Journal articles: 'Planet-disc interaction'

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Ragusa, Enrico, Giovanni Rosotti, Jean Teyssandier, Richard Booth, Cathie J. Clarke, and Giuseppe Lodato. "Eccentricity evolution during planet–disc interaction." Monthly Notices of the Royal Astronomical Society 474, no. 4 (December 1, 2017): 4460–76. http://dx.doi.org/10.1093/mnras/stx3094.

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Friebe, Marc F., Tim D. Pearce, and Torsten Löhne. "Gap carving by a migrating planet embedded in a massive debris disc." Monthly Notices of the Royal Astronomical Society 512, no. 3 (March 11, 2022): 4441–54. http://dx.doi.org/10.1093/mnras/stac664.

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ABSTRACT When considering gaps in debris discs, a typical approach is to invoke clearing by an unseen planet within the gap, and derive the planet mass using Wisdom overlap or Hill radius arguments. However, this approach can be invalid if the disc is massive, because clearing would also cause planet migration. This could result in a calculated planet mass that is incompatible with the inferred disc mass, because the predicted planet would in reality be too small to carve the gap without significant migration. We investigate the gap that a single embedded planet would carve in a massive debris disc. We show that a degeneracy is introduced, whereby an observed gap could be carved by two different planets: either a high-mass, barely migrating planet, or a smaller planet that clears debris as it migrates. We find that, depending on disc mass, there is a minimum possible gap width that an embedded planet could carve (because smaller planets, rather than carving a smaller gap, would actually migrate through the disc and clear a wider region). We provide simple formulae for the planet-to-debris disc mass ratio at which planet migration becomes important, the gap width that an embedded planet would carve in a massive debris disc, and the interaction time-scale. We also apply our results to various systems, and in particular show that the disc of HD 107146 can be reasonably well-reproduced with a migrating, embedded planet. Finally, we discuss the importance of planet–debris disc interactions as a tool for constraining debris disc masses.

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Lufkin, G., T. Quinn, J. Wadsley, J. Stadel, and F. Governato. "Simulations of gaseous disc-embedded planet interaction." Monthly Notices of the Royal Astronomical Society 347, no. 2 (January 11, 2004): 421–29. http://dx.doi.org/10.1111/j.1365-2966.2004.07208.x.

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Rein, Hanno. "Planet-disc interaction in highly inclined systems." Monthly Notices of the Royal Astronomical Society 422, no. 4 (April 10, 2012): 3611–16. http://dx.doi.org/10.1111/j.1365-2966.2012.20869.x.

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De Val-Borro, M., R. G. Edgar, P. Artymowicz, P. Ciecielag, P. Cresswell, G. D'Angelo, E. J. Delgado-Donate, et al. "A comparative study of disc-planet interaction." Monthly Notices of the Royal Astronomical Society 370, no. 2 (August 1, 2006): 529–58. http://dx.doi.org/10.1111/j.1365-2966.2006.10488.x.

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Ida, Shigeru, Takayuki Muto, Soko Matsumura, and Ramon Brasser. "A new and simple prescription for planet orbital migration and eccentricity damping by planet–disc interactions based on dynamical friction." Monthly Notices of the Royal Astronomical Society 494, no. 4 (May 4, 2020): 5666–74. http://dx.doi.org/10.1093/mnras/staa1073.

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ABSTRACT During planet formation, gravitational interaction between a planetary embryo and the protoplanetary gas disc causes orbital migration of the planetary embryo, which plays an important role in shaping the final planetary system. While migration sometimes occurs in the supersonic regime, wherein the relative velocity between the planetary embryo and the gas is higher than the sound speed, migration prescriptions proposed thus far describing the planet–disc interaction force and the time-scales of orbital change in the supersonic regime are inconsistent with one another. Here we discuss the details of existing prescriptions in the literature and derive a new simple and intuitive formulation for planet–disc interactions based on dynamical friction, which can be applied in both supersonic and subsonic cases. While the existing prescriptions assume particular disc models, ours include the explicit dependence on the disc parameters; hence, it can be applied to discs with any radial surface density and temperature dependence (except for the local variations with radial scales less than the disc scale height). Our prescription will reduce the uncertainty originating from different literature formulations of planet migration and will be an important tool to study planet accretion processes, especially when studying the formation of close-in low-mass planets that are commonly found in exoplanetary systems.

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Toci, Claudia, Giuseppe Lodato, Valentin Christiaens, Davide Fedele, Christophe Pinte, Daniel J. Price, and Leonardo Testi. "Planet migration, resonant locking, and accretion streams in PDS 70: comparing models and data." Monthly Notices of the Royal Astronomical Society 499, no. 2 (September 25, 2020): 2015–27. http://dx.doi.org/10.1093/mnras/staa2933.

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ABSTRACT The disc surrounding PDS 70, with two directly imaged embedded giant planets, is an ideal laboratory to study planet–disc interaction. We present 3D smoothed particle hydrodynamics simulations of the system. In our simulations, planets, which are free to migrate and accrete mass, end up in a locked resonant configuration that is dynamically stable. We show that features observed at infrared (scattered light) and millimetre (thermal continuum) wavelengths are naturally explained by the accretion stream on to the outer planet, without requiring a circumplanetary disc around Planet c. We post-processed our near-infrared synthetic images in order to account for observational biases known to affect high-contrast images. Our successful reproduction of the observations indicates that planet–disc dynamical interactions alone are sufficient to explain the observations of PDS 70.

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Chen, Jhih-Wei, and Min-Kai Lin. "Dusty disc–planet interaction with dust-free simulations." Monthly Notices of the Royal Astronomical Society 478, no. 2 (May 4, 2018): 2737–52. http://dx.doi.org/10.1093/mnras/sty1166.

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Stoll, Moritz H. R., Giovanni Picogna, and Wilhelm Kley. "Planet-disc interaction in laminar and turbulent discs." Astronomy & Astrophysics 604 (July 27, 2017): A28. http://dx.doi.org/10.1051/0004-6361/201730668.

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Muñoz, D. J., K. Kratter, V. Springel, and L. Hernquist. "Planet–disc interaction on a freely moving mesh." Monthly Notices of the Royal Astronomical Society 445, no. 4 (October 29, 2014): 3475–95. http://dx.doi.org/10.1093/mnras/stu1918.

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Nelson, Richard P., and John C. B. Papaloizou. "The interaction of a giant planet with a disc with MHD turbulence — II. The interaction of the planet with the disc." Monthly Notices of the Royal Astronomical Society 339, no. 4 (March 2003): 993–1005. http://dx.doi.org/10.1046/j.1365-8711.2003.06247.x.

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Hsieh, He-Feng, and Min-Kai Lin. "Migrating low-mass planets in inviscid dusty protoplanetary discs." Monthly Notices of the Royal Astronomical Society 497, no. 2 (July 20, 2020): 2425–41. http://dx.doi.org/10.1093/mnras/staa2115.

