T.; Wurm, G. Nature Physics 2020a, 16, 225-229.

[2] Jungmann, F.; Steinpilz, T.; Teiser, J.; Wurm, G. Journal of Physics Communications 2018, 2 095009, 095009.

[3] Jungmann, F.;Wurm, G. Astronomy and Astrophysics 2021, DOI: https://doi.org/10.1051/0004-6361/202039430.

[4] Steinpilz, T.; Jungmann, F.; Joeris, K.; Teiser, J.; Wurm, G. New Journal of Physics 2020b, 22, 093025.

[5] Teiser, J.; Kruss, M.; Jungmann, F.; Wurm, G. The Astrophysical Journal Letters 2021, 908, L22.

How to cite: Jungmann, F., Teiser, J., Kruss, M., Steinpilz, T., Joeris, K., and Wurm, G.: Charge moderated preplanetary growth from single grains to giant aggregates, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-265, https://doi.org/10.5194/epsc2021-265, 2021.

EPSC2021-219
Gerhard Wurm et al.

Protoplanetary disks are thought to harbor deadzones, regions in their interior, where the ionization fraction is too low to trigger MRI turbulence. This has quite severe consequences for accretion and planet formation. 
So far, the dominant source considered for ionization is high energy radiation from external cosmic rays over stellar radiation to radioactive decay. Especially, external radiation might indeed be attenuated too much before reaching parts of the midplane in disks. Radiation might not be the only source of ionization though.

In recent years, we carried out a number of laboratory experiments on collisional charging (tribocharging) of grains related to planet formation. Being mm-size, in a range where fragmentation and bouncing dominate, these particles are large and, although charged, might not be relevant in the context of MRI themselves directly. 

An underlying assumption though is that triboelectric charge generated in collisions among grains stays on the grains. In this case, grain charging and aggregation as part of early particle growth on one side and MRI building on gas ionization on the other side would be distinct processes. However, what we recently found in a number of different experiments, is that tribocharging of grains also charges the ambient gas.

In one set of microgravity experiments, we observed that the charge on two particles before and after a collision is not conserved. On the order of 20\% of the pre-charge on a grain is discharged into the environment. To mention a second experiment, the number of ions detected in a gas flow after passing a granular medium increases strongly if the particles undergo collisions, i.e. are charged. There are experiments with further evidence but these two clearly show that charge is leaking into the ambient atmosphere during collisions.

In detail, the charging depends on the collision frequencies and particle sizes, which are model dependent. We also caution that these are only first experiments in this direction, but, in any case, estimates suggest that ionization rates within the gas might regularly be way larger than e.g. provided by radiation at the surface of a disk. If this holds, the charge balance in the midplane of protoplanetary disks might be quite different than previously assumed. The obvious and severe consequence might simply be that there are just no deadzones.

How to cite: Wurm, G., Jungmann, F., van Unen, H., Voellings, N., Schoenau, L., and Teiser, J.: Does Leakage of Charge in Particle Collisions Kill the Concept of Deadzones?, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-219, https://doi.org/10.5194/epsc2021-219, 2021.

EPSC2021-161
Ryuki Hyodo et al.

A notable challenge of planet formation is to find a path to directly form planetesimals from small particles. Small particles are, in general, challenged to grow beyond meter size due to the “growth barrier” and the “drift barrier”.

Over the last few decades, magnetohydrodynamic (MHD) simulations have shown that a region where ionization is too low for the magneto-rotational instability (MRI) to operate (i.e., a “dead zone”) might ubiquitously exist in the inner part of the disk midplane, and that only surface layers are magnetically active, supporting accretion. These indicate a nonuniform turbulence structure.

In this study, we aim to understand how drifting pebbles pile up in a protoplanetary disk with a nonuniform turbulence structure (Figure 1). We consider a disk structure in which the midplane turbulence viscosity (i.e., diffusion of pebbles is characterized by a distinct non-dimensional parameter (αmid)) increases with the radius in protoplanetary disks, such as in the outer region of a dead zone. We consider that the gas accretion toward the central star is characterized by a distinct non-dimensional parameter (αacc). We perform 1D diffusion-advection simulations of pebbles that include back-reaction (the inertia) to the radial drift and the vertical and radial diffusions of pebbles for a given pebble-to-gas mass flux (Fp/g).

