We investigate a repulsion mechanism between two low-mass planets migrating in a protoplanetary disk, for which the relative migration switches from convergent to divergent. This mechanism invokes density waves emitted by one planet transferring angular momentum to the coorbital region of the other and then directly to it through the horseshoe drag. We formulate simple analytical estimates, which indicate when the repulsion mechanism is effective. One condition for a planet to be repelled is that it forms a partial gap in the disk and another is that this should contain enough material to support angular momentum exchange with it. Using two-dimensional hydrodynamical simulations, we obtain divergent migration of two super-Earths embedded in a protoplanetary disk because of repulsion between them and verify these conditions. To investigate the importance of resonant interaction, we study the migration of planet pairs near first-order commensurabilities. It appears that proximity to resonance is significant but not essential. In this context we find repulsion still occurs when the gravitational interaction between the planets is removed, suggesting the importance of angular momentum transfer through waves excited by another planet. This may occur through the scattering of coorbital material (the horseshoe drag), or material orbiting close by. Our results indicate that if conditions favor the repulsion between two planets described above, we expect to observe planet pairs with their period ratios greater, often only slightly greater, than resonant values or possibly rarity of commensurability.
We study the formation of the 9:7 mean motion resonance in a system of two low-mass planets (m 1 = m 2 = 3M ⊕ ) embedded in a gaseous protoplanetary disk employing a full 2D hydrodynamic treatment of the disk-planet interactions. Our aim is to determine the disk properties that favor a capture of two equal-mass super-Earths into this second -order resonance. For this purpose, we have performed a series of numerical hydrodynamic simulations of the system of two super-Earths migrating in disks with a variety of different initial parameters and found conditions for the permanent or temporary locking in the 9:7 resonance. We observe that capture occurs during the convergent migration of planets if their resonance angle at the moment of arrival at the resonance assumes values in a certain range (inside a window of capture). The width of such a window depends on the relative migration and circularization rates that are determined by the disk parameters. The window is wide if the relative migration rate is slow, and it becomes narrower as the relative migration rate increases. The window will be closed if the migration rate is sufficiently high, and the capture will not take place. We illustrate also how the 9:7 resonance window of capture is affected by the initial eccentricities and the initial orbits of the planets.
<p class="western" lang="en-GB" align="justify">Past, present and forthcoming space missions (e.g. Kepler/K2, TESS, CHEOPS, JWST, PLATO, ARIEL) and ground-based observational facilities (e.g. VLT, VLTI, ALMA) were, are and will be the sources of the high quality data necessary to unveil the properties of the planetary systems. Thanks to them the recent enormous increase in number of known planets gives a unique opportunity to study the processes responsible for planet formation and evolution in more detail. The observed properties of numerous planets allow for the robust constraints to be put on planet formation models. Both ground and space-based surveys have derived distributions of fundamental planetary properties like the frequency of planets in the mass-distance and radius-distance planes, the planetary mass function, the eccentricity distribution, or the planetary mass-radius relation. Now it is possible to compare the theoretical predictions with the observed properties of the planet population as a whole. The technique used for this comparison is known as the planet population synthesis [1-4]. One of the assumptions in this method is the migration rate of the planets. At the early stages of the evolution, when planets are still embedded in a gaseous disc, the tidal interactions between the disc and planets cause the planetary orbital migration. The orbital migration may play an important role in shaping stable planetary configurations. The outcome of the simulation depends strongly on the way in which the planets migrate. An understanding of this stage of the evolution will provide insight on the most frequently formed architectures, which in turn are relevant for determining the planet habitability.</p> <p class="western" lang="en-GB" align="justify">There has been recently an important development in the understanding of the orbital migration of planets which are able to open a partial gap in the protoplanetary disc (e.g. [5], [6], and references therein). It has been shown that such planets migrate differently than it has been assumed till now [7]. This subject is now at the leading edge of the studies of the dynamical interactions that occur in newly formed planetary systems. Here, we are going to present our most recent results on the two super-Earths migrating in a gaseous protoplanetary disc.</p> <p class="western" lang="en-GB" align="justify">[1] Mordasini, C., Alibert, Y., Benz, W. (2009), Extrasolar planet population synthesis. I. Method, formation tracks, and mass-distance distribution, A&A, 501, 1139</p> <p class="western" lang="en-GB" align="justify">[2] Mordasini, C., Alibert, Y., Benz, W., Naef, D. (2009), Extrasolar planet population synthesis. II. Statisticalcomparison with observations, A&A, 501, 1139</p> <p class="western" lang="en-GB" align="justify">[3] Alibert, Y., Carron, F., Fortier, A., et al. (2013), Theoretical models of planetary system formation: mass vs. semi-major axis, A&A, 558, A109</p> <p class="western" lang="en-GB" align="justify">[4] Benz, W., Ida, S., Alibert, Y., Lin, D., & Mordasini, C. (2014), Planet Population Synthesis, Protostars and Planets VI, 691</p> <p class="western" lang="en-GB" align="justify">[5] Robert C. M. T., Crida A., Lega E., M&#233;heut H., Morbidelli A. (2018) Toward a new paradigm for Type II migration, A&A, 617, A98</p> <p class="western" lang="en-GB" align="justify">[6] Kanagawa, K. D., Tanaka, H., & Szuszkiewicz, E, (2018), Radial migration of gap-opening planets in protoplanetary disks. I. The case of a single planet ApJ, 861, 140</p> <p class="western" lang="en-GB" align="justify">[7] Duffell, P. C., Haiman, Z., MacFadyen, A. I., D&#8217;Orazio, D. J., Farris, B. D. (2014), The Migration of&#160; Gap-Opening Planets is not Locked to Viscous Disk Evolution , ApJL, 792, L10</p>
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.