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ABSTRACT Disc-driven planet migration is integral to the formation of planetary systems. In standard, gas-dominated protoplanetary discs, low-mass planets or planetary cores undergo rapid inwards migration and are lost to the central star. However, several recent studies indicate that the solid component in protoplanetary discs can have a significant dynamical effect on disc–planet interaction, especially when the solid-to-gas mass ratio approaches unity or larger and the dust-on-gas drag forces become significant. As there are several ways to raise the solid abundance in protoplanetary discs, for example through disc winds and dust trapping in pressure bumps, it is important to understand how planets migrate through a dusty environment. To this end, we study planet migration in dust-rich discs via a systematic set of high-resolution, two-dimensional numerical simulations. We show that the inwards migration of low-mass planets can be slowed down by dusty dynamical corotation torques. We also identify a new regime of stochastic migration applicable to discs with dust-to-gas mass ratios of ≳0.3 and particle Stokes numbers ≳0.03. In these cases, disc–planet interaction leads to the continuous development of small-scale, intense dust vortices that scatter the planet, which can potentially halt or even reverse the inwards planet migration. We briefly discuss the observational implications of our results and highlight directions for future work.

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Lai, Dong, Francois Foucart, and Douglas N. C. Lin. "Evolution of spin direction of accreting magnetic protostars and spin-orbit misalignment in exoplanetary systems." Proceedings of the International Astronomical Union 6, S276 (October 2010): 295–99. http://dx.doi.org/10.1017/s1743921311020345.

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AbstractRecent observations have shown that in many exoplanetary systems the spin axis of the parent star is misaligned with the planet's orbital axis. These have been used to argue against the scenario that short-period planets migrated to their present-day locations due to tidal interactions with their natal discs. However, this interpretation is based on the assumption that the spins of young stars are parallel to the rotation axes of protostellar discs around them. We show that the interaction between a magnetic star and its circumstellar disc can (although not always) have the effect of pushing the stellar spin axis away from the disc angular momentum axis toward the perpendicular state and even the retrograde state. Planets formed in the disc may therefore have their orbital axes misaligned with the stellar spin axis, even before any additional planet-planet scatterings or Kozai interactions take place. In general, magnetosphere–disc interactions lead to a broad distribution of the spin–orbit angles, with some systems aligned and other systems misaligned.

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Morohoshi, K., and H. Tanaka. "Gravitational interaction between a planet and an optically thin disc." Monthly Notices of the Royal Astronomical Society 346, no. 3 (December 2003): 915–23. http://dx.doi.org/10.1111/j.1365-2966.2003.07140.x.

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Chametla, R. O., and O. Chrenko. "Spreading pressure bumps in gas-dust discs can stall planet migration via planet-vortex interactions." Monthly Notices of the Royal Astronomical Society 512, no. 2 (March 8, 2022): 2189–201. http://dx.doi.org/10.1093/mnras/stac611.

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ABSTRACT We investigate the gravitational interaction between low- to intermediate-mass planets ($M_p \in [0.06-210]\, \mathrm{ M}_{\oplus }$) and two previously formed pressure bumps in a gas-dust protoplanetary disc. We explore how the disc structure changes due to planet-induced perturbations and also how the appearance of vortices affects planet migration. We use multifluid 2D hydrodynamical simulations and the dust is treated in the pressureless-fluid approximation, assuming a single grain size of $5\, \mu {\mathrm{m}}$. The initial surface density profiles containing two bumps are motivated by recent observations of the protoplanetary disc HD163296. When planets are allowed to migrate, either a single planet from the outer pressure maximum or two planets from each pressure maximum, the initial pressure bumps quickly spread and merge into a single bump which is radially wide and has a very low amplitude. The redistribution of the disc material is accompanied by the Rossby Wave Instability and an appearance of mini-vortices that merge in a short period of time to form a large vortex. The large vortex induces perturbations with a spiral wave pattern that propagate away from the vortex as density waves. We found that these vortex-induced spiral waves strongly interact with the spiral waves generated by the planet and we called this mechanism the ‘Faraway Interaction’. It facilitates much slower and/or stagnant migration of the planets and it excites their orbital eccentricities in some cases. Our study provides a new explanation for how rocky planets can come to have a slow migration in protoplanetary discs where vortex formation occurs.

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Rometsch, Thomas, Peter J. Rodenkirch, Wilhelm Kley, and Cornelis P. Dullemond. "Migration jumps of planets in transition discs." Astronomy & Astrophysics 643 (November 2020): A87. http://dx.doi.org/10.1051/0004-6361/202038311.

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Context. Transition discs form a special class of protoplanetary discs that are characterised by a deficiency of disc material close to the star. In a subgroup, inner holes in these discs can stretch out to a few tens of au while there is still mass accretion onto the central star observed at the same time. Aims. We analyse the proposition that this type of wide transition disc is generated by the interaction of the disc with a system of embedded planets. Methods. We performed two-dimensional hydrodynamics simulations of a flat disc. Different equations of state were used including locally isothermal models and more realistic cases that consider viscous heating, radiative cooling, and stellar heating. Two massive planets (with masses of between three and nine Jupiter masses) were embedded in the disc and their dynamical evolution due to disc–planet interaction was followed for over 100 000 yr. The simulations account for mass accretion onto the star and planets. We included models with parameters reminiscent of the system PDS 70. To assess the observability of features in our models we performed synthetic ALMA observations. Results. For systems with a more massive inner planet, there are phases where both planets migrate outward engaged in a 2:1 mean motion resonance via the Masset-Snellgrove mechanism. In sufficiently massive discs, the resulting formation of a vortex and the interaction with it can trigger rapid outward migration of the outer planet where its distance can increase by tens of au in a few thousand years. After another few thousand years, the outer planet rapidly migrates back inwards into resonance with the inner planet. We call this emerging composite phenomenon a migration jump. Outward migration and the migration jumps are accompanied by a high mass accretion rate onto the star. The synthetic images reveal numerous substructures depending on the type of dynamical behaviour. Conclusions. Our results suggest that the outward migration of two embedded planets is a prime candidate for the explanation of the observed high stellar mass accretion rate in wide transition discs. The models for PDS 70 indicate it is not currently undergoing a migration jump but might very well be in a phase of outward migration.

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Ataiee, S., and W. Kley. "The role of disc torques in forming resonant planetary systems." Astronomy & Astrophysics 635 (March 2020): A204. http://dx.doi.org/10.1051/0004-6361/201936390.