We report a new mechanism, the “no-drift” runaway pile-up (i.e., instability), that leads to a runaway accumulation of pebbles in disks, thus favoring the formation of planetesimals by streaming and/or gravitational instabilities. This occurs when pebbles drifting in from the outer disk and entering a dead zone experience a decrease in vertical turbulence. Consequently, the scale height of the pebble then decreases, and, for small enough values of the turbulence in the dead zone and high values of the pebble-to-gas flux ratio, the back-reaction of pebbles on gas leads to a significant decrease in their drift velocity and thus their non-steady-state accumulation (i.e., a local runaway pile-up of pebbles). This process is independent of the existence of a pressure bump and/or pebble growth.

 

Figure 1: Schematic illustration of pebble drift and its pile-up within a protoplanetary disk with a dead zone. The disk gas accretion is characterized by alpha-parameter (αacc), while the midplane diffusivity, being a dead zone (αdead << αacc) in the inner region, is characterized by αmid. During the inward drift of pebbles, the pebble scale height Hp decreases as Hp is proportional to αacc1/2 until a KH instability prevents it from becoming smaller. A smaller Hp leads to an elevated local midplane concentration of pebbles within a thinner midplane layer. The elevated midplane pebble-to-gas ratio causes the back-reaction to be more effective in reducing the radial drift velocity of pebbles. Such a physical interplay with a sufficiently large pebble-to-gas mass flux results in a continuous accumulation of pebbles in a runaway fashion (i.e., the “no-drift” runaway pile-up). Redrawn from Hyodo, Ida, Guillot (2021) A&A, 645, L9.

How to cite: Hyodo, R., Ida, S., and Guillot, T.: Planetesimal formation by the “no-drift” mechanism, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-161, https://doi.org/10.5194/epsc2021-161, 2021.

EPSC2021-697
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ECP
Steven Rendon Restrepo and Pierre Barge

    Large scale vortices are thought to be natural outcomes of hydrodynamic instabilities in protoplanetary disks, as for instance the Rossby Wave Instability [1] or Baroclinic instability. Analytical and numerical studies showed that they can be long-lived and catalyze efficiently dust material concentration (e.g) [2], [3] and encourage to think they could play a role in protoplanetary-disk evolution and planetesimal formation. Their presence in the outer regions of circumstellar disks is possibly betrayed by recent observations of lopsided structures with ALMA and VLT [4], [5] and raises also a question: what is the importance of disk self-gravity on their structure and evolution.

    We present 2D hydrodynamical simulations of steady vortices evolving under the effect of their own gravity. The goal is to study their evolution and the possibility of gravitational collapse. Are particularly addressed the structure, migration, mass, and physical variables characterizing these self-gravitating structures. We also pay special attention to the case of very massive vortices.

Figure 1. From left to right: Rossby number and density (in log scale) perturbations induced by a large scale vortex after 171 orbital periods at 7.5 AU.

[1] Lovelace, R. V. E., Li, H., Colgate, S. A., & Nelson, A. F. 1999, ApJ, 513, 805

[2] Barge, P. & Sommeria, J. 1995, A&A, 295, L1

[3] Raettig N, Klahr H Lyra W, 2015, ApJ804

[4] Tsukagoshi, T., Muto, T., Nomura, H., et al. 2019, ApJ, 878, L8

[5] Dong, R., Liu, S.-y., Eisner, J., et al. 2018, ApJ, 860, 124

How to cite: Rendon Restrepo, S. and Barge, P.: Selfgravitating vortices in protoplanetary disks, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-697, https://doi.org/10.5194/epsc2021-697, 2021.

EPSC2021-814
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ECP
Steven Rendon Restrepo and Pierre Barge

    Large scale vortices are thought to be natural outcomes of hydrodynamic instabilities in protoplanetary disks, as for instance the Rossby Wave Instability [1] or Baroclinic instability. Analytical and numerical studies showed that they can be long-lived and catalyze efficiently dust material concentration [2], [3] what encourages to think they could play a role in protoplanetary-disk evolution and planetesimal formation. Their presence in the outer regions of circumstellar disks is possibly betrayed by recent observations of lopsided structures with ALMA and VLT [4], [5].

    We present our latest results of two-phase 3D numerical simulations in which the solid particles are embedded in the gas and described as a second pressureless fluid.  The goal is to discuss the sedimentation of the dust phase in the protoplanetary disk midplane, and the dust trapping mechanism induced by 3D vortices. We will also address the question if 3D vortices are more stable to the streaming instability than 2D vortices.