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Context. The most accurate method for modelling planetary migration and hence the formation of resonant systems is using hydrodynamical simulations. Usually, the force (torque) acting on a planet is calculated using the forces from the gas disc and the star, while the gas accelerations are computed using the pressure gradient, the star, and the planet’s gravity, ignoring its own gravity. For a non-migrating planet the neglect of the disc gravity results in a consistent torque calculation while for a migrating case it is inconsistent. Aims. We aim to study how much this inconsistent torque calculation can affect the final configuration of a two-planet system. We focus on low-mass planets because most of the multi-planetary systems, discovered by the Kepler survey, have masses around ten Earth masses. Methods. Performing hydrodynamical simulations of planet–disc interaction, we measured the torques on non-migrating and migrating planets for various disc masses as well as density and temperature slopes with and without considering the self-gravity of the disc. Using this data, we found a relation that quantifies the inconsistency, used this relation in an N-body code, and performed an extended parameter study modelling the migration of a planetary system with different planet mass ratios and disc surface densities, to investigate the impact of the torque inconsistency on the architecture of the planetary system. Results. Not considering disc self-gravity produces an artificially larger torque on the migrating planet that can result in tighter planetary systems. The deviation of this torque from the correct value is larger in discs with steeper surface density profiles. Conclusions. In hydrodynamical modelling of multi-planetary systems, it is crucial to account for the torque correction, otherwise the results favour more packed systems. We examine two simple correction methods existing in the literature and show that they properly correct this problem.

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Veronesi, Benedetta, Enrico Ragusa, Giuseppe Lodato, Hossam Aly, Christophe Pinte, Daniel J. Price, Feng Long, Gregory J. Herczeg, and Valentin Christiaens. "Is the gap in the DS Tau disc hiding a planet?" Monthly Notices of the Royal Astronomical Society 495, no. 2 (May 9, 2020): 1913–26. http://dx.doi.org/10.1093/mnras/staa1278.

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ABSTRACT Recent millimetre-wavelength surveys performed with the Atacama Large Millimeter Array (ALMA) have revealed protoplanetary discs characterized by rings and gaps. A possible explanation for the origin of such rings is the tidal interaction with an unseen planetary companion. The protoplanetary disc around DS Tau shows a wide gap in the ALMA observation at 1.3 mm. We construct a hydrodynamical model for the dust continuum observed by ALMA assuming the observed gap is carved by a planet between one and five Jupiter masses. We fit the shape of the radial intensity profile along the disc major axis varying the planet mass, the dust disc mass, and the evolution time of the system. The best-fitting model is obtained for a planet with $M_{\rm p}=3.5\, \mathrm{ M}_{\rm Jup}$ and a disc with $M_{\rm dust}= 9.6\,\times \,10^{-5}\, \mathrm{ M}_{\odot }$. Starting from this result, we also compute the expected signature of the planet in the gas kinematics, as traced by CO emission. We find that such a signature (in the form of a ‘kink’ in the channel maps) could be observed by ALMA with a velocity resolution between $0.2-0.5\, \rm {kms}^{-1}$ and a beam size between 30 and 50 mas.

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Cridland, Alexander J., Ralph E. Pudritz, and Matthew Alessi. "Physics of planet trapping with applications to HL Tau." Monthly Notices of the Royal Astronomical Society 484, no. 1 (January 5, 2019): 345–63. http://dx.doi.org/10.1093/mnras/stz008.

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ABSTRACT We explore planet formation in the HL Tau disc and possible origins of the prominent gaps and rings observed by ALMA. We investigate whether dust gaps are caused by dynamically trapped planetary embryos at the ice lines of abundant volatiles. The global properties of the HL Tau disc (total mass and size) at its current age are used to constrain an evolving analytic disc model describing its temperature and density profiles. By performing a detailed analysis of the planet–disc interaction for a planet near the water ice line including a rigorous treatment of the dust opacity, we confirm that water is sufficiently abundant (1.5 × 10−4 molecules per H) to trap planets at its ice line due to an opacity transition. When the abundance of water is reduced by 50 ${{\ \rm per\ cent}}$ planet trapping disappears. We extend our analysis to other planet traps: the heat transition, dead zone edge, and the CO2 ice line and find similar trapping. The formation of planets via planetesimal accretion is computed for dynamically trapped embryos at the water ice line, dead zone, and heat transition. The end products orbit in the inner disc (R < 3 au), unresolved by ALMA, with masses that range between sub-Earth to 5 Jupiter masses. While we find that the dust gaps correspond well with the radial positions of the CO2, CH4, and CO ice lines, the planetesimal accretion rates at these radii are too small to build large embryos within 1 Myr.

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Thun, Daniel, and Wilhelm Kley. "Migration of planets in circumbinary discs." Astronomy & Astrophysics 616 (August 2018): A47. http://dx.doi.org/10.1051/0004-6361/201832804.

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Aims. The discovery of planets in close orbits around binary stars raises questions about their formation. It is believed that these planets formed in the outer regions of the disc and then migrated through planet-disc interaction to their current location. Considering five different systems (Kepler-16, -34, -35, -38, and -413) we model planet migration through the disc, with special focus on the final orbital elements of the planets. We investigate how the final orbital parameters are influenced by the disc and planet masses. Methods. Using two-dimensional, locally isothermal, and viscous hydrodynamical simulations, we first model the disc dynamics for all five systems, followed by a study of the migration properties of embedded planets with different masses. To strengthen our results, we apply two grid-based hydrodynamical codes using different numerics (PLUTO and FARGO3D). Results. For all systems, we find that the discs become eccentric and precess slowly. We confirm the bifurcation feature in the precession period – gap-size diagram for different binary mass ratios. The Kepler-16, -35, -38, and -413 systems lie on the lower branch and Kepler-34 on the upper one. For systems with small binary eccentricity, we find a new non-monotonic, loop-like feature. In all systems, the planets migrate to the inner edge of the disc cavity. Depending on the planet-disc mass ratio, we observe one of two different regimes. Massive planets can significantly alter the disc structure by compressing and circularising the inner cavity and they remain on nearly circular orbits. Lower-mass planets are strongly influenced by the disc, their eccentricity is excited to high values, and their orbits are aligned with the inner disc in a state of apsidal corotation. In our simulations, the final locations of the planets are typically too large with respect to the observations because of the large inner gaps of the discs. The migrating planets in the most eccentric discs (around Kepler-34 and -413) show the largest final eccentricity in agreement with the observations.

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Papaloizou, John C. B., and Richard P. Nelson. "The interaction of a giant planet with a disc with MHD turbulence — I. The initial turbulent disc models." Monthly Notices of the Royal Astronomical Society 339, no. 4 (March 2003): 983–92. http://dx.doi.org/10.1046/j.1365-8711.2003.06246.x.

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Bollati, Francesco, Giuseppe Lodato, Daniel J. Price, and Christophe Pinte. "The theory of kinks – I. A semi-analytic model of velocity perturbations due to planet–disc interaction." Monthly Notices of the Royal Astronomical Society 504, no. 4 (April 27, 2021): 5444–54. http://dx.doi.org/10.1093/mnras/stab1145.

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ABSTRACT A new technique to detect protoplanets is by observing the kinematics of the surrounding gas. Gravitational perturbations from a planet produce peculiar ‘kinks’ in channel maps of different gas species. In this paper, we show that such kinks can be reproduced using semi-analytic models for the velocity perturbation induced by a planet. In doing so we (i) confirm that the observed kinks are consistent with the planet-induced wake; (ii) show how to quantify the planet mass from the kink amplitude; in particular, we show that the kink amplitude scales with the square root of the planet mass for channels far from the planet velocity, steepening to linear as the channels approach the planet; and (iii) show how to extend the theory to include the effect of damping, which may be needed in order to have localized kinks.

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Pierens, A., M.-K. Lin, and S. N. Raymond. "Vortex instabilities triggered by low-mass planets in pebble-rich, inviscid protoplanetary discs." Monthly Notices of the Royal Astronomical Society 488, no. 1 (June 28, 2019): 645–59. http://dx.doi.org/10.1093/mnras/stz1718.

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Abstract In the innermost regions of protoplanerary discs, the solid-to-gas ratio can be increased considerably by a number of processes, including photoevaporative and particle drift. Magnetohydrodynamic disc models also suggest the existence of a dead zone at R ≲ 10 au, where the regions close to the mid-plane remain laminar. In this context, we use two-fluid hydrodynamical simulations to study the interaction between a low-mass planet (∼1.7 M⊕) on a fixed orbit and an inviscid pebble-rich disc with solid-to-gas ratio ϵ ≥ 0.5. For pebbles with Stokes numbers St = 0.1, 0.5, multiple dusty vortices are formed through the Rossby wave instability at the planet separatrix. Effects due to gas drag then lead to a strong enhancement in the solid-to-gas ratio, which can increase by a factor of ∼103 for marginally coupled particles with St = 0.5. As in streaming instabilities, pebble clumps reorganize into filaments that may plausibly collapse to form planetesimals. When the planet is allowed to migrate in an Minimum Mass Solar Nebula (MMSN) disc, the vortex instability is delayed due to migration but sets in once inward migration stops due a strong positive pebble torque. Again, particle filaments evolving in a gap are formed in the disc while the planet undergoes an episode of outward migration. Our results suggest that vortex instabilities triggered by low-mass planets could play an important role in forming planetesimals in pebble-rich, inviscid discs, and may significantly modify the migration of low-mass planets. They also imply that planetary dust gaps may not necessarily contain planets if these migrated away.

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Strugarek, A., R. Fares, V. Bourrier, A. S. Brun, V. Réville, T. Amari, Ch Helling, et al. "MOVES – V. Modelling star–planet magnetic interactions of HD 189733." Monthly Notices of the Royal Astronomical Society 512, no. 3 (April 1, 2022): 4556–72. http://dx.doi.org/10.1093/mnras/stac778.

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ABSTRACT Magnetic interactions between stars and close-in planets may lead to a detectable signal on the stellar disc. HD 189733 is one of the key exosystems thought to harbour magnetic interactions, which may have been detected in 2013 August. We present a set of 12 wind models at that period, covering the possible coronal states and coronal topologies of HD 189733 at that time. We assess the power available for the magnetic interaction and predict its temporal modulation. By comparing the predicted signal with the observed signal, we find that some models could be compatible with an interpretation based on star–planet magnetic interactions. We also find that the observed signal can be explained only with a stretch-and-break interaction mechanism, while that the Alfvén wings scenario cannot deliver enough power. We finally demonstrate that the past observational cadence of HD 189733 leads to a detection rate of only between 12 and 23 per cent, which could explain why star–planet interactions have been hard to detect in past campaigns. We conclude that the firm confirmation of their detection will require dedicated spectroscopic observations covering densely the orbital and rotation period, combined with scarcer spectropolarimetric observations to assess the concomitant large-scale magnetic topology of the star.

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Johansen, Anders, Shigeru Ida, and Ramon Brasser. "How planetary growth outperforms migration." Astronomy & Astrophysics 622 (February 2019): A202. http://dx.doi.org/10.1051/0004-6361/201834071.

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Planetary migration is a major challenge for planet-formation theories. The speed of type-I migration is proportional to the mass of a protoplanet, while the final decade of growth of a pebble-accreting planetary core takes place at a rate that scales with the mass to the two-thirds power. This results in planetary growth tracks (i.e., the evolution of the mass of a protoplanet versus its distance from the star) that become increasingly horizontal (migration dominated) with the rising mass of the protoplanet. It has been shown recently that the migration torque on a protoplanet is reduced proportional to the relative height of the gas gap carved by the growing planet. Here we show from 1D simulations of planet–disc interaction that the mass at which a planet carves a 50% gap is approximately 2.3 times the pebble isolation mass. Our measurements of the pebble isolation mass from 1D simulations match published 3D results relatively well, except at very low viscosities (α < 10−3) where the 3D pebble isolation mass is significantly higher, possibly due to gap edge instabilities that are not captured in 1D. The pebble isolation mass demarks the transition from pebble accretion to gas accretion. Gas accretion to form gas-giant planets therefore takes place over a few astronomical units of migration after reaching first the pebble isolation mass and, shortly after, the 50% gap mass. Our results demonstrate how planetary growth can outperform migration both during core accretion and during gas accretion, even when the Stokes number of the pebbles is small, St ~ 0.01, and the pebble-to-gas flux ratio in the protoplanetary disc is in the nominal range of 0.01–0.02. We find that planetary growth is very rapid in the first million years of the protoplanetary disc and that the probability for forming gas-giant planets increases with the initial size of the protoplanetary disc and with decreasing turbulent diffusion.

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Kurbatov, E. P., and D. V. Bisikalo. "The role of atmospheric outflows in the migration of hot Jupiters." Monthly Notices of the Royal Astronomical Society 506, no. 3 (July 15, 2021): 3128–37. http://dx.doi.org/10.1093/mnras/stab1690.

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ABSTRACT Many of observed hot Jupiters are subject to atmospheric outflows. Numerical simulations have shown that the matter escaping from the atmosphere can accumulate outside the orbit of the planet, forming a torus. In a few 108 yr, the mass of the torus can become large enough to exert a significant gravitational effect on the planet. Accumulation of mass, in its own turn, is hindered by the activity of the star, which leads to the photoevaporation of the torus matter. We explore the role of these and other factors in the planet’s migration in the epoch when the protoplanetary disc has already disappeared. Using HD 209458 system as an example, we show that the gravitational interaction with the torus leads to the possibility of migration of the planet to its observable position, starting from an orbit ≳0.3 au.

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Bitsch, Bertram, Andre Izidoro, Anders Johansen, Sean N. Raymond, Alessandro Morbidelli, Michiel Lambrechts, and Seth A. Jacobson. "Formation of planetary systems by pebble accretion and migration: growth of gas giants." Astronomy & Astrophysics 623 (March 2019): A88. http://dx.doi.org/10.1051/0004-6361/201834489.