Figure 1. Left : Three 3D vortices generated by the Rossby Wave instability. Right : Same as left but two vortices merged after few orbital periods

[1] Lovelace, R. V. E., Li, H., Colgate, S. A., & Nelson, A. F. 1999, ApJ, 513, 805

[2] Barge, P. & Sommeria, J. 1995, A&A, 295, L1

[3] Raettig N, Klahr H Lyra W (2015), ApJ804

[4] Tsukagoshi, T., Muto, T., Nomura, H., et al. 2019, ApJ, 878, L8

[5] Dong, R., Liu, S.-y., Eisner, J., et al. 2018, ApJ, 860, 124

How to cite: Rendon Restrepo, S. and Barge, P.: 3D simulations of dust trapping in gaseous vortices, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-814, https://doi.org/10.5194/epsc2021-814, 2021.

EPSC2021-862
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solicited
Julia Venturini

In this talk I will review our current understanding of planet formation on the outer parts of the protoplanetary disk. We will address questions such as: what type of planetary compositions do we expect? What are the differences with planet formation in the inner disk? Is there a type of planet formation model (e.g pebble vs. planetesimal accretion) that provides a better match with observations? Are there observational trends that we cannot explain? What theoretical challenges do we still face? What new observational constraints will arise in the next years? 

How to cite: Venturini, J.: Planet formation on the outer disk, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-862, https://doi.org/10.5194/epsc2021-862, 2021.

EPSC2021-833
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ECP
Mathis Houllé et al.

In the current theories of planet formation, the amount of energy that a forming gas giant retains from its accretion flow is still unknown. This unconstrained parameter has a large impact on the post-formation evolution of the new planet, as it defines its initial temperature and luminosity. Models have been developed, ranging from “hot-start” models assuming that all the energy is retained internally, to “cold-start” ones assuming that everything is radiated away, and "warm-start" ones in between. Their coexistence introduces large degeneracies on the determination of age and mass in direct imaging observations, as these studies use the cold or hot-start models to infer these parameters from the observed luminosity of a planet. A promising way of solving this problem is the study of atomic emission lines originating from the hot gas shocked by the accretion flow. Recently, Aoyama et al. (2018, 2020) presented simulations of hydrogen lines emitted by the accretion shock onto the circumplanetary disk and the planetary surface. They showed that the line luminosity and width can be used to infer the protoplanet mass, thus giving an estimation that is independent from the evolution models. They applied it to the case of PDS70 b and c (Aoyama & Ikoma 2019, Hashimoto et al. 2020), but were ultimately limited by the spectral resolution of the MUSE observations they used (R ~ 2500). In this context, our team recently proposed and carried out a pilot program using the VLT/ESPRESSO fiber-fed spectrograph, equipped with very high resolution (R = 190 000), to characterize the Hα line of the young substellar companion GQ Lup b. We will present in this poster how these observations were conducted, the methods used to remove the contamination from the host star, and the results we obtained.

How to cite: Houllé, M., Sedaghati, E., Figueira, P., and Vigan , A.: A high-resolution search for the Hα emission line of the accreting companion GQ Lup b with ESPRESSO, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-833, https://doi.org/10.5194/epsc2021-833, 2021.

EPSC2021-813
Aurélie Astoul and Adrian Barker

In close two-body astrophysical systems, like Hot-Jupiter systems, tidal interactions often drive the dynamical evolution of the system on secular timescales, modifying body spins and the orbit of the planet (e.g. Mathis 2019). Most stars around which planets have been discovered are cool stars and feature a convective envelope which is magnetised, as shown by ground-based Zeeman broadening/Doppler imaging techniques and 3D (magneto-)hydrodynamical simulations. Moreover, strong surface magnetic fields have also recently been inferred through star-planet interaction in Hot-Jupiter giant gaseous planets (e.g. Cauley et al. 2019). Due to the tidal potential of the companion (star or planet), tidal flows are generated in the convective layers and dissipated through friction mechanisms, like viscous or Ohmic turbulent damping (e.g. Duguid et al. 2020, Astoul et al. 2019). This tidal dissipation leads to the redistribution and exchange of angular momentum in the convective shell and with the companion, respectively. In the most compact systems, non-linear effects are likely to have a significant impact on the tidal dissipation and change the zonal flows triggering differential rotation, as shown in the hydrodynamical study of Favier et al. (2014).