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Giant planets migrate though the protoplanetary disc as they grow their solid core and attract their gaseous envelope. Previously, we have studied the growth and migration of an isolated planet in an evolving disc. Here, we generalise such models to include the mutual gravitational interaction between a high number of growing planetary bodies. We have investigated how the formation of planetary systems depends on the radial flux of pebbles through the protoplanetary disc and on the planet migration rate. Our N-body simulations confirm previous findings that Jupiter-like planets in orbits outside the water ice line originate from embryos starting out at 20–40 AU when using nominal type-I and type-II migration rates and a pebble flux of approximately 100–200 Earth masses per million years, enough to grow Jupiter within the lifetime of the solar nebula. The planetary embryos placed up to 30 AU migrate into the inner system (rP < 1AU). There they form super-Earths or hot and warm gas giants, producing systems that are inconsistent with the configuration of the solar system, but consistent with some exoplanetary systems. We also explored slower migration rates which allow the formation of gas giants from embryos originating from the 5–10 AU region, which are stranded exterior to 1 AU at the end of the gas-disc phase. These giant planets can also form in discs with lower pebbles fluxes (50–100 Earth masses per Myr). We identify a pebble flux threshold below which migration dominates and moves the planetary core to the inner disc, where the pebble isolation mass is too low for the planet to accrete gas efficiently. In our model, giant planet growth requires a sufficiently high pebble flux to enable growth to out-compete migration. An even higher pebble flux produces systems with multiple gas giants. We show that planetary embryos starting interior to 5 AU do not grow into gas giants, even if migration is slow and the pebble flux is large. These embryos instead grow to just a few Earth masses, the mass regime of super-Earths. This stunted growth is caused by the low pebble isolation mass in the inner disc and is therefore independent of the pebble flux. Additionally, we show that the long-term evolution of our formed planetary systems can naturally produce systems with inner super-Earths and outer gas giants as well as systems of giant planets on very eccentric orbits.

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Sommer, Maximilian, Petr Pokorný, Hajime Yano, and Ralf Srama. "Apsidal alignment in migrating dust - Crescent features caused by eccentric planets." Proceedings of the International Astronomical Union 15, S364 (October 2021): 259–61. http://dx.doi.org/10.1017/s1743921322000035.

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AbstractCircumstellar discs are known to exist in great variety, from gas-rich discs around the youngest stars to evolved debris discs such as the solar system’s zodiacal cloud. Through gravitational interaction, exoplanets embedded in these discs can generate density variations, imposing potentially observable structural features on the disc such as rings or gaps. Here we report on a mirrored double crescent pattern arising in simulations of discs harbouring a small, moderately eccentric planet - such as Mars. We show that the structure is a result of a directed apsidal precession occurring in particles that migrate the planet’s orbital region under Poynting-Robertson drag. We further analyze the strength of this effect with respect to planet and particle parameters.

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Mordasini, C., P. Mollière, K. M. Dittkrist, S. Jin, and Y. Alibert. "Global models of planet formation and evolution." International Journal of Astrobiology 14, no. 2 (August 19, 2014): 201–32. http://dx.doi.org/10.1017/s1473550414000263.

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AbstractDespite the strong increase in observational data on extrasolar planets, the processes that led to the formation of these planets are still not well understood. However, thanks to the high number of extrasolar planets that have been discovered, it is now possible to look at the planets as a population that puts statistical constraints on theoretical formation models. A method that uses these constraints is planetary population synthesis where synthetic planetary populations are generated and compared to the actual population. The key element of the population synthesis method is a global model of planet formation and evolution. These models directly predict observable planetary properties based on properties of the natal protoplanetary disc, linking two important classes of astrophysical objects. To do so, global models build on the simplified results of many specialized models that address one specific physical mechanism. We thoroughly review the physics of the sub-models included in global formation models. The sub-models can be classified as models describing the protoplanetary disc (of gas and solids), those that describe one (proto)planet (its solid core, gaseous envelope and atmosphere), and finally those that describe the interactions (orbital migration and N-body interaction). We compare the approaches taken in different global models, discuss the links between specialized and global models, and identify physical processes that require improved descriptions in future work. We then shortly address important results of planetary population synthesis like the planetary mass function or the mass–radius relationship. With these statistical results, the global effects of physical mechanisms occurring during planet formation and evolution become apparent, and specialized models describing them can be put to the observational test. Owing to their nature as meta models, global models depend on the results of specialized models, and therefore on the development of the field of planet formation theory as a whole. Because there are important uncertainties in this theory, it is likely that the global models will in future undergo significant modifications. Despite these limitations, global models can already now yield many testable predictions. With future global models addressing the geophysical characteristics of the synthetic planets, it should eventually become possible to make predictions about the habitability of planets based on their formation and evolution.

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Fang, Tong, and Hongping Deng. "Extreme close encounters between proto-Mercury and proto-Venus in terrestrial planet formation." Monthly Notices of the Royal Astronomical Society 496, no. 3 (June 20, 2020): 3781–85. http://dx.doi.org/10.1093/mnras/staa1785.

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ABSTRACT Modern models of terrestrial planet formation require solids depletion interior to 0.5–0.7 au in the planetesimal disc to explain the small mass of Mercury. The Earth and Venus analogues emerge after ∼100 Myr collisional growth, while Mercury forms in the diffusive tails of the planetesimal disc. We carried out 250 N-body simulations of planetesimal discs with mass confined to 0.7–1.0 au to study the statistics of close encounters that were recently proposed as an explanation for the high iron mass fraction in Mercury. We formed 39 Mercury analogues in total and all proto-Mercury analogues were scattered inwards by proto-Venus. Proto-Mercury typically experiences six extreme close encounters (closest approach smaller than six Venus radii) with Proto-Venus after Proto-Venus acquires 0.7 Venus Mass. At such close separation, the tidal interaction can already affect the orbital motion significantly such that the N-body treatment itself is invalid. More and closer encounters are expected should tidal dissipation of orbital angular momentum accounted. Hybrid N-body hydrodynamic simulations, treating orbital and encounter dynamics self-consistently, are desirable to evaluate the degree of tidal mantle stripping of proto-Mercury.

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Regály, Zs. "Torques felt by solid accreting planets." Monthly Notices of the Royal Astronomical Society 497, no. 4 (August 29, 2020): 5540–49. http://dx.doi.org/10.1093/mnras/staa2181.