In this context, we also investigate how the addition of non-linearities affect the tidal flow properties, the energy and angular momentum balances, thanks to 3D (magneto-)hydrodynamic non-linear simulations of an adiabatic and incompressible convective shell. In our neutrally-stratified model, the action of convective eddies on tides is simply taken into account through an effective viscosity. Moreover, we have chosen a body forcing where the equilibrium tide (the quasi-hydrostatic tidal flow component) acts as an effective force to excite tidal waves, while using stress-free boundary conditions. As a result, our perturbed flow is decomposed into a non-wave like part (the equilibrium tide) plus (magneto-)inertial waves. In that respect, our model differs from the above mentioned study which is using an incoming radial flow at the surface to excite inertial waves. In particular, within our more realistic set-up, we are able to identify and assess the importance of the different types of non-linearities (wave/wave, non wave-like/non wave-like, or mixed), and thus discuss unphysical contributions leading to non expected angular momentum evolution for some simulations observed in Favier et al. (2014). By removing these contributions, we also demonstrate that differential rotation can develop in the shell (left figure, azimuthal velocity in a meridional cut) due to the anisotropic deposition of angular momentum in hydrodynamical simulations (right figure, kinetic energy in a meridional cut), which would not be the case in magneto-hydrodynamic simulations according to our early results. Moreover, we show new results for the amplitude of the energy stored in these zonal flows, as well as angular momentum evolution. In particular, we find that non-linearities tends to smooth the frequency dependence of tidal dissipation by lowering it compared to linear predictions (as in Jouve & Ogilvie 2014 using a Cartesian box). As the dissipation of tidal waves in convective envelopes is a major part of total tidal dissipation for close low-mass stars and giant gaseous planets, the inclusion of non-linear effects in its estimation can deeply modify the tidal efficiency (the tidal quality factor) and the associated tidal migration/spins timescales.

How to cite: Astoul, A. and Barker, A.: Non-linear effects on tides in the convective envelope of low-mass stars and giant gaseous planets, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-813, https://doi.org/10.5194/epsc2021-813, 2021.

EPSC2021-376
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ECP
Maximilian Zimmermann and Elke Pilat-Lohinger

Introduction:

Roughly 50 % of solar-like stars are part of binary star systems. Yet, only about 1801 of the nearly 4700 exoplanet candidates are part of a binary or multiple star system.
Yet, not all of the known planets in binary systems are in coplanar orbits. Some are misaligned with respect to the binary star orbital plane up to 90◦ (see catalogue1).
We want to investigate the late stages of terrestrial planet formation in binary star systems, with special emphasis on the dynamical evolution of the embryo planetesimal disks. We restrict ourselves to S-type motion, meaning the disk objects orbit only the primary star. To take the effects of gravitational interactions among disk objects into account a massive parallelized force calculation is applied, which has been recently developed by one of the authors [4]. The planar binary-star-disk configuration defines our reference plane. For simplicity the binary stars are inclined instead of aligning the disk objects on various inclinations.

Methods and Setup:

For solving the equation of motions the Bulirsch-Stoer (BS) method is applied. It is an extrapolation method which takes different results for a timestep τ for the extrapolation of a result for “infinity“ substeps. Furthermore, the method is massively parallelized on graphical processing units (GPU).
The collisions among disk objects are handled so-far with the so-called “perfect merging“. This setup allows simulations up to 10000 gravitational interacting disk objects for about 1 Myr in a reasonable computation time.
The intial setups for the equal mass binary star systems are shown in table 1.

Table 1: Initial parameters of the binary star systems

a[au] e i[°]
30 0.0 0
30 0.0 20
30 0.0 45
30 0.2 20
30 0.2 45
60 0.0 20
60 0.0 45

 

The circumprimary planetesimal disk extends between 1 and 4 au and is initially dynamically cold. For the given binary star systems the disk lies within the area of stable motion [2]. In this study the simulations have been performed using 2000 planetesimals and 25 planetary embryos for a time of 1 Myr for each binary stars listed in table 1.

Results:

The simulations of inclined tight binary stars (ab = 30 au) show an oscillation of the planetesimals’ and embryos’ inclination about binary stars inclination between imin = 0° to imax = 2 · ib although the disk was dynamically cold at the beginning of the simulation. Figure 1 shows the case for ib = 20°.

Figure 2 shows the inward migration of the planetary embryos in the case of ib = 45° . This effect seems to be stronger for the planetary embryos which are located in the inner part of the disk (a < 2 au) as well as for higher inclinations of the binary stars.