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ABSTRACT The solid material of protoplanetary discs forms an asymmetric pattern around a low-mass planet ($M_\mathrm{p}\le 10\, \mathrm{ M}_\oplus$) due to the combined effect of dust–gas interaction and the gravitational attraction of the planet. Recently, it has been shown that although the total solid mass is negligible compared to that of gas in protoplanetary discs, a positive torque can be emerged by a certain size solid species. The torque magnitude can overcome that of gas which may result in outward planetary migration. In this study, we show that the accretion of solid species by the planet strengthens the magnitude of solid torque being either positive or negative. We run two-dimensional, high-resolution ($1.5\,\rm {K}\times 3\,\rm {K}$) global hydrodynamic simulations of an embedded low-mass planet in a protoplanetary disc. The solid material is handled as a pressureless fluid. Strong accretion of well-coupled solid species by an $M_\mathrm{p}\lesssim 0.3\, \mathrm{ M}_\oplus$ protoplanet results in the formation of such a strongly asymmetric solid pattern close to the planet that the positive solid torque can overcome that of gas by two times. However, the accretion of solids in the pebble regime results in increased magnitude negative torque felt by protoplanets and strengthened positive torque for Earth-mass planets. For $M_\mathrm{p}\ge 3\, \mathrm{ M}_\oplus$ planets, the magnitude of the solid torque is positive, however, independent of the accretion strength investigated. We conclude that the migration of solid accreting planets can be substantially departed from the canonical type-I prediction.

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Marshall, J., J. Horner, and A. Carter. "Dynamical simulations of the HR8799 planetary system." International Journal of Astrobiology 9, no. 4 (August 19, 2010): 259–64. http://dx.doi.org/10.1017/s1473550410000297.

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AbstractHR8799 is a young (20–160 Myr) A-dwarf main sequence star with a debris disc detected by IRAS (InfraRed Astronomical Satellite). In 2008, it was one of two stars around which exoplanets were directly imaged for the first time. The presence of three Jupiter-mass planets around HR8799 provoked much interest in modelling the dynamical stability of the system. Initial simulations indicated that the observed planetary architecture was unstable on timescales much shorter than the lifetime of the star (~105 yr). Subsequent models suggested that the system could be stable if the planets were locked in a 1:2:4 mutual mean motion resonance (MMR). In this work, we have examined the influence of varying orbital eccentricity and the semi-major axis on the stability of the three-planet system, through dynamical simulations using the MERCURY n-body integrator. We find that, in agreement with previous work on this system, the 1:2:4 MMR is the most stable planetary configuration, and that the system stability is dominated by the interaction between the inner pair of planets. In contrast to previous results, we find that with small eccentricities, the three-planet system can be stable for timescales comparable to the system lifetime and, potentially, much longer.

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Lanza, A. F. "Stellar magnetic cycles." Proceedings of the International Astronomical Union 5, S264 (August 2009): 120–29. http://dx.doi.org/10.1017/s1743921309992523.

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AbstractThe solar activity cycle is a manifestation of the hydromagnetic dynamo working inside our star. The detection of activity cycles in solar-like stars and the study of their properties allow us to put the solar dynamo in perspective, investigating how dynamo action depends on stellar parameters and stellar structure. Nevertheless, the lack of spatial resolution and the limited time extension of stellar data pose limitations to our understanding of stellar cycles and the possibility to constrain dynamo models. I briefly review some results obtained from disc-integrated proxies of stellar magnetic fields and discuss the new opportunities opened by space-borne photometry made available by MOST, CoRoT, Kepler, and GAIA, and by new ground-based spectroscopic or spectropolarimetric observations. Stellar cycles have a significant impact on the energetic output and circumstellar magnetic fields of late-type active stars which affects the interaction between stars and their planets. On the other hand, a close-in massive planet could affect the activity of its host star. Recent observations provide circumstantial evidence of such an interaction with possible consequences for stellar activity cycles.

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Kunovac Hodžić, Vedad, Amaury H. M. J. Triaud, David V. Martin, Daniel C. Fabrycky, Heather M. Cegla, Andrew Collier Cameron, Samuel Gill, et al. "The EBLM project – VII. Spin–orbit alignment for the circumbinary planet host EBLM J0608-59 A/TOI-1338 A." Monthly Notices of the Royal Astronomical Society 497, no. 2 (July 15, 2020): 1627–33. http://dx.doi.org/10.1093/mnras/staa2071.

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ABSTRACT A dozen short-period detached binaries are known to host transiting circumbinary planets. In all circumbinary systems so far, the planetary and binary orbits are aligned within a couple of degrees. However, the obliquity of the primary star, which is an important tracer of their formation, evolution, and tidal history, has only been measured in one circumbinary system until now. EBLM J0608-59/TOI-1338 is a low-mass eclipsing binary system with a recently discovered circumbinary planet identified by TESS. Here, we perform high-resolution spectroscopy during primary eclipse to measure the projected stellar obliquity of the primary component. The obliquity is low, and thus the primary star is aligned with the binary and planetary orbits with a projected spin–orbit angle β = 2${_{.}^{\circ}}$8 ± 17${_{.}^{\circ}}$1. The rotation period of 18.1 ± 1.6 d implied by our measurement of vsin i⋆ suggests that the primary has not yet pseudo-synchronized with the binary orbit, but is consistent with gyrochronology and weak tidal interaction with the binary companion. Our result, combined with the known coplanarity of the binary and planet orbits, is suggestive of formation from a single disc. Finally, we considered whether the spectrum of the faint secondary star could affect our measurements. We show through simulations that the effect is negligible for our system, but can lead to strong biases in vsin i⋆ and β for higher flux ratios. We encourage future studies in eclipse spectroscopy test the assumption of a dark secondary for flux ratios ≳1 ppt.

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Rozner, Mor, Evgeni Grishin, and Hagai B. Perets. "The aeolian-erosion barrier for the growth of metre-size objects in protoplanetary discs." Monthly Notices of the Royal Astronomical Society 496, no. 4 (June 27, 2020): 4827–35. http://dx.doi.org/10.1093/mnras/staa1864.

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ABSTRACT Aeolian erosion is a destructive process that can erode small-size planetary objects through their interaction with a gaseous environment. Aeolian erosion operates in a wide range of environments and under various conditions. Aeolian erosion has been extensively explored in the context of geophysics in terrestrial planets. Here we show that aeolian erosion of cobbles, boulders, and small planetesimals in protoplanetary discs can constitute a significant barrier for the early stages of planet formation. We use analytic calculations to show that under the conditions prevailing in protoplanetary discs small bodies ($10\!-\!10^4 \, \rm {m}$) are highly susceptible to gas-drag aeolian erosion. At this size-range aeolian erosion can efficiently erode the planetesimals down to tens-cm size and quench any further growth of such small bodies. It thereby raises potential difficulties for channels suggested to alleviate the metre-size barrier. Nevertheless, the population of ∼decimetre-size cobbles resulting from aeolian erosion might boost the growth of larger (>km size) planetesimals and planetary embryos through increasing the efficiency of pebble-accretion, once/if such large planetesimals and planetary embryos exist in the disc.

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Krumholz, Mark R., Michael J. Ireland, and Kaitlin M. Kratter. "Dynamics of small grains in transitional discs." Monthly Notices of the Royal Astronomical Society 498, no. 2 (August 21, 2020): 3023–42. http://dx.doi.org/10.1093/mnras/staa2546.

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ABSTRACT Transitional discs have central regions characterized by significant depletion of both dust and gas compared to younger, optically thick discs. However, gas and dust are not depleted by equal amounts: gas surface densities are typically reduced by factors of ∼100, but small dust grains are sometimes depleted by far larger factors, to the point of being undetectable. While this extreme dust depletion is often attributed to planet formation, in this paper we show that another physical mechanism is possible: expulsion of grains from the disc by radiation pressure. We explore this mechanism using 2D simulations of dust dynamics, simultaneously solving the equation of radiative transfer with the evolution equations for dust diffusion and advection under the combined effects of stellar radiation and hydrodynamic interaction with a turbulent, accreting background gas disc. We show that, in transition discs that are depleted in both gas and dust fraction by factors of ∼100–1000 compared to minimum mass Solar nebular values, and where the ratio of accretion rate to stellar luminosity is low ($\dot{M}/L \lesssim 10^{-10}\, \mathrm{ M}_\odot$ yr$^{-1}\, \mathrm{ L}_\odot ^{-1}$), radiative clearing of any remaining ${\sim}0.5\, \mu\mathrm{ m}$ and larger grains is both rapid and inevitable. The process is size-dependent, with smaller grains removed fastest and larger ones persisting for longer times. Our proposed mechanism thus naturally explains the extreme depletion of small grains commonly found in transition discs. We further suggest that the dependence of this mechanism on grain size and optical properties may explain some of the unusual grain properties recently discovered in a number of transition discs. The simulation code we develop is freely available.

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Teyssandier, J., and G. Ogilvie. "Growth of eccentricity in planet-disc interactions." EAS Publications Series 82 (2019): 415–22. http://dx.doi.org/10.1051/eas/1982036.

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The origin and wide distribution of eccentricities in planetary systems remains to be explained, in particular in the context of planet-disc interactions. Here we present a set of linear equations that describe the behavior of small eccentricities in a protoplanetary system consisting of a gaseous disc and a planet. Eccentricity propagates through the disc by means of pressure, and is exchanged with the planet via secular interactions. Excitation and damping of eccentricity can occur through Lindblad and corotation resonances, as well as viscosity. Three-dimensional effects allow for an eccentric mode to be trapped in the inner parts of the disc. This eccentric mode can easily grow within the disc's lifetime. An eccentric mode dominated by the planet can also grow, although less rapidly. Application to a hot Jupiter surrounded by a gaseous disc suggests that the eccentricity of the planet can grow. Finally, the linear theory is compared to hydrodynamical simulations, and a very good agreement is found.

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Paardekooper, S. J. "Disc-planet interactions in subkeplerian discs." Astronomy & Astrophysics 506, no. 2 (September 15, 2009): L9—L12. http://dx.doi.org/10.1051/0004-6361/200913184.

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Nelson, Richard P., and Sijme-Jan Paardekooper. "Numerical Simulations of Disc-Planet Interactions." Advanced Science Letters 4, no. 2 (February 1, 2011): 244–57. http://dx.doi.org/10.1166/asl.2011.1213.

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Fitzmaurice, Evan, David V. Martin, and Daniel C. Fabrycky. "Sculpting the circumbinary planet size distribution through resonant interactions with companion planets." Monthly Notices of the Royal Astronomical Society 512, no. 4 (March 21, 2022): 5023–36. http://dx.doi.org/10.1093/mnras/stac741.

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ABSTRACT Resonant locking of two planets is an expected outcome of convergent disc migration. The planets subsequently migrate together as a resonant pair. In the context of circumbinary planets, the disc is truncated internally by the binary. If there were only a single planet, then this inner disc edge would provide a natural parking location. However, for two planets migrating together in resonance there will be a tension between the inner planet stopping at the disc edge and the outer planet continuing to be torqued inwards. In this paper, we study this effect, showing that the outcome is a function of the planet–planet mass ratio. Smaller outer planets tend to be parked in a stable exterior 2:1 or 3:2 resonance with the inner planet, which remains near the disc edge. Equal or larger mass outer planets tend to push the inner planet past the disc edge and too close to the binary, causing it to be ejected or sometimes flipped to an exterior orbit. Our simulations show that this process may explain an observed dearth of small (<3 R⊕) circumbinary planets, since small planets are frequently ejected or left on long-period orbits, for which transit detection is less likely. This may also be an effective mechanism for producing free-floating planets and interstellar interlopers like ‘Oumuamua.

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Franchini, Alessia, Rebecca G. Martin, and Stephen H. Lubow. "Multiplanet disc interactions in binary systems." Monthly Notices of the Royal Astronomical Society 491, no. 4 (November 22, 2019): 5351–60. http://dx.doi.org/10.1093/mnras/stz3175.

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ABSTRACT We investigate the evolution of a multiplanet–disc system orbiting one component of a binary star system. The planet–disc system is initially coplanar but misaligned to the binary orbital plane. The planets are assumed to be giants that open gaps in the disc. We first study the role of the disc in shaping the mutual evolution of the two planets using a secular model for low initial tilt. In general, we find that the planets and the disc do not remain coplanar, in agreement with previous work on the single planet case. Instead, the planets and the disc undergo tilt oscillations. A high-mass disc between the two planets causes the planets and the disc to nodally precess at the same average rate but they are generally misaligned. The amplitude of the tilt oscillations between the planets is larger while the disc is present. We then consider higher initial tilts using hydrodynamical simulations and explore the possibility of the formation of eccentric Kozai–Lidov (KL) planets. We find that the inner planet’s orbit undergoes eccentricity growth for a large range of disc masses and initial misalignments. For a low disc mass and large initial misalignment, both planets and the disc can undergo KL oscillations. Furthermore, we find that sufficiently massive discs can cause the inner planet to increase its inclination beyond 90° and therefore to orbit the binary in a retrograde fashion. The results have important implications for the explanation of very eccentric planets and retrograde planets observed in multiplanet systems.

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Teyssandier, Jean, and Dong Lai. "A simplified model for the secular dynamics of eccentric discs and applications to planet–disc interactions." Monthly Notices of the Royal Astronomical Society 490, no. 3 (October 18, 2019): 4353–65. http://dx.doi.org/10.1093/mnras/stz2919.

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ABSTRACT We develop a simplified model for studying the long-term evolution of giant planets in protoplanetary discs. The model accounts for the eccentricity evolution of the planets and the dynamics of eccentric discs under the influences of secular planet–disc interactions and internal disc pressure, self-gravity, and viscosity. Adopting the ansatz that the disc precesses coherently with aligned apsides, the eccentricity evolution equations of the planet–disc system reduce to a set of linearized ordinary differential equations, which allows for fast computation of the evolution of planet–disc eccentricities over long time-scales. Applying our model to ‘giant planet + external disc’ systems, we are able to reproduce and explain the secular behaviours found in previously published hydrodynamical simulations. We re-examine the possibility of eccentricity excitation (due to secular resonance) of multiple planets embedded in a dispersing disc, and find that taking into account the dynamics of eccentric discs can significantly affect the evolution of the planets’ eccentricities.