Summary and Conclusions:

We investigated the dynamical evolution of misaligned (=ˆ variation in the inclination of the binary stars) protoplanetary disks for various binary star configurations with planetesimal disks containing about 2025 mutual gravitational interacting objects.
This study showed that in the case of inclined tight binary stars case the rapid increase in the inclination of the disk objects slows down the planetary embryos growth compared to the coplanar case [4]. Additionally, the planar case shows an outward migration of the outer planetasimals, while the inclined systems indicate an inward migration of planetary embryos (see figure 3), which is possibly caused by Kozai migration [3].

Acknowledgements

M.Z. and E.P-L want to acknowledge the support by the Austrian FWF - project no. P33351-N.

References

  • [1] Jensen, E. and Akeson, R.: Misaligned protoplanetary disks in a young binary star system. Nature 2014, Vol. 511, pp 567-569
  • [2] Pilat-Lohinger, E. and Dvorak, R.: Stability of S-type orbits in binaries. Celestial Mechanics and Dynamical Astronomy 82.2, pp. 143-153, 2002
  • [3] Wu, Y., Murray, N.: Planet migration and binary companions: The case of HD 80606B. The Astrophysical Journal, 589, pp. 605-614, 2003
  • [4] Zimmermann, M.: The influence of binary systems on planetesimal disks. Master thesis, University of Vienna, 2021

How to cite: Zimmermann, M. and Pilat-Lohinger, E.: Dynamical evolution of planetesimal disks in inclined binarystar systems, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-376, https://doi.org/10.5194/epsc2021-376, 2021.

EPSC2021-853
|
ECP
David Jorge et al.

Abstract

We aim to understand the impact of different refractory element ratios such as Mg, Si, and Fe on the composition of planets. We use the thermodynamic equilibrium code GGchem to simulate the condensation of solids in a minimum mass solar nebula around main sequence G-type stars within 150pc. We extract the stellar elemental composition from the Hypatia database. We find that a lower Mg/Si ratio shifts the condensation sequence from forsterite and SiO to enstatite and quartz; a lower Fe/S ratio leads to the formation of FeS and FeS2 and little or no Fe-bearing silicates. Ratios of refractory elements translate directly from the gas phase to the condensed phase for T<1000K. However, ratios with respect to volatile elements (e.g. oxygen and sulphur) in the condensates – the building blocks of planets – differ from the original stellar composition. Our results can have important implications for planet interiors, which depend strongly on the degree of oxidization and the sulphur abundance.

1. Introduction

Planets form from solid material residing in the disk around a young star. Both the star and the disk are composed oft he same material (inherited from the collapsing cloud). In the inner disk (inside a few au), material is likely sublimating and solidifying repeatedly due to episodic accretion events and stellar luminosity peaks. Small variations from solar abundances (within 0.5dex), especially also for refractory elements, are ubiqutous in the solar neighborhood. The question is whether such small element abundance fluctuations have a noticeable impact on the composition of a planet condensing from the planet forming disk.

2. Methods

We selected from the Hypatia Database [4] single solar-type main-sequence stars within 150 pc. We select stars that have as complete as possible chemical abundance data and draw six sample stars, representative of the typical spreads in the elements ratios (see Fig. 1).

Figure 1: Ratios of the refractory elements Mg, Si and Fe, as well as S, for main-sequence G-type stars within 150pc. Black dots represent the location of the six sample stars. A red dot indicates a star for which we inferred missing abundances from the median of the known abundances. 

We use the GGchem code developed by [2] and re-written and updated by [6]. The thermo-chemical data are taken from the NIST-JANAF and the geophysical SUPCRTBL databases. The code has been successfully benchmarked against the public TEA code [1]. Given a specific temperature and pressure, the code calculates the various molecules and condensates forming by minimizing the Gibbs free energy. We choose 24 elements (H, He, Li, C, N, O, Na, Mg, Al, Si, S, Cl, K, Ca, Ti, V, Cr, Mn, Fe, Ni, Zr, W, F, P), leading to 552 molecules and 241 condensates. We use the pT-profile of the Minimum Mass Solar Nebula from [3] and assume that different parts of the disk do not mix and that planets are forming in situ. 

We sample the results of the condensation sequences by defining locations for the formation of hypothetical planets. Besides the current locations of Mercury, Venus, Earth, Mars, and the Asteroid belt in the Solar system, we also use 1000, 1250 and 1500K, mimicking that solar system planets likely formed at higher temperatures (dynamical evolution).