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Teyssandier, Jean, and Gordon I. Ogilvie. "Growth of eccentric modes in disc–planet interactions." Monthly Notices of the Royal Astronomical Society 458, no. 3 (March 7, 2016): 3221–47. http://dx.doi.org/10.1093/mnras/stw521.

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Lin, Min-Kai, and John C. B. Papaloizou. "Edge modes in self-gravitating disc-planet interactions." Monthly Notices of the Royal Astronomical Society 415, no. 2 (June 13, 2011): 1445–68. http://dx.doi.org/10.1111/j.1365-2966.2011.18797.x.

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Pérez, Sebastián, S. Casassus, and P. Benítez-Llambay. "Observability of planet–disc interactions in CO kinematics." Monthly Notices of the Royal Astronomical Society: Letters 480, no. 1 (June 18, 2018): L12—L17. http://dx.doi.org/10.1093/mnrasl/sly109.

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Debras, Florian, Clément Baruteau, and Jean-François Donati. "Revisiting migration in a disc cavity to explain the high eccentricities of warm Jupiters." Monthly Notices of the Royal Astronomical Society 500, no. 2 (October 30, 2020): 1621–32. http://dx.doi.org/10.1093/mnras/staa3397.

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ABSTRACT The distribution of eccentricities of warm giant exoplanets is commonly explained through planet–planet interactions, although no physically sound argument favours the ubiquity of such interactions. No simple, generic explanation has been put forward to explain the high mean eccentricity of these planets. In this paper, we revisit a simple, plausible explanation to account for the eccentricities of warm Jupiters: migration inside a cavity in the protoplanetary disc. Such a scenario allows to excite the outer eccentric resonances, a working mechanism for higher mass planets, leading to a growth in the eccentricity while preventing other, closer resonances to damp eccentricity. We test this idea with diverse numerical simulations, which show that the eccentricity of a Jupiter-mass planet around a Sun-like star can increase up to ∼0.4, a value never reached before with solely planet–disc interactions. This high eccentricity is comparable to, if not larger than, the median eccentricity of warm Saturn- to Jupiter-mass exoplanets. We also discuss the effects such a mechanism would have on exoplanet observations. This scenario could have strong consequences on the disc lifetime and the physics of inner disc dispersal, which could be constrained by the eccentricity distribution of gas giants.

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Sotiriadis, Sotiris, Anne-Sophie Libert, and Sean N. Raymond. "Formation of terrestrial planets in eccentric and inclined giant planet systems." Astronomy & Astrophysics 613 (May 2018): A59. http://dx.doi.org/10.1051/0004-6361/201731260.

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Aims. Evidence of mutually inclined planetary orbits has been reported for giant planets in recent years. Here we aim to study the impact of eccentric and inclined massive giant planets on the terrestrial planet formation process, and investigate whether it can possibly lead to the formation of inclined terrestrial planets. Methods. We performed 126 simulations of the late-stage planetary accretion in eccentric and inclined giant planet systems. The physical and orbital parameters of the giant planet systems result from n-body simulations of three giant planets in the late stage of the gas disc, under the combined action of Type II migration and planet-planet scattering. Fourteen two- and three-planet configurations were selected, with diversified masses, semi-major axes (resonant configurations or not), eccentricities, and inclinations (including coplanar systems) at the dispersal of the gas disc. We then followed the gravitational interactions of these systems with an inner disc of planetesimals and embryos (nine runs per system), studying in detail the final configurations of the formed terrestrial planets. Results. In addition to the well-known secular and resonant interactions between the giant planets and the outer part of the disc, giant planets on inclined orbits also strongly excite the planetesimals and embryos in the inner part of the disc through the combined action of nodal resonance and the Lidov–Kozai mechanism. This has deep consequences on the formation of terrestrial planets. While coplanar giant systems harbour several terrestrial planets, generally as massive as the Earth and mainly on low-eccentric and low-inclined orbits, terrestrial planets formed in systems with mutually inclined giant planets are usually fewer, less massive (<0.5 M⊕), and with higher eccentricities and inclinations. This work shows that terrestrial planets can form on stable inclined orbits through the classical accretion theory, even in coplanar giant planet systems emerging from the disc phase.

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Schäfer, C., R. Speith, M. Hipp, and W. Kley. "Simulations of planet-disc interactions using Smoothed Particle Hydrodynamics." Astronomy & Astrophysics 418, no. 1 (April 2004): 325–35. http://dx.doi.org/10.1051/0004-6361:20034034.

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Velasco Romero, David A., Maria Han Veiga, Romain Teyssier, and Frédéric S. Masset. "Planet–disc interactions with discontinuous Galerkin methods using GPUs." Monthly Notices of the Royal Astronomical Society 478, no. 2 (May 5, 2018): 1855–65. http://dx.doi.org/10.1093/mnras/sty1192.

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Mercer, Anthony, and Dimitris Stamatellos. "Planet formation around M dwarfs via disc instability." Astronomy & Astrophysics 633 (January 2020): A116. http://dx.doi.org/10.1051/0004-6361/201936954.

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Context. Around 30 per cent of the observed exoplanets that orbit M dwarf stars are gas giants that are more massive than Jupiter. These planets are prime candidates for formation by disc instability. Aims. We want to determine the conditions for disc fragmentation around M dwarfs and the properties of the planets that are formed by disc instability. Methods. We performed hydrodynamic simulations of M dwarf protostellar discs in order to determine the minimum disc mass required for gravitational fragmentation to occur. Different stellar masses, disc radii, and metallicities were considered. The mass of each protostellar disc was steadily increased until the disc fragmented and a protoplanet was formed. Results. We find that a disc-to-star mass ratio between ~0.3 and ~0.6 is required for fragmentation to happen. The minimum mass at which a disc fragment increases with the stellar mass and the disc size. Metallicity does not significantly affect the minimum disc fragmentation mass but high metallicity may suppress fragmentation. Protoplanets form quickly (within a few thousand years) at distances around ~50 AU from the host star, and they are initially very hot; their centres have temperatures similar to the ones expected at the accretion shocks around planets formed by core accretion (up to 12 000 K). The final properties of these planets (e.g. mass and orbital radius) are determined through long-term disc-planet or planet–planet interactions. Conclusions. Disc instability is a plausible way to form gas giant planets around M dwarfs provided that discs have at least 30% the mass of their host stars during the initial stages of their formation. Future observations of massive M dwarf discs or planets around very young M dwarfs are required to establish the importance of disc instability for planet formation around low-mass stars.

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Journal articles on the topic 'Planet-disc interaction'